We describe techniques of encoding compressed images and video such that the encoded bit stream is resilient to transmission errors which occur on typical noisy channels, particularly to and from mobile users. These errors may occur in the form of random bit errors, bursty bit errors or packet losses, or combinations of these, and the proposed techniques are shown to suffer only gradual and graceful degradation as the error rate increases. This contrasts markedly with the severe error sensitivity of conventional image compression standards, such as JPEG and MPEG. A key tool that we employ is the error resilient entropy code (EREC)⁶ which largely overcomes the problems of loss of synchronization and severe error propagation, inherent in most entropy coded data streams. Unlike traditional forward error correction methods, the error-resilient techniques which we employ do not add significant redundancy to the compressed data and therefore do not waste capacity or degrade the compression performance under good channel conditions. They are shown to work particularly well with wavelet compression because the localized image defects, which errors do cause, are less visible with wavelets than with DCT-based compression, due to the smoother boundaries of the wavelet basis functions.

In order to achieve high data compression, high fidelity images, multi-resolution imaging, and N-to-N teleconferencing, we propose a biorthogonal subband wavelet for the N-to-N teleconferencing which includes a wavelet compression algorithm, a wavelet based motion estimation, and a network design operatively connecting visual communication terminals.

A wavelet-based video compression scheme that combines a tree coder and the multiresolution motion estimation (MRME) is presented in this paper. Based on the correlation between wavelet coefficients in interlevel subbands, tree coders outperform DCT-based transform coders for still images, especially at low bit rates. They also offer many advantages such as: (1) they support progressive transmission, (2) they have control over the bit rate, (3) they eliminate blocky artifacts and (4) their image quality degrades smoothly versus lowering bit rates. In addition, multiscale wavelet representation of an image facilitates the application of the coder in the video communication environment to satisfy quality and resolution requirements from video phones to HDTV. Using multiresolution representation of successive images in a sequence, MRME offers an effective fast algorithm for block-based motion estimation/compensation. Motion vectors between successive frames at the lowest resolution are used as the reference for motion estimation at higher resolutions. Choosing a smaller block size at a lower resolution and a smaller window size at a higher resolution can speed up the time-consuming computation for motion estimation. By arranging its roots, a block-based tree coder can be used for encoding areas that cannot be easily predicted. A simplified frame and block classification used in MPEG-1 are applied adaptively for different scenes and areas. Preliminary results show that this approach is effective in decreasing computational complexity and bit rate. Further optimization and expansion of the basic scheme can make it applicable for video transmission under various bandwidth limitations.

Progressive transmission is one of the most important performance factors for wavelet/subband based coding schemes. Depending on the applications, an image is first decomposed using the wavelet packet, or the pyramidal paradigm, and then wavelet coefficients can be quantized and coded into a bit stream. Moreover, selective compression, as well as browsing are important functions for many applications. these important functions rely on an efficient labeling scheme of subbands, so that they can be navigated efficiently. Because of the sequential nature of the wavelet decomposition/reconstruction, image subbands must be carefully ordered for efficient image retrieval, transmission, and parallelization. The importance of subband management cannot be overestimated for processing of mega/tera-byte images. In this paper we propose a stack based data structure for recursive ordering of wavelet subbands. Based on our scheme, one can easily optimize placement of subbands, so that different subbands can be efficiently reconstructed or navigated to avoid performance bottlenecks.

This paper describes a communication protocol for interactive image exchange on using only a region of interest (ROI) in an image. This protocol uses a wavelet tree coder to handle large image sizes. It provides a means for convenient storage and retrieval of medical images in a digitized format. Because of the narrow bandwidth of telecommunications networks, lossy image compression is necessary for fast image transmission at low cost. In many applications, only a small portion of a large medical image is of interest to the user. It is unnecessary and unwise to treat all image pixels equally. Insignificant areas should be highly compressed to minimize the total number of bits, thereby reducing transmission time and costs without losing the diagnostic quality of the image. This communication protocol is designed for users who wish to interact with one another and exchange images selectively. In this protocol, images are compressed and decompressed from the most important ROIs. The protocol progressively improves the image quality based on the users' chosen criteria. The compression and decompression processes can be stopped at any time to provide sufficient diagnostic information at the lowest possible cost. We have implemented and tested this algorithm on an image that has been compressed using a generalized self-similarity tree.

Compression of video for low bitrate communication is studied in this paper. Use of vector quantization in the H.263 framework is proposed. A variable rate residual vector quantizer with a transform vector quantizer in the first stage is used along with a strategy to adapt the bit-rate to the activity in the block. This ability to adapt the bit- rate is very important for very low bitrate compression. The proposed multistage quantizer combined with an adaptive arithmetic codec produced very good results. The variability in the bit-rate was achieved by using smaller block sizes in the later stages of quantizer along with selective quantization of only high energy blocks at the later stages. Performance comparison of the proposed codec with that of H- 263 indicates that there is superior compression results especially bitrates less than 8kb/s.

It is shown that the high-resolution transform code framework is not appropriate to evaluate the performance of current image transform codes. The compression performance depends essentially on the precision of non-linear image approximations in the chosen orthogonal basis. At low bit rates, for a number of bit per pixel R that is below 1, the distortion is D(R) approximately R^1-2(gamma ). The constant (gamma) is typically of the order of 1 for natural images decomposed in a wavelet basis.

The direct differentiation of a noisy signal ds/dt is known to be inaccurate. Differentiation can be improved by employing the Dirac (delta) -function introduced into a convolution product denoted by (direct product) and then integrated by parts: ds/dt equals ds/dt (direct product) (delta) equals - s (direct product) d(delta) /dt. The Schwartz Gaussian representation of the delta function is then explicitly used in the differentiation. It turns out that such a convolution approach to the first and the second derivatives produces a pair of mother wavelets the combination of which is the complex generalization of the Mexican hat called a Hermitian hat wavelet. It is shown that the Hermitian filter is a single oscillation wavelet having much lower frequency bandwidth than the Mortlet or Gabor wavelet. As a result of Nyquist theorem, a fewer number of grid points would be needed for the discrete convolution operation. Therefore, the singularity characteristic will not be overly smeared and the noise can be smoothed away. The phase plot of the Hermitian wavelet transform in terms of the time scale and frequency domains reveal a bifurcation discontinuity of a noisy cusp singularity at the precise location of the singularity as well as the scale nature of the underlying dynamics. This phase plot is defined as (theta) (t/a) equals tan^-1 [(ds/dt)/(-d²s/dt²] equals tan^-1 [((d(delta) (t/a)dt) (direct product) s)/((d²(delta) (t/a)/dt²) (direct product) s)] applied to a real world data of the Paraguay river levels.

As the amount of multidimensional remotely sensed data is growing tremendously, Earth scientists need more efficient ways to search and analyze such data. In particular, extracting image content is emerging as one of the most powerful tools to perform data mining. One of the most promising methods to extract image content is image classification, which provides a labeling of each pixel in the image. In this paper, we concentrate on neural classifiers and show how information obtained through wavelet transform can be integrated in such a classifier. After a systematic dimensionality reduction by a principal component analysis technique, we apply a local spatial frequency analysis. This local analysis with a composite edge/texture wavelet transform provides statistical texture information of the landsat imagery testset. The network is trained with both radiometric landsat/thematic mapper bands and with the additional texture bands provided by the wavelet analysis. The paper describes the type of wavelets chosen for this application, and several sets of results are presented.

Wavelet shrinkage, radial basis function (RBF) have been studied for signal reconstructions. We first use these methods to approximate four specific functions which represent various spatially nonhomogeneous phenomena. Next, we apply these methods to analyze a time series of Paraguay River levels. From the preliminary experiments, we show that wavelet shrinkage was the best estimator. With similar result, secondly came AWTNN and lastly came RBF networks.

Wavelet analysis is becoming an increasingly popular tool in the geoscience community due to its good localizations in time and frequency. In this study, wavelet analysis is used to examine the time-frequency structure of the globally integrated atmospheric angular momentum produced by the Goddard Earth Observing Systems data assimilation system. The modulus of the wavelet transform shows distinct oscillations at annual, semi-annual and intraseasonal time scales. A covariance function between the wavelet coefficients and another quantity is developed to quantify their relationships at different time scales. The results show that the global atmospheric angular momentum is associated with seasonal variations of the midlatitude westerlies, intraseasonal variations in the tropical and subtropical regions, and midlatitude planetary-scale and synoptic-scale wave activities.

A single pixel of a Landsat image has seven channels receiving 0.1 to 10 microns of radiation from the ground within a 20 by 20 meter footprint. In principle, the pattern of seven values can be utilized to identify ground sources within the pixel footprint by using methodologies called spectral blind demixing of unknown sources when the reflectance matrix W_ij for the ith object and the jth band is either partially or difficult to measure in the outer space.

Stratified structures have a widely usage in aerospace technologies. Free oscillation testing method (FOM) used for testing of stratified structures with large acoustic decay coefficient. Early faults detection was performed by analysis of energy spectrum of recorded mechanical oscillations.But sizes and depths of faults cannot be estimated using this method. For the first time estimation of fault's size and depth performed by us using two new ideas: 1. transient characteristics in FOM was measured and considered as a non stationary signals; 2. wavelet packet algorithm sued for analysis of such signals. We have found signal basis in Pollen parameter space for analyzing FOM signal using modification of wavelet packet algorithm. Discriminant function (DF) associated with faults' size is linear. DF associated with faults' depth is one-valued. This method also can be useful for tasks of mine and mine-like targets detection.

Wavelet theory is a whole new signal analysis theory in recent years, and the appearance of which is attracting lots of experts in many different fields giving it a deepen study. Wavelet transformation is a new kind of time. Frequency domain analysis method of localization in can-be- realized time domain or frequency domain. It has many perfect characteristics that many other kinds of time frequency domain analysis, such as Gabor transformation or Viginier. For example, it has orthogonality, direction selectivity, variable time-frequency domain resolution ratio, adjustable local support, parsing data in little amount, and so on. All those above make wavelet transformation a very important new tool and method in signal analysis field. Because the calculation of complex wavelet is very difficult, in application, real wavelet function is used. In this paper, we present a necessary and sufficient condition that the real wavelet function can be obtained by the complex wavelet function. This theorem has some significant values in theory. The paper prepares its technique from Hartley transformation, then, it gives the complex wavelet was a signal engineering expert. His Hartley transformation, which also mentioned by Hartley, had been overlooked for about 40 years, for the social production conditions at that time cannot help to show its superiority. Only when it came to the end of 70s and the early 80s, after the development of the fast algorithm of Fourier transformation and the hardware implement to some degree, the completely some positive-negative transforming method was coming to take seriously. W transformation, which mentioned by Zhongde Wang, pushed the studying work of Hartley transformation and its fast algorithm forward. The kernel function of Hartley transformation.

Gaussian modulated sinusoids are used in S-transform to extract time-local and space-local spectral information. Similar data sets recorded at neighboring spatial locations may be used with cross spectral analysis to determine frequency localized velocity spectrum. The 2D S-transform is used in image analysis for space localized wavenumber spectra. Local changes in the image spectrum are used to define textural boundaries on images. This paper summarizes several of the research projects involving S-transforms currently in progress at the University of Western Ontario including the application of the 2D S-transform to texture analysis, recognition, and the classification of images.

This paper presents an empirical modeling of the role of environment for Automatic Speech Recognition systems in real world, taken in the framework of an Artificial Life methodology. Environment is modeled as an active system which triggers the shift between the training and testing states of automatic speech recognition systems (ASRSs) which are built from ANNs. First an initial set of ASRSs are created to recognize speech under the constraints of an unpredictable acoustic world. The training of the ASRSs starts and goes on until ASRSs no longer decrease their error classification in the current acoustic environment because of noises. This moment is detected by the reactive environment and the structure of the ASRSs are changed. The simulation performed with mathematical models of real rooms as environment showed that our system could be used as a prediction tool of ASRSs performances for the study of any speech perceiver based on ANNs or on hidden Markov models. Moreover, it is shown that on a task of French digits recognition, the new method performs better than conventional ones.

When multiple radar targets are close to each other, the return signals form these targets are overlapped in time. Therefore, by applying conventional motion compensation algorithms designed for single target, the multiple targets cannot be resolved, and each individual target cannot be clearly imaged. However, each individual target may have its own velocity and direction different from others. These different Doppler histories can be utilized to separate target from each other. By taking time-frequency transforms, different Doppler changing rates can be estimated. Using each estimated Doppler changing rate and making phase correction, each individual target may be imaged. In this paper, we first review algorithms for radar imaging of multiple moving targets, then, analyze the performance of these algorithms, and, finally discuss the advantages and limitations of these algorithms by using simulated radar data.

The structural features of Chinese character are suitable for the recognition process of handprinted Chinese character because of the advantage of high tolerances to distortions and style variations. The extraction of the stroke feature is very difficult. Wavelet transformation which is a powerful tool in image analysis is used to analyze the Chinese character image in this paper, and then the process of the extraction stroke is concise and distinct.

It is well known that images can be greatly compressed by exploiting the self-similar redundancies. In this paper, the self-similarities of wavelet transform are analyzed, and it is discovered that corresponding subbands of different scale detail signals are similar. An image coding method is proposed according to this property. The typical self-affirm transform is modified such that it is adapted to DWT coefficient encoding. An adaptive quantization method of the transform parameters s, is given. Firstly, a J-order discrete wavelet transform of the original image, denoted by LL₀, is performed. That is, LL is decomposed into LL_{j + 1}, LH_{j + 1, HL$_j + 1}, for 0 <EQ j <EQ J - 1. Secondly, LL_{J$. is encoded based on DCT. Thirdly, HL(subscript J} LH_J and HH_J are quantized and run- length coded. Fourthly, HL_j, LH_j and HH_j for 1 <EQ j <EQ J - 1, are encoded with modified self- similar transforms. HL_j, LH_j, and HH_j are divided into non-overlapping range blocks. For each range block R_{i (epsilon} HL_j, a domain block D_j (epsilon) HL_{j + 1}, which best matches R_j, is found, and the parameter s₁ of the corresponding transform is determined and adaptively quantized. Several kinds of images are compressed with this method. Experimental results demonstrate that this method can compress images significantly while keeping a very good fidelity. Besides, the algorithm is faster than typical fractal image coding methods because less searching is needed.

The 2-D continuous wavelet transform (CWT) has been used by a number of authors, in a wide variety of physical problems.1 - 3 In all cases, its main purpose is the analysis of images, that is, the detection of specific features such as hierarchical structures or particular discontinuities, edges, filaments, contours, boundaries between areas of different luminosity, etc. Of course, the type of wavelet chosen depends on the precise aim. In fact, the 2-D CWT is based on the 2-D dimensional Euclidean group with dilations, the scr-called twcr-dimensional similitude group, SIM(2).4 It is the purpose of this paper to explore this connection further and draw some of its practical consequences.

A set of bi-orthogonal wavelet transforms are developed based on an extension of Sweldens; lifting method for variable support wavelet bases. The bi-orthogonal wavelet has advantages of compact support for both the transform and inverse transform process, and, like the Zernike and Legendre polynomials, can be designed to pass localized polynomial variations of orders m up to the limit, depending on the width of support of the lesser support width of either the wavelet or the scaling function. Features of this wavelet set include symmetry of the wavelet and scaling functions. The wavelet and scaling functions of a given order m are related to their pair of duals through simple relations involving position shifts and sign changes. A general method for producing transform functions is given, and results are shown for up to m equals 3, which treats up to 7th order polynomial insensitivity. The set of transforms is tested against a sample image and results show the possibilities for compression. It appears the lowest order wavelet yields the best performance for simple compression techniques on the image used. This m equals 0 transform shows the least degradation from truncation and tends to treat small regions effectively. Despite the advantages of higher order wavelets with respect to fluctuations, these tend to artificially create noise information which is passed on to the next processing stage.

Since the traditional wavelet and wavelet packet coefficients do not exactly represent the strength of signal components at the very time(space)-frequency tilling, group- normalized wavelet packet transform (GNWPT), is presented for nonlinear signal filtering and extraction from the clutter or noise, together with the space(time)-frequency masking technique. The extended F-entropy improves the performance of GNWPT. For perception-based image, soft-logic masking is emphasized to remove the aliasing with edge preserved. Lawton's method for complex valued wavelets construction is extended to generate the complex valued compactly supported wavelet packets for radar signal extraction. This kind of wavelet packets are symmetry and unitary orthogonal. Well-defined wavelet packets are chosen by the analysis remarks on their time-frequency characteristics. For real valued signal processing, such as images and ECG signal, the compactly supported spline or bi- orthogonal wavelet packets are preferred for perfect de- noising and filtering qualities.

We present the interval interpolating wavelet transform for fast image compression. Comparing with the common used wavelet coding, this method is more systematically stable, with less computing complexity and the inherent parallel processing. In theory, it has the nearly optimal minimax compression characteristics. The simulation shows that the interval interpolating wavelet transform are more qualified and remove the artificial blocking effects. The interval wavelet is introduced to deal with the boundary points of the finite localized image. This method does not only improve the compress rate, but also deletes the quantization aliasing of the boundary pixels.

Wavelet is a powerful theory, but its successful application still needs suitable programming tools. Java is a simple, object-oriented, distributed, interpreted, robust, secure, architecture-neutral, portable, high-performance, multi- threaded, dynamic language. This paper addresses the design and development of a cross-platform software environment for experimenting and applying wavelet theory. WaveJava, a wavelet class library designed by the object-orient programming, is developed to take advantage of the wavelets features, such as multi-resolution analysis and parallel processing in the networking computing. A new application architecture is designed for the net-wide distributed client-server environment. The data are transmitted with multi-resolution packets. At the distributed sites around the net, these data packets are done the matching or recognition processing in parallel. The results are fed back to determine the next operation. So, the more robust results can be arrived quickly. The WaveJava is easy to use and expand for special application. This paper gives a solution for the distributed fingerprint information processing system. It also fits for some other net-base multimedia information processing, such as network library, remote teaching and filmless picture archiving and communications.

In recent work, a recursive divide-and-conquer approach was developed for path-minimization problems such as the traveling salesman problem (TSP). The approach is based on multiple-resolution clustering to decompose a problem into minimally-dependent parts. It is particularly effective for large-scale, fractal data sets, which exhibit clustering on all scales, and hence at all resolutions. This leads to the application of wavelets for performing the necessary multiple-resolution clustering. While the general topic of multiple-resolution clustering via wavelets is relatively immature, it has been explored for certain specific applications. However, nothing in the literature addresses the specific type of multiple-resolution clustering needed for the divide-and-conquer approach. That is the primary goal of this paper.

The structure of paraunitary modulated filter bank with power complementary prototype filter and arbitrary unitary modulation matrix is derived. By replacing the unitary modulation matrix of the analysis filter bank with left invertible matrix, one obtains biorthogonal modulated filter bank with power complementary linear phase lowpass prototype filter. Moreover, undersampled frequency domain overlapped filter bank can be constructed by designing modulation matrix with larger number of channels than decimation and the proposed structure allows arbitrary number of frequency channels to be overlapped. Unfolding technique is introduced to design frequency domain overlapped M band modulated filter bank. Application in quadrature modulation system is discussed.

This paper presents a new time-domain-based factorization algorithm for perfect-reconstruction filter bank. In the proposed algorithm, the polyphase transfer matrix is decomposed into elementary blocks using LU representation which can also be implemented by ladder structure. Consequently, perfect reconstruction is structurally imposed and the resulting system is robust to coefficient quantization. We presented an iterative design procedure to obtain perfect reconstruction filter bank with different desired specification on each subband filters. Given several subband filters, a block LU factorization algorithm is presented for perfect reconstruction filter bank completion. Special properties such as linear phase and FIR solution are discussed and parameterization of paraunitary completion under block LU factorization is derived. Block ladder structure are presented for efficient implementation. The proposed structure can be used to design perfect reconstruction filter bank with higher dimension. An example in mapping of 1D perfect reconstruction filter bank with LU representation into 2D perfect reconstruction filter bank with diamond shaped passband using nonrectangular transform is discussed.

A method based on wavelet shrinkage theory is proposed to reduce the truncation artifact in magnetic resonance imaging (MRI). This wavelet-based method takes advantages of various optimal and near-optimal properties of wavelets and wavelet shrinkage, which cannot be achieved by the methods based on other basis. Another advantage is that its performance does not degrade significantly in an environment with low SNR, which is usually the case in MRI applications. Different wavelet bases, including a recently proposed shift-invariant wavelet basis, are explored for improving the performance of the proposed approach. The proposed method is analyzed and compared with the conventional technique, based on Fourier analysis, using both simulated and real MR images.

There has recently been a growing interest in SAR imaging on account of its importance in a variety of applications. One reason for its gain in popularity is its ability to image terrain at extraordinary rates. Acquiring data at such rates, however, has drawbacks in the from of exorbitant costs in data storage and transmission over relatively slow channels. To alleviate these and related costs, we propose a segmentation driven compression technique using hierarchical stochastic modeling within a multiscale framework. Our approach to SAR image compression is unique in that we exploit the multiscale stochastic structure inherent in SAR imagery. This structure is well captured by a set of scale auto-regressive models that accurately characterize the evolution in scale of homogeneous regions for different classes of terrain. We thus use them to generate a multiresolution segmentation of the image. We subsequently use the segmentation in tandem with the corresponding models within a pyramid encoder to provide a robust, hierarchical compression technique which in addition to coding the segmentation, codes the image with high compression ratios and remarkable image quality.

The association of target track files established and maintained by physically separated sensors based solely upon metrics data does not provide sufficient performance to meet some weapon system requirements. Association algorithms that match tracks based on similarities in the Fourier power spectra derived from the targets' signatures are routinely employed to improve post-mission confidence in track associations made between airborne IR tracking sensors and ground or ship-based radar frequency (RF) sensors that view common target suites during live exercises. The problem with Fourier techniques is that long viewing times are required to obtain usable power spectral density estimates; our mission scenarios impose a time constraint that is about one order of magnitude less. Faster algorithms are required for real-time embedded interceptor and BMC⁴I applications. This paper documents preliminary results we have obtained using a prototype, wavelet-based algorithm to automate the rapid, one-to-one association of RF and IR target tracks using features extracted from short signature histories maintained in the track files. The primary physical phenomenon that is exploited by the algorithm is the frequency content in the target signature, which is induced by the target's body dynamics. No a priori knowledge of the expected signature dynamics is assumed. Given a group of targets that are observed by two or more sensors, each sensor independently establishes and maintains its own track files while viewing the targets from physically isolated platforms. The sensors may have different sample rates and may operate in different regions of the RF spectrum; concurrent viewing is not required. The algorithm automatically detects and extracts signature glints as a preprocessing step, saving the glint as a preprocessing step, saving the glint data in separate 'channels' for further processing and employs wavelet shrinkage to attenuate any white noise that may be present in the signature data. Individual sensor track files are treated as separate pattern classes within an adaptive, statistical pattern recognition framework. The class feature vectors are formed from the magnitudes of the wavelet packet crystal coefficients. Clustering transformations are applied to each 'class', Fisher's linear discriminant is employed to minimize the intraclass scatter while maximizing the interclass scatter, and a modified Mahalanobis distance is then used as a metric to quantify the similarity between each possible pair of classes. Evidence is provided that suggests the wavelet packet crystal energies used by the association algorithm may be of some utility in the detection of closely spaced objects. The algorithm and the analyses are discussed within the context of a two-sensor scenario, but the algorithm is equally applicable to multiple sensor applications.

In this paper, we present a fast block time-recursive algorithm for the computation of short-time Fourier transform, and apply the algorithm to inverse SAR image processing. Simulation results are given and the computational complexity is discussed. The block time- recursive algorithm provides a fast vehicle for processing ISAR images on a real-time basis.

Recently, there has been a great deal of interest in the application of wavelet transforms to signal processing applications. As an example, to obtain the source density function for a wideband radar or sonar signal from the measurement of scattered signals it is desirable to first perform the wavelet transform of the received signal before processing it. The use of the wavelet transform allows the selection of basis functions which are matched to the transmitted signal. Fundamentally, the wavelet transform of a signal is the correlation of the signal with a basis function derived from a mother wavelet and its scaled versions called daughter wavelets. Thus any real-time correlator can be used for the implementation of the wavelet transform. Since a 1D input signal produces a 2D wavelet transform, optical correlators provide a natural advantage over conventional electronic implementations. The VanderLugt correlator, the joint transform correlator and its derivative, the quasi-Fourier transform joint transform correlator can all be used to implement the wavelet transform, provided a spatial light modulator is used to convert the electrical input signal into an appropriate optical signal. The concept of the smart pixel is to integrate both electronic processing and individual optical devices. Arrays of these smart pixels would then bring with them the advantage of parallelism that optics could provide. Smart pixels can function as spatial light modulators providing additional electronic processing features. They are naturally well-suited to realizing wavelet transforms.

We address two ISAR imaging problems by utilizing adaptive joint time-frequency (JTF) processing ideas. In the first application, the adaptive JTF processing is applied to extract non-point scattering resonant features from an ISAR image. By applying JTF processing to the down range dimension,w e show that it is possible to extract the strongly frequency-dependent components from the data that correspond to resonant features on the target.Our results show that non-point scattering mechanisms can be completely removed from the original ISAR image, leading to a cleaned image containing only physically meaningful point scatterers. The non-point scattering mechanisms, when displayed in the frequency-aspect plane, can be used to identify target resonances and cut-off phenomena. In the second application, we utilize adaptive JTF processing to address the motion compensation issue. By applying JTF processing to the cross range dimension, we track how the Doppler frequency varies as a function of imaging time. We then derive the target motion and remove this effect from the data. In both applications, the adaptive JTF engine preserves the phase information in the original data. Consequently, the two processing blocks can be cascaded to achieve both motion compensation and feature extraction.

Range profiles generated by a high range resolution radar have been used for non-cooperative target identification, especially in cases when radar range-Doppler image cannot be generated due to various reasons. Since a range profile is inherently a transient phenomenon, underlying features may not be identified in the time domain or frequency domain alone.However, the joint time-frequency analysis may provide a localized time-frequency information for identifying significant features of targets. A basis set, which is natural to the signal and called the natural frame, can be derived from the signal's energy distribution in the joint time-frequency domain. In this paper, the natural frame decomposition is used for best representing radar range profiles, a time-frequency ridge detector is applied for finding the natural frame set, which can be used as the target features for classification.

The paper will discuss the use of wavelet algorithms in the processing of x-ray imagery. X-ray imaging technology is currently being employed by various government agencies to detect the presence of undesirable contraband in shipping vessels and containers. The DoD Counter Drug Technology Development Office has sponsored the development of several of these systems. This paper will describe the capability of these algorithms to aid an operator by providing images that have ben corrected to provide the proper dynamic range in local areas. This capability will enable the presentation of images with significant dynamic range, where the useful information is presented adjusted to the local objects. We will also show the application of wavelet algorithms to the detection of contraband objects. These detection level algorithms are low level algorithms designed to develop candidate objects for processing by higher level algorithms. These higher level algorithms can then be used to aid operators in the screening of baggage and shipping vessels for contraband.

Computer aided target recognition (ATR) is introduced to reduce the false alarm rate (FAR) based on a pair of x-ray images. We assume that a homogeneous texture feature persists throughout the area of interest (AOI) in cases of contraband drug substances. We introduce an adaptive edge- texture wavelet transform (WT) in order to match the substance texture. Furthermore, we introduce a feature persistence measure in terms of a multi-resolution fractal dimension analysis. Results of an FPM plotted against the size of the box region show that the reflectance AOI is similar to the false contraband; but that of actransmitted AOI reveals a different fractal dimension between the positive and negative contrabands. Thus we can reduce the FAR.

A drug detection system using neural networks is applied to the problem of detecting cocaine stimulants in backscatter and transmission images of baggage generated by the AS and E 101 x-ray mobile van. This system automatically locates and evaluates potential targets of interest by merging intensity and geometric data form backscatter and transmission x-ray images and outlines the suspicious regions in red. Two neural networks are used to analyze the combination of both backscatter and transmission data; the first network analyzes suspicious regions from the images and outputs a probability that the region contains drugs, and the second integrates all such regions from a bag and outputs a probability that the bag contains drugs. The system performance approaches that of expert human operators in detecting drugs. It can benefit inspection by reducing the number of bags that the human needs to inspect thereby increasing the number of bags that a human can process in a given time.

Image coding based on subband decomposition with DPCM and PCM has received much attention in the areas of image compression research and industry. In this paper we present a new adaptive image subband coding with discrete wavelet transform, discrete cosine transform, and a modified DPCM. The main contribution of this work is the development of a simple, yet effective image compression and transmission algorithm. An important feature of this algorithm is the hybrid modified DPCM coding scheme which produces both simple, but significant, image compression and transmission coding.

Registration of images is of great importance in the fields of aerial surveillance, automatic target recognition, machine vision and medical imaging. Wavelets are tools that are being used to analyze signals and images. Wavelets in some sense are alternatives to Fourier transforms. Wavelets provide excellent time and frequency localization properties when compared to Fourier transforms. Singularities and irregular structures carry very important information about edges. Wavelets are excellent tools for detecting these singularities and characterizing the regularity of the function using Lipschitz exponents as shown by mallat et. al. In this paper we use the wavelet modulus maxima which is the strict local maxima of the modulus of the wavelet of the modulus of the wavelet transform to locate the singularities at each scale. homologous points from two similar images are then used to register the images using a best fit criteria. The objective function being that the difference image is a minimum image. The technique exploits inter image redundancy in addition to the intra image redundancy in sets of similar images after they have been registered. This lead to higher compression ratios. It also permits the use of any existing compression technique to exploit intra image redundancy.

A wavelet transform image decomposition technique was utilized for compression and analysis of the ultrasonic images obtained by a computerized ultrasonic gauging system (CUGS). CUGS can generate very precise topographical maps of the outer and inner surfaces of tubes during various stages of manufacture and life-cycle of the parts. Measurements of the tube dimensions are obtained with a resolution of 2.5 micrometers and accuracies of the order to 10 micrometers or better. A typical output of CUGS is an ultrasonic image, in which the horizontal and vertical axes represent the axial and angular position of the part, respectively. Wavelet-based image analysis has been utilized to obtain representations of the same image with different resolutions and to enhance image features such as erosion pattern without the loss of localization. In the application discussed CUGS is utilized to map the wear of the internal surface of steel tubes, before and after exposure to extreme environments involving temperature, pressure, corrosive gases and mechanical forces.

Biological vision systems of higher life forms naturally divide space, time, and color domains into a relatively few bandpass components. In the spatial domain, the division is primarily into a low frequency bandpass channel and a high frequency bandpass channel. Wavelet analysis also divides input into low and high band representations. Chips originally designed to exploit filtering functionality of biological retinas can also be used to perform fast analog decomposition of imagery into subsequent vision wavelet components. These filtering concepts are presented in connection to previously developed retinal processors and compared to conventional wavelet filters. Although perfect reconstruction is not performed by biological systems, it is used here as a metric for measuring level of information corruption inherent in biological filter models.

Recent advances in areas such as wavelet mathematics, and artificial neural networks have resulted in improved image compression, restoration, and filtering techniques. Although these techniques are capable of achieving excellent performance in terms of image quality, their computational complexity often requires expensive, and specialized hardware to run in near real time. Even general purpose parallel processing boards exceed the cost, size, and weight constraints of many applications including, remote sensors, security systems, commercial and home video teleconferencing. This paper describes a low cost board which supports a video compression, restoration, and filter system. The WaveNet board has been optimized for wavelet based compression techniques, and neural network based filters.

We present a method for automatically registering images based on nonlinear compression. The method involves three steps: (i) analysis of the complexity of the images, (ii) high level compression for extracting control points in the images, (iii) registration of the images by matching control points. The first step analyzes the complexity of the given images. It numerically computes from any image a complexity index which determines the efficiency at which the image can be compressed. This index is used in the second step of the algorithm to select coefficients in the wavelet representation of the image to produce a highly compressed image. The wavelet coefficients of the highly compressed image are then transformed to pixel values. Only a few pixel values are nontrivial. The third stage of the algorithm uses a point alignment technique to identify matching control points and to erect the registering transformations. The algorithm is tested on two quite different scenes: a portrait, representing an uncomplicated scene, and a Landsat TM image of the Pacific Northwest. In both cases, images are tested which differ by a rotation and which differ by a rigid transformation. The algorithm allows a choice of different metrics in which to do the compression and selection of control points.

We propose an invariant descriptor for recognizing complex patterns and objects composed of closed regions such as printed Chinese characters. The method transforms a 2D image into 1D line moments, performs wavelet transform on the moments, and then applies Fourier transform on each level of the wavelet coefficients and the average. The essential advantage of the descriptor is that a multiresolution querying strategy can be employed in the recognition process and that it is invariant to shift, rotation, and scaling of the original image. Experimental results show that the descriptor proposed in this paper is a reliable tool for recognizing Chinese characters.

2D local spectral information can be obtained form an image using Instantaneous Wavevector (IW). This 2D function is a vector quantity found by taking the gradient of the phase of the analytic image. Several synthetic images will be presented to illustrate the utility of IW analysis, and its application to OH airglow images will be discussed. The IW of an image gives us the dominant wavevector present at any point in the image. The amplitude of the analytic image gives us the magnitude of this component, and the phase differences of the analytic image between successive images allow us to infer the velocity of these waves. This method is used to determine phase velocities of internal waves from Hydroxyl airglow data. The instrument used, UWOSCR, is a scanning radiometer in the near infra-red, taking an 256 pixel image of the OH airglow every minute.

A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice data. For example, analysis of the 'blobs' in a low-order, Gaussian- derivative wavelet transform extracts the glottal-closing rate, while the ridges of a high-order wavelet transform give good indication of the formant frequencies and allow automatic word and phrase segmentation.

A number of parameters are extracted from speech signals using adaptive wavelets based on evolutionary programming and quasi-Newton methods. Their features will be applied to a text-independent speaker verification system. Adaptive wavelet networks are an effective tool in speech signal approximations as weighted linear combinations of translated and dilated mother wavelets. These parameters can be used as features for each speaker. Conventional quasi-Newton methods for the network have the high possibility of falling into a local minimum, at which point a self-adaptive evolutionary algorithm is applied to escape it. A set of model parameters, used as input to a fuzzy inference system, is one that has properties of low intra-speaker variation, and, at the same time, high inter-speaker variation. The fuzzy inference system proposed for speaker verification is a classifier that will determine whether the utterance is made by the authorized speaker. This fuzzy inference system derives valuable information from each model parameter of each utterance spoken by several speakers from database to construct a fuzzy rule-based verification system.

An effective realization of a frequency modulation identification scheme requires an analysis tool which is capable of crisply extracting a signal's frequency fluctuations over time. Such an analysis should be digitally tractable, computationally efficient, concise, noise robust, and not too sensitive to time-shifts. In all these respects, non-orthogonal wavelet transforms (NOWTs) are well suited for the analysis of FM signals. Because no orthogonality is required of the wavelet family, the analyzing wavelet may be chosen almost arbitrarily. This freedom may be exploited to specify special families of wavelets which are defined directly in the frequency domain on a frequency interval of support described by a center frequency, and bandwidth. In general, these parameters may be used to tune the wavelet family to a particular class of signals of interest. A signal's frequency modulation may be estimated through simple coherent identification schemes in the NOWT domain, e.g., thresholding. Identification may then be subsequently performed via a simple nearest neighbor thresholded classifier using a specified metric (notion of distance). This approach is applied to a small test set of mono-component and multi-component synthetic FM signals and shown to yield 100% identification success at signal to noise ratios greater than -4dB using a Morlet based NOWT. For comparison, the same data set yields 100% identification success for signal to noise ratios only as low as 0dB when comparing signals directly in the time domain, i.e., via a matched filter technique.

Many results in approximation theory, nonparametric regression, and adaptive signal representation assume that the signal is a smooth function or nonstationary in some smooth sense. These assumptions are not always applicable and perhaps even more importantly the times where the signal is not smooth are themselves important features to preserve in the signal representation. Previously, computationally efficient methods were developed to implement these approaches for the relatively simple problem of estimating multiple change points from a piecewise constant signal. In this paper, this approach is presented in the modern framework of waveform dictionaries, bases libraries, and atomic decomposition.

The characterization and construction of translation invariant multiresolution system is discussed. Multiresolution basis that provides optimal performance in approximating functions with different translation is considered. Translation variance is defined to be the variance of the energy when projecting input signal under different translation to the vector space constructed by multiresolution basis. It is proved that the translation variant property of all the multiresolution basis onto themselves is a complete representation of the translation variant property of the multiresolution system. By considering scale limited signal expansion in multiresolution analysis, optimal signal adapted multiresolution basis function is defined. The results are used to design optimal signal adapted translation invariant multiresolution basis. Simulation results on the signal adapted translation invariant multiresolution basis in detection problems are presented. The constructed system outperforms tradition multiresolution system that uses translation variant basis.

Direct sequence spread spectrum signaling is often used as a means of providing reliable digital communications in potentially hostile environments. In this paper, the performance of interference mitigation algorithms using transform domain excision and Wiener filtering are presented. In the presence of single-tone and narrow-band Gaussian jammers, block and lapped transform domain excisers are evaluated and compared. Results illustrating the performance of transform domain Wiener filters in the presence of various frequency tone interferers are also presented. In practice, adaptive Wiener filtering is often approximated using the least mean-square adaptive algorithm. Under certain conditions, the convergence rate of these algorithms can be improved in the transform domain through the use of power normalization. Results depicting such improvements in the presence of narrow-band interference are discussed herein.

Recently, a new class of spreading codes has been developed based upon the time-frequency duality of multirate filter bank structures. Unlike the maximal length sequences, these new codes are not limited to being binary valued. Instead, the elements of the sequences are determined by an optimization process which emphasizes certain desirable code properties. In this paper, spreading codes based upon multirate filter banks are developed for use in a cellular or microcellular channel in which partial synchronization is maintained between the users. This situation allows the cross-correlation between the codes to be optimized over a fraction of the total range of possible phase shifts between the codes. COdes are designed for an example set of channel conditions and bit error rate results are generated. These results show that the new codes perform better than conventional Gold codes.

Recent success in wavelet coding is mainly attributed to the recognition of importance of data organization. There has been several very competitive wavelet codecs developed, namely, Shapiro's Embedded Zerotree Wavelets (EZW), Servetto et. al.'s Morphological Representation of Wavelet Data (MRWD), and Said and Pearlman's Set Partitioning in Hierarchical Trees (SPIHT). In this paper, we propose a new image compression algorithm called Significant-Linked Connected Component Analysis (SLCCA) of wavelet coefficients. SLCCA exploits both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. A so-called significant link between connected components is designed to reduce the positional overhead of MRWD. In addition, the significant coefficients' magnitude are encoded in bit plane order to match the probability model of the adaptive arithmetic coder. Experiments show that SLCCA outperforms both EZW and MRWD, and is tied with SPIHT. Furthermore, it is observed that SLCCA generally has the best performance on images with large portion of texture. When applied to fingerprint image compression, it outperforms FBI's wavelet scalar quantization by about 1 dB.

Digital halftoning is the process to render continuous-tone images on binary display devices such as printers. Although the transmission of halftone images to printers can be compressed using established lossless protocols, lossy compression methods of the original image can achieve higher efficiencies. We present some experimental work in developing a reversible wavelet-based image compression algorithm that is tuned for halftoning. We also describe a rendering algorithm which is based on the wavelet coefficients from the compressed domain, and which matches the number of dots to the average image intensity at multiple resolutions. Additionally, we address the issue of inverse halftoning using wavelet decompositions of the halftone data.

There exists a great variety of numerical methods to solve differential equations. With the advent of wavelet analysis, new approaches have been tried: the wavelet-based methods. One of the main points in this kind of approach is the use of the multi-resolution structure of wavelet bases to reduce the number of degrees of freedom needed to represent the approximate solutions. Wavelet-based methods usually use Galerkin, Petrov-Galerkin or even collocation schemes. We discuss here a unified framework for analyzing the performance of these different schemes. It uses the concepts of restriction and prolongation operators. Using this formalism, we give an overview of some recent results on the representation of differential operators in the wavelet context.

The relationship between wavelets, Laplace pyramids and QMF are now well established. IN recent years biorthogonal wavelets have become of increased interest because, compared with orthogonal wavelets, they are symmetric and linear phase. In this paper the Hut function is used as a scaling function to construct a biorthogonal wavelet family, we call Hutlets. A realization with perfect reconstruction, multiplier-free quadrature mirror filters using RNS technic is proposed.THe approximation-filter is a CIC lowpass, the detail-filter is a CHPC highpass, and the reconstruction filters are IIRs. Exact pole-zero annihilation is guaranteed by implementing polynomial filters, over an integer ring, in the residue arithmetic system. Since CIC and CHPC designs rely on the exact annihilation of selected poles-zeros, a new facilitating technology is required which is fast, compact, and numerically exact. How this can be achieved is the thrust of this paper. An application of the Hutlets to pulse amplitude modulated signals is explained.

We have developed a highly effective continuous wavelet transform formalism for Sturm-Liouville eigenvalue problems, -(partial)_x²(Psi)(x) + V(x)(Psi)(x) equals E(Psi)(x), involving an arbitrary rational polynomial potential function V(x). Our method enables the exact generation of wavelet transforms of the type W(Psi)(a,b) equals (integral) dx(1/(square root)a)W((x-b)/a)(Psi)(x), where W(x) equals -N(partial)_xⁱe^-Q(x) and Q(x) equals (Sigma)_{n equals 0}^2N (Xi)_nxⁿ, provided i (is greater than or equal to) 1, and (Xi)_2N (is greater than) 0. This first principles approach emphasizes the use of dilated and translated power moments, (mu)_a,b(p) equals (integral) dxx^pe^-Q(x/a)(Psi)(x + b). For the broad class of problems defined above, a finite number of the moments satisfy a closed, coupled, set of first order differential equations with respect to the inverse scale variable: (partial)_(1/a)(mu) _a,b(k) equals (Sigma)_{l equals 0}^{(m(subscript)s)}M_E,a,b(k,l)(mu)_a,b(l), where m_s is problem dependent. Using moment eigenvalue methods, one can solve the infinite scale problem, a equals (infinity) , and proceed to numerically integrate the coupled first order equations. For the class of wavelet functions being considered, the wavelet transform, W(Psi) , is a linear superposition of the moments and therefore trivially obtainable. Reconstruction of the corresponding solution, (Psi) , ensues by either using well known dyadic wavelet reconstruction methods, or evaluating the a yields 0 limit of certain moments. The second approach is equivalent to a wavelet reconstruction that is based upon integrating over all values of the scale and translation variables. We also discus a generalization of this formalism permitting its application to 2D Sturm-Liouville PDEs.

We review the optical wavelets proposed by Onural and the electromagnetic wavelets proposed by Kaiser. We show that the wavelet transform of the electromagnetic wavelets can be computed with the direct inner product in the space time between the field and the scaled and shifted wavelets.In the case of monochromatic field, Kaiser's physical wavelets become monochromatic spherical wavelets.

We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This non-linear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the non-linear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and non-linear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.

Wavelet transform is being used for many real-time signal and image processing applications. Many applications can tolerate certain level of compromise in accuracy for a faster speed. In this paper we propose a wavelet processor architecture to support approximated calculation of the wavelet transform.Our design uses the fixed point number system to simplify the hardware design and the computation procedures. By using a table look-up technique, one can predict the range of an output coefficient, so that the computation of coefficients need not be completed. This technique can be efficiently implemented in the wavelet processor for in-line thresholding. By adjusting the thresholding level, one can achieve different levels of computational accuracy and speed. Our simulation results on processing of speech and musical data show that this thresholding technique is quite effective and flexible.

This paper concentrates on how to construct wavelets according to the practical needs of computer vision and image processing. At first, a theory for the construction of dyadic wavelets has been established. The resulted dyadic wavelets possess zero-symmetric or zero-antisymmetric property, and can also be fastly decayed so that they are suitable for edge detection. Then an algebra approach for the construction of orthogonal wavelets is proposed. It facilitates the selection of best wavelet for a given image processing task such as image compression.

This paper presents an algorithm that jointly optimizes a lattice vector quantizer (LVQ) and an entropy coder in a subband coding at all ranges of bit rate. Estimation formulas for both entropy and distortion of lattice quantized subband images are derived. From these estimates, we then develop dynamic algorithm optimizing the LVQ and entropy coder together for a given entropy rate. Compared to previously reported min-max approaches, or approaches using asymptotic distortion bounds, the approach reported in this paper quickly designs a highly accurate optimal entropy- constrained LVQ at all range of bit rates. The corresponding wavelet-based image coder has better coding performance comparing with other subband coders that use entropy- constrained LVQ, especially at low bit rates.

In this paper, three classes of basis functions are considered for segmenting scaled and rotated textured images. The first is the orthonormal, compactly supported Daubechies and the discrete Haar bases, the second class is the biorthogonal basis and the third is the non orthogonal Gabor basis. Texture operators are constructed from the bases functions based on the notion of multiresolution analysis. The textures are scaled and rotated and the basis functions are used to expand them. Certain features are computed on the expansions and used by a classifier to recognize and subsequently segment the texture mosaics. Experimental results on different texture mosaics show that the features obtained from the Daubechies, biorthogonal basis perform well in recognizing transformed textures. The concept of multiresolution representation is shown to be useful for invariant texture segmentation.

Battlefield reconnaissance through tactical surveillance video systems requires transmission of images through a limited bandwidth and capacity to achieve aided target recognition (ATR), of which some lossy compression is indispensable. Based on available resolution, ATR can have three functionality goals: (1) detection of a target, (2) recognition of target classes, and (3) identification of individual target membership. Thus, it is desirable to build an intelligent lookup table which maps a specific ATR goal into an appropriate image compression. Such a table may be built implicitly be employing the exemplar training procedure of artificial neutral networks. In order to illustrate this concept, we will introduce a computational metric called feature persistence measure, useful for x-ray luggage inspections, and further generalized here to capture human performance in a tactical imaging scenario.

The error resilient entropy coding of the Cambridge University group adapts variable-length blocks of data into fixed-length slots with known positions, in order to protect against possible channel errors during transmission of the discrete wavelet transform (DWT) coefficients. These coefficients have ben compressed based on the standard compression scheme using scalar quantization, runlength and Huffman coding. The DWT bi-orthogonal wavelet is used. The code is illustrated with relatively good performance for FLIR images, compressed at up to 0.09 bits per pixel, and bit error rates at about 10^-3. No additional attempt is made to perform decompression restoration.

Here we detect singularities with generalized quadrature processing using the recently developed Hermitian Hat wavelet. Our intended application is radar target detection for the optimal fuzzing of ship self-defense munitions. We first develop a wavelet-based fractal noise model to represent sea clutter. We then investigate wavelet shrinkage as a way to reduce and smooth the noise before attempting wavelet detection. Finally, we use the complex phase of the Hermitian Hat wavelet to detect a simulated target singularity in the presence of our fractal noise.

A genetic algorithm for the selection of wavelet packet bases for various tasks is proposed. We introduce a transform operator to convert the constrained combinatorial basis selection problem to an unconstrained numerical optimization problem. This algorithm offers a great deal of flexibility for the selection of wavelet packet bases in terms of different criteria for different tasks. To demonstrate the performance of this algorithm, we present two examples respectively for signal approximation and signal classification. Although the algorithm is described with wavelet packets, it can also be used for the selection of other tree structured local bases, such as local trigonometric bases.

Current railroad wayside Hot Bearing Detector systems were developed in the 1960s to identify failing friction bearings. While the electronics used in these systems have been upgraded to microprocessor technology, the basic detection principles have not changed over the last 30 years. In this paper, we present a novel method to detect, recognize, and classify a variety of railroad wheel-bearing defects using audible acoustic signals at several different train speeds. Our algorithm consists of a data preprocessor, a feature extractor, and a single multilayer neural network. The feature extractor can use any one of four different transforms to generate feature vectors from input acoustic data: the fast Fourier transform (FFT), the continuous wavelet transform, the discrete wavelet transform, and the wavelet packet. The classification performance using each feature vector type is presented. This algorithm can be applied to many kinds of bearings in rotational machinery to perform nondestructive fault detection and identification.