In order to improve the performance of multi-frame blind deconvolution algorithm, the analysis was conducted on the image restoration quality and convergence rate of the multi-frame blind deconvolution algorithm using Conjugate Gradient + Brent, Conjugate Gradient + Dbrent, Conjugate Gradient + Macopt, and L-BFGS + Wolfe combination optimization algorithms. The mathematical principles of above optimization algorithms were elaborated in detail, and they were introduced into the multi-frame blind deconvolution algorithm to achieve high quality restored images. Theoretical and experimental results indicate that the L-BFGS + Wolfe combination algorithm has the fastest convergence rate, but the restoration quality is lower compared to the other combination algorithms; Compared with the other combination algorithms, the Conjugate Gradient + Brent/Dbrent combination algorithm can obtain higher quality restored images, but its convergence rate is slower; The convergence rate and restoring quality of the Conjugate Gradient +Macopt combination algorithm are between L-BFGS + Wolfe and Conjugate Gradient + Brent/Dbrent.
Multi-Frame Blind Deconvolution (MFBD) algorithm is the mainstream post-processing method for atmospheric turbulence degraded images. The restoration of a single object from multiple images requires several minutes or even tens of minutes, which severely limits MFBD’s practical application. To achieve the goal of fast restoration, this paper proposes hybrid MPI-CUDA (Message Passing Interface-Compute Unified Device Architecture) accelerated MFBD algorithm. In this hybrid programming model, MPI is responsible for assigning computing tasks, and CUDA is responsible for parallel computing. Hybrid MPI-CUDA accelerated MFBD algorithm has been tested on simulated images and achieved satisfactory results. The execution speed for restoring a single high-resolution image from multiple blurred images has been increased by over 50-fold.
Space object images obtained through ground-based telescopes tend to be heavily blurred and degraded by the atmospheric turbulence as well as detection noise and aberrations of optical systems. Multi-Frame Blind Deconvolution (MFBD) is currently the mainstream image restoration algorithm for images degraded by the atmospheric turbulence. MFBD jointly estimates the original image of object and the corresponding point spread functions (PSFs) from a sequence of short-exposure images. From our experience, there are still a lot of space for the improvement of the traditional MFBD algorithm. The mixed-Gaussian noise model that accounts for both the photonic and detector noise is used to replace the stationary Gaussian noise model. The L2-L1 (quadratic-linear) regularization method is used to replace originally used TV regularization method or Tikhonov regularization method. The phase annealing method is used to improve the quality of initial phase estimation and the multi-round iterative MFBD algorithm is preliminarily implemented. The simulation results demonstrate that the restored images obtained by the multi-round iterative MFBD algorithm often have better quality than that restored by traditional MFBD.
Adaptive optics plays an important role to compensate the atmosphere turbulence therefore concentrate the laser energy for satellite-ground laser communication. However, as the satellite especially LEO (Low-Earth orbit) moves, the communication laser from downlink (satellite to ground) and uplink (ground to satellite) will experience a different turbulence path, called the point ahead angle (PAA). PAA can be much larger than the atmosphere isoplanatic angle for strong turbulence or fast moving satellites, causing the AO system not working. For now there is no simple and effective way to solve this problem. In this paper, a new wavefront sensing technique called Projected Pupil Plane Pattern (PPPP) is used, where the Rayleigh backscattered light of the uplink laser is used to sense the uplink path of the turbulence. Specifically, PPPP uses at least two scattered images from two different heights to reconstruct the integrated turbulence phase due to the TIE (transport-of-intensity). As PPPP uses the uplink laser itself, the PAA problem is solved automatically. We demonstrate that PPPP method can be effectively used as a simple wavefront sensor in the adaptive optics system for satellite-ground laser communication by numerical simulation for 1m class ground telescope and AO system. Several important PPPP coefficients such as the propagation heights, number of Zernike Modes for reconstruction are studied, and their optimum choices are given.
Space objects images taken through large ground-based telescopes usually suffer from a degradation due to atmospheric turbulence, In order to reduce the cost of Charge-coupled Device (CCD) and improve the image signal-tonoise ratio, ground-based telescopes are usually designed with down-sampling, the observed image is blurry and aliased. We present a Super-Resolution (SR) algorithm to restore under-sampled image sequences with randomly varying blur, the algorithm significantly improves the quality and resolution of space object images degraded by atmospheric turbulence, it is a unifying framework that simultaneously performs Multi-frame Blind Deconvolution (MFBD) and SR in a maximum a posteriori (MAP) framework. The object and the Point Spread Function (PSF) are estimated by minimizing a cost function coming from the MAP criteria, the Total Variation (TV) regularization is imposed on the object estimation, TV regularization is remarkably effective to suppress the noise and to preserve the sharp edges in the image. We use the conjugate gradient method for the minimization for its fast convergence. Encouraging simulation results demonstrate that the restored image produced by this algorithm often have better quality than MFBD.
KEYWORDS: Point spread functions, Signal to noise ratio, Deconvolution, Image restoration, Image quality, Data modeling, Image processing, Telescopes, Imaging systems
Multi-frame blind deconvolution (MFBD) is a commonly used method of image post-processing technique to restore high-resolution image from the image observed through ground-based telescopes. During the restoration process, the frequencies with low signal-to-noise (SNR) ratio in the spectrum of the image which are called “spectrum holes” can easily lead to noise amplification effect. Hence there is a filtering idea by calculating the “spectrum holes” to impose the frequency domain constraint in MFBD. Hundreds of images observed through ground-based telescopes are often needed to obtain high quality images, which makes a considerable cost of computation. We discard the information in the images that have not been selected to improve the speed of the process. In this paper, we use the compact blind deconvolution algorithm (CMFBD). A small number of images with better quality as “control frames” is firstly selected to run the traditional MFBD, under such treatment, we can use relative less time to quickly obtain the PSFs corresponding to the “control frames”, and then, the PSFs corresponding to the “non-control frames” is obtained through the “consistency” principle which we assume object is the same in each frame. In CMFBD the non-selected data frames is used to provide an additional constraint on the PSF estimates for the selected data frames.
High-resolution imaging with large ground-based telescope is challenging due to atmospheric turbulence. Adaptive optics (AO) system can provide real-time compensation for the wavefront distortion in the pupil of the telescope. However, the observed images still suffer from a blurring caused by the residual wavefront. Numerical post-processing with a good approximation of the residual wavefront can help to effectively remove the blur. In this paper, a gradients measurement model for the Shack-Hartmann wavefront sensor (WFS) in a closed-loop AO system is built. The model is based on the frozen flow hypothesis with knowledge of the wind velocities of atmospheric turbulence layers. Then a high resolution residual wavefront reconstruction method using multiframe Shack-Hartmann WFS measurements and deformable mirror voltages is presented. Numerical results show that the method can effectively improve the spatial resolution and accuracy of the reconstructed residual wavefront.
High-resolution imaging with large ground-based telescopes is limited by atmospheric turbulence. The observed images are usually blurred with unknown point spread functions (PSFs) defined in terms of the wavefront distortions of light. To effectively remove the blur, numerical postprocessing with a good approximation of the wavefront is required. The gradient measurements of the wavefront recorded by Shack–Hartmann wavefront sensor (WFS) can be used to estimate the wavefront. A gradients measurement model for Shack–Hartmann WFS is built. This model is based on the frozen flow hypothesis and uses a least-squares-fit of tip and tilt across the subaperture in the WFS to genarate the averaged gradient measurements. Then a high-resolution wavefront reconstruction method using multiframe Shack–Hartmann WFS measurements is presented. The method uses high cadence WFS data in a Bayesian framework and takes into account the available a priori information of the wavefront phase. Numerical results show that the method can effectively improve the spatial resolution and accuracy of the reconstructed wavefront in different seeing conditions.
Multi-frame blind deconvolution (MFBD) is a well-known numerical restoration technique for obtaining highresolution images of astronomical targets through the Earth’s turbulent atmosphere. The performance of MFBD algorithms depend on initial estimates for the object and the PSFs. Even though the observed image might be close to the object and could be used for the initial estimate for the object, as is often the case with the PSFs, we lack prior knowledge on the PSFs for each image. In order to provide high-quality initial estimates and improve the performance of the MFBD algorithm, one of the most effective methods is to introducing an imaging Shack-Hartmann Wave-front sensor which is similar to the traditional Shack-Hartmann Wave-front sensor but with a smaller number of lenslets across the aperture, and to process the data using a multi-channel joint restoration algorithm. In this paper, we proposed a multi-channel joint restoration algorithm which involves the usage of an imaging Shack Hartmann channel data alongside with the science camera data to improve the overall performance of the MFBD restoration algorithm. The numerical results are given in order to illustrate the performance of the joint restoration process.
High-resolution Wavefront reconstruction using the frozen-flow hypothesis requires the wind velocities of all significant layers of turbulence in the atmosphere, which can be estimated from the time-delayed autocorrelation of the wavefront sensor (WFS) measurements. In this paper, we present a method to estimate the wind velocities of the frozen-flow atmospheric turbulence layers using the slope measurements of a Shack-Hartmann WFS. This method is tested by simulation experiments and the simulation results show that our method is efficient and the error is acceptable.
The atmospheric turbulence is a principal limitation to space objects imaging with ground-based telescopes. In order to obtain high-resolution images, post-processing is a necessary tool to overcome the effects of atmospheric turbulence. In this paper, we propose a multi-frame blind deconvolution algorithm based on the consistency constraints. We apply parametrization on the image and the PSFs, and present the minimization problem by conjugate gradient method through an alternating iterative framework. We also determine the regularization parameter adaptively at each step. Experimental results show that the proposed method can recover high quality image from turbulence degraded images effectively.
We demonstrate a maximum a posteriori (MAP) blind image deconvolution algorithm with bandwidth over-constrained and total variation (TV) regularization to recover a clear image from the AO corrected images. The point spread functions (PSFs) are estimated by bandwidth limited less than the cutoff frequency of the optical system. Our algorithm performs well in avoiding noise magnification. The performance is demonstrated on simulated data.
We propose a speckle imaging algorithm in which we use the improved form of spectral ratio to obtain the Fried parameter, we also use a filter to reduce the high frequency noise effects. Our algorithm makes an improvement in the quality of the reconstructed images. The performance is illustrated by computer simulations.
This paper presents a technique that performs multi-frame super-resolution of differently exposed images. The method first employs a coarse-to-fine image registration method to align image in both spatial and range domain. Then an image fusion method based on the maximum a posterior (MAP) is used to reconstruct a high-resolution image. The MAP cost function includes a data fidelity term and a regularized term. The data fidelity term is in the L2 norm, and the regularized term employs Huber-Markov prior which can reduce the noise and artifacts while reserving image edges. In order to reduce the influence of registration errors, the high-resolution image estimate and registration parameters are refined alternatively by minimizing the cost function. Experiments with synthetic and real images show that the photometric registration reduce the grid-like artifacts in the reconstructed high-resolution image, and the proposed multi-frame super resolution method has a better performance than the interpolation-based method with lower RMSE and less artifacts.
This paper describes an approach to reconstructing wavefronts on finer grid using the frozen flow hypothesis (FFH), which exploits spatial and temporal correlations between consecutive wavefront sensor (WFS) frames. Under the assumption of FFH, slope data from WFS can be connected to a finer, composite slope grid using translation and down sampling, and elements in transformation matrices are determined by wind information. Frames of slopes are then combined and slopes on finer grid are reconstructed by solving a sparse, large-scale, ill-posed least squares problem. By using reconstructed finer slope data and adopting Fried geometry of WFS, high-resolution wavefronts are then reconstructed. The results show that this method is robust even with detector noise and wind information inaccuracy, and under bad seeing conditions, high-frequency information in wavefronts can be recovered more accurately compared with when correlations in WFS frames are ignored.
This paper presents a technique that performs coarse-to-fine image registration both in spatial and range domain. The goal of image registration is to estimate geometric and photometric parameters via minimization of an objective function in the least square sense. In order to reduce the probability of falling into a local optimal solution, the algorithm employs a coarse-to-fine strategy. In the coarse step, an illumination offset and contrast invariant feature detector which is named SURF is used to estimate affine motion parameters between the reference image and the target image, and then the intensity of corresponding pixels is used to directly estimate contrast and bias parameters based on RANSAC. In the fine step, the estimated parameters obtained in the coarse step are used as a good initial estimation, and photometric and affine motion parameters are refined alternatively via minimizing the objective function. Experiments on simulated and real images show that the proposed image registration method is superior to the feature-based method used in the coarse step and the groupwise image registration algorithm proposed by Bartoli.
Shift-invariant motion blur can be modeled as a convolution of the true latent image and the blur kernel with additive noise. Blind motion de-blurring estimates a sharp image from a motion blurred image without the knowledge of the blur kernel. This paper proposes an improved edge-specific motion de-blurring algorithm which proved to be fit for processing remote sensing images. We find that an inaccurate blur kernel is the main factor to the low-quality restored images. To improve image quality, we do the following contributions. For the robust kernel estimation, first, we adapt the multi-scale scheme to make sure that the edge map could be constructed accurately; second, an effective salient edge selection method based on RTV (Relative Total Variation) is used to extract salient structure from texture; third, an alternative iterative method is introduced to perform kernel optimization, in this step, we adopt l1 and l0 norm as the priors to remove noise and ensure the continuity of blur kernel. For the final latent image reconstruction, an improved adaptive deconvolution algorithm based on TV-l2 model is used to recover the latent image; we control the regularization weight adaptively in different region according to the image local characteristics in order to preserve tiny details and eliminate noise and ringing artifacts. Some synthetic remote sensing images are used to test the proposed algorithm, and results demonstrate that the proposed algorithm obtains accurate blur kernel and achieves better de-blurring results.
An imaging system is constructed by atmosphere turbulence and ground-based telescope when the latter is used to observe a space object. The wavefront measurement produced by adaptive optics system can be used to estimate the point spread function (PSF) of the imaging system since it contains the wavefront aberration information of the light from the object. But the detector noise of the wavefront sensor (WFS) will inevitably bring estimation error. Based on the statistical theory, a method is presented to improve the PSF estimation accuracy by eliminating the noise error from the wavefront measurement. The numerical simulation shows that the estimation error of this method could be lower than 10%. It also indicates that the higher the signal-noise ratio (SNR) of the WFS is, the more frames of the wavefront measurements are used, and the bigger the Fried constant is, the more accurate the estimation will be. The work in this paper can be applied to performance evaluation of imaging system, deconvolution of AO images, as well as photometric analysis of space object.
The wavefront sensor is used in adaptive optics (AO) to detect the atmospheric distortion, which feeds back to the deformable mirror to compensate for this distortion. While the Shack–Hartmann sensor has been widely used, the plenoptic sensor was proposed in recent years. The two different wavefront sensing methods have different interpretations and numerical consequences, though they are both slope-based. The plenoptic sensor is compared with the Shack–Hartmann sensor in a closed-loop AO system. Simulations are performed to investigate their performances under closed-loop conditions. The plenoptic sensors both without and with modulation are discussed. The results show that the closed-loop performance of the plenoptic sensor without modulation is worse than that of the Shack–Hartmann sensor when the star for observation is brighter than magnitude 7, but better when the star is fainter. The closed-loop performance of the plenoptic sensor could be improved by modulation, except for the faint star. In summary, the limiting magnitude of the astronomical AO system may be improved by using the plenoptic sensor instead of the Shack–Hartmann sensor, and the modulation of the plenoptic sensor is more suitable for the bright star.
In adaptive optics (AO) system, the detector noise is one of the main error sources of Shack-Hartmann wavefront sensor (SH-WFS). Based on the statistical analysis of the noise, a noise error estimation method is presented by using multiframe of the Hartmann spots pattern and the centroid displacements calculated from them. A numerical simulation system for wavefront measuring is built, and used to verify the validity of this method. It shows that the estimation error of this method could be lower than 2%, provided that the signal-noise-ratio (SNR) is sufficient for the WFS working normally. We studied the least frames of data that are required for the method when the SNR of the WFS is at different levels. It indicates that fewer frames are required as the SNR level is higher, and only 2 frames of data are required when the SNR level is high enough. For different types of detector noise, we have analyzed the influence of the accuracy of their prior information on the estimation error. It shows that the influence of the readout noise is strong, and the influence of the photon-noise, the dark-current noise and the sky-background noise is neglectable, since the WFS is usually exposed shortly. The work in this paper can be of certain significance in estimating the point spread function of AO system with the WFS measurements.
Speckle imaging techniques are effective post-processing methods to eliminate atmospheric perturbations on the imaging
of space objects, in which speckle interferometry and bispectrum methods are usually used to estimate the magnitude and
phase spectrum of the objects separately. The spectral ratio technique used in this paper is convenient and efficient to
evaluate r0, which is crucial for calibrating the speckle transfer function in the magnitude estimation. It is shown that
power spectrum, the second moment of the magnitude spectrum, needs bias removal whereas bispectrum processing does
not. Reconstructed images from the observed data of binary stars and Jupiter are presented.
In a high-energy laser, the thermal aberrations degrade the beam quality and reduce the laser’s output power. Adaptive optics (AO) technique based on a stochastic parallel gradient (SPGD) algorithm can be used to compensate for the distortions in real time to clean up the laser beam. Such a beam clean-up system was simulated and experiments were conducted to study the optimization of the parameters of the gain coefficient and the amplitude of the perturbation. The results show that the convergence property of the SPGD algorithm is improved after the parameters being optimized.
The feasibility of realizing beam cleanup of high power lasers using stochastic parallel gradient descent (SPGD)
wavefront control method has been demonstrated numerically. The numerical model of an adaptive optics system
comprising a 44-element deformable mirror and a far-field system performance metric sensor is first setup which
operates with the SPGD wavefront control method. The system is then used to correct for the dynamic aberrations of a
laser beam where the phase screens of the beam are constructed from the simulation data of a high power laser system
and are introduced into the light wave time sequentially according to the iteration rate of the SPGD wavefront controller.
The correction results show that the beam cleanup system investigated here can effectively compensate for the dynamic
aberrations of the laser beam involved.
Coherent beam combination of fiber laser arrays plays an important role in realizing high power, high radiance fiber laser
systems. The stochastic parallel gradient descent (SPGD) algorithm is a newly developed optimization method using the
technique of parallel perturbation and stochastic approximation and it is expected that this algorithm can reduce the cost
and complexity of a high power fiber laser system when incorporated in its beam combination scheme. In this paper, a
numerical simulation model about the fiber laser beam combination system is then established based on beam-quality-metric optimization method. The SPGD algorithm is introduced and used to realize the beam-quality-metric
maximization, leading to the maximum output power of the fiber laser system. The results of numerical simulation
indicate that the far-field beam intensity optimization method using SPGD algorithm can realize coherent beam
combination of fiber laser arrays effectively.
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