By omitting local decay and phase evolution,
traditional MRI models each datum as a sample
from k-space so that reconstruction can be implemented
by FFTs. Single-shot parameter assessment by
retrieval from signal encoding (SS-PARSE) acknowledges
local decay and phase evolution, so it models
each datum as a sample from (k, t)-space rather than
k-space. Local decay and frequency vary continuously
in space. Because of this, discrete models in space
can cause artifacts in the reconstructed parameters.
Increasing the resolution of the reconstructed parameters
can more accurately capture the spatial variations,
but the resolution is limited not only by computational
complexity but also by the size of the acquired data.
For a limited data set used for reconstruction, simply
increasing the resolution may cause the reconstruction
to become an underdetermined problem. This paper
presents a solution to this problem based on cubic
convolution interpolation.
KEYWORDS: Error analysis, Magnetic resonance imaging, Signal processing, Data acquisition, Functional magnetic resonance imaging, Computer programming, K band, Distortion, Data modeling, Interference (communication)
Quantitative and spatially accurate maps of local NMR relaxation rates from single-shot acquisitions are of value for
functional MRI and dynamic contrast studies. Addressing this need is SS-PARSE (Single-shot parameter assessment by
recovery from signal encoding), a recently introduced MRI technique for mapping magnetization magnitude and phase,
frequency, and net transverse decay rate R2* from a single-shot (<70 msec) signal. Instead of implicitly modeling the
local signal as arising from a constant magnetization vector, SS-PARSE models the evolution in phase and the decay in
amplitude of the local signal and estimates the local parameter maps producing the observed signal. Because the local
signal model used is fundamentally more accurate than the model implicitly used in most current MRI methodology, SS-PARSE
maps are inherently free from geometric errors due to off-resonance frequencies. The accuracy of the parameter
estimates is determined by (a) the information available in the signal (the form of the local signal model, the sampling
pattern, and random noise), and by (b) the effectiveness of the estimation algorithm in extracting the information present
in the signal. Sources of bias and random errors are discussed. The performance of the method is investigated using
experimental phantom data.
By acknowledging local decay and phase
evolution, single-shot parameter assessment by retrieval
from signal encoding (SS-PARSE) models each
datum as a sample from (k, t)-space rather than
k-space. This more accurate model promises better
performance at a price of more complicated reconstruction
computations. Normally, conjugate-gradients
is used to simultaneously estimate local image magnitude,
decay, and frequency. Each iteration of the
conjugate-gradients algorithm requires several evaluations
of the image synthesis function and one evaluation
of gradients. Because of local decay and frequency
and the non-Cartesian trajectory, fast algorithms
based on FFT cannot be effectively used to accelerate
the evaluation of the image synthesis function and gradients.
This paper presents a fast algorithm to compute
the image synthesis function and gradients by linear
combinations of FFTs. By polynomial approximation
of the exponential time function with local decay and
frequency as parameters, the image synthesis function
and gradients become linear combinations of non-
Cartesian Fourier transforms. In order to use the FFT,
one can interpolate non-Cartesian trajectories. The
quality of images reconstructed by the fast approach
presented in this paper is the same as that of the
normal conjugate-gradient method with significantly
reduced computation time.
This paper describes a method for reconstructing images in magnetic resonance spectroscopic imaging (MRSI) using finite element methods and incorporating a priori information into the image reconstruction using a model. The reconstructed image is modeled as a projection of the desired metabolic intensity function onto a set of basis functions. For a general set of basis functions that span the reconstruction space, this problem is shown to result in a set of linear equations. For non- orthogonal basis functions, a singular value decomposition (SVD) technique can be used to obtain a least-squares estimate of the unknown coefficients. Polynomial basis functions with a large rectangular support region were tested and shown to lack the local control necessary to sufficiently resolve some important clinical features of interest (e.g., transmural myocardial infarction). Bilinear finite elements were selected for this problem because they are a basis set with very local support. Various sized finite elements were tested with simulated and phantom myocardium data similar to those that might be obtained from a gated phosphocreatine MRSI patient study. The conclusions of this investigation were: a) finite elements can give the desired local control to resolve clinically relevant lesions such as (simulated) transmural myocardial infarction, b) finite elements are robust in the presence of k-space additive Gaussian noise, and c)editing of the singular values was shown to be important to achieve optimum results. Remaining difficulties with the method include (a) O(N3) SVD computational complexity as the finite elements are made smaller, and (b) 'blockiness' in the reconstructed image due to the regular rectangular nature of elements.
Functional images in medicine, such as phosphorus magnetic resonance spectroscopic imaging (SI) images or perfusion studies in nuclear medicine (NM) using 99mTc-HMPAO, are low in resolution compared to x-ray CT or proton MR (anatomic) images. This paper describes an improved, rapid method for enhancing the accuracy and resolution of functional medical images. While both functional and anatomic images are often available for the organ under study, few attempts have been made to use the a priori information in the anatomic images to improve the poor resolution of the corresponding functional images. The proposed technique assumes that compartments can be identified in a high resolution anatomic image of the region under study, and each of these compartments is assumed to contain a spatially heterogeneous concentration of metabolite. The spatial variation of the metabolite is modelled by a series expansion. Application of the method is derived for both MR spectroscopic images, and scintigrams. Noise-free and noisy simulation studies of spectroscopic images are presented which show that the method is robust in the presence of noise, and also when the assumed model is mismatched to the function which describes the actual metabolite compartmental concentration.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.