Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Wavelet-regularized reconstruction for rapid MRI
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
Under-determined non-cartesian MR reconstruction with non-convex sparsity promoting analysis prior
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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Recently Compressed Sensing (CS) based techniques are being used for reconstructing magnetic resonance (MR) images from partially sampled k-space data. CS based reconstruction techniques can be categorized into three categories based on the objective function: (i) synthesis prior, (ii) analysis prior and (iii) mixed (analysis+synthesis) prior. Each of these can be further subdivided into convex and non-convex forms. There is also a wide choice available for the sparsifying transforms, viz. Daubechies wavelets (orthogonal and redundant), fractional spline wavelet (orthogonal), complex dualtree wavelet (redundant), contourlet (redundant) and finite difference (redundant). Previous studies in MR image reconstruction have used a various combinations of objective functions (priors) and sparsifying transforms; and each of these studies claimed the superiority of their method over others. In this work, we will review and evaluate the popular MR image reconstruction techniques and show that analysis prior with complex dualtree wavelets yields the best reconstruction results. We have evaluated our experimental results on real data. The metric for quantitative evaluation is the Normalized Mean Squared Error. Our qualitative evaluation is based both on the reconstructed and the difference images. The other significant contribution of this paper is the development of convex and non-convex versions of synthesis, analysis and mixed prior algorithms from a uniform majorization-minimization framework. The algorithms are compared with a state-of-the-art CS based techniques; the proposed ones have better reconstruction accuracy and are only fractionally slow. The algorithms that are derived in this paper are all efficient first order algorithms that are easy to implement.