On the choice of Compressed Sensing priors and sparsifying transforms for MR image reconstruction: An experimental study

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. (C) 2012 Elsevier B.V. All rights reserved.