Sparse recovery algorithms based on dictionary learning for MR image reconstruction

Compressive Sensing is the present sampling paradigm which acquires only useful data, and hence reduces the acquisition time, eliminates the necessity of fast analog to digital converters and data compression stage, prior to transmission. Challenge lies in recovering the data from these few samples, which are far below Nyquist rate. Compressive sensing accomplishes this, provided the signal is sparse in either signal domain or transform domain. It is particularly useful to employ compressive sensing for Magnetic Resonance (MR) imaging as these images can be sparsely represented in transform domain. A patch based dictionary can reconstruct images with great accuracy even at very high undersampling rates, as it exploits patch based sparsity. This paper investigates the performance of three different recovery strategies - Orthogonal Matching Pursuit, Compressive Sampling Matching Pursuit and Basis Pursuit on different MR images when integrated with an adaptive patch based dictionary.