Hierarchical prior based sparse representation for compressed sensing MRI

Abstract

Compressed sensing (CS) allows accelerated magnetic resonance imaging (MRI) by highly undersampling k-space data. The key to high quality CS-MRI reconstruction is rational utilization of the sparsity of image in a certain transform domain. Existing CS-MRI methods commonly uses l0 norm or l1 norm to enforce the sparsity of image coefficients but lack parameter adaptation. In this work, a patch level sparse representation is derived from the joint maximum a posteriori (MAP) estimation under a probabilistic model, which adopts a hierarchical prior to characterize sparse image coefficients. The corresponding image reconstruction model is efficiently optimized by alternating direction method of multipliers (ADMM). Simulation results reveal that the proposed approach achieves higher reconstruction performance than competing CS-MRI methods, and is proven to be superior to general Ip norm based methods.