Compressed sensing magnetic resonance imaging based on dictionary updating and block-matching and three-dimensional filtering regularisation

Compressed sensing (CS) enables that magnetic resonance (MR) images can be exactly reconstructed from undersampled k-space data by exploiting the sparsity of MR images in some analytical sparsifying transform or some dictionary. Recent methods are exploiting adaptive patch-based dictionaries for image recovery by alternating between dictionary learning step and image reconstruction step. In this study, the authors propose a novel MR image reconstruction algorithm utilising dictionary updating, which consists of three steps: sparse coding, dictionary updating and image reconstruction. In the dictionary updating step, they perform a first-order series expansion for dictionary-coefficient matrix product via recursive method, and propose an efficient method to solve the new dictionary updating problem. To improve the reconstruction quality, the proposed block-matching and three-dimensional (3D) filtering regularisation is incorporated into the authors' image CS recovery, which can combine the self-similarities within the image, the 3D transform sparsity and the local sparsity into image recovery process. Experimental simulations demonstrate their proposed algorithms can obtain better reconstruction quality than the previous CS algorithms.