MRI reconstruction based on Bayesian piecewise sparsity constraint and adaptive 3D transform

Abstract

Sparse representation of image is crucial to a promising reconstruction in compressed sensing magnetic resonance imaging (CS-MRI), which significantly accelerates imaging process by highly undersampling k-space data. However, realizing high sparsity and estimation accuracy of image coefficients directly affects the visual quality of the reconstructed image. In this work, an adaptive 3D transform learning method is developed to efficiently enhance the sparsity of coefficients produced by 3D transform on similar patches. In addition, we also consider the statistical characteristics of 3D coefficients, and build a probabilistic model that employs Gaussian scale mixture (GSM) prior for the grouped 3D coefficients with close magnitude levels. Based on Bayesian inference, a piecewise sparsity constraint is derived from maximum a posterior (MAP) estimation of 3D coefficients. Furthermore, the combination of piecewise sparsity constraint and adaptive 3D transform allows one to establish a novel CS-MRI reconstruction model and the corresponding numerical algorithms are deduced under the framework of alternating direction method of multipliers (ADMM). Compared to several advanced CS-MRI methods, the proposed approach better suppresses artifacts and preserves more image features with superior performance metrics.