Bayesian sparse regularization for parallel MRI reconstruction using complex Bernoulli–Laplace mixture priors

Parallel imaging technique using several receiver coils provides a fast acquisition of magnetic resonance imaging (MRI) images with high temporal and/or spatial resolutions. Against this background, the most difficult task is the full field of view images reconstruction without noise, distortions and artifacts. In this context, SENSitivity Encoding is considered the most often used parallel MRI (pMRI) reconstruction method in the clinical application. On the one side, solving the inherent reconstruction problems has known significant progress during the last decade. On the other side, the sparse Bayesian regularization for signal/image recovery has generated a great research interest especially when large volumes of data are processed. The purpose of this paper is to develop a novel Bayesian regularization technique for sparse pMRI reconstruction. The new technique is based on a hierarchical Bayesian model using a complex Bernoulli–Laplace mixture in order to promote two sparsity levels for the target image. The inference is conducted using a Markov chain Monte Carlo sampling scheme. Simulation results obtained with both synthetic and real datasets are showing the outperformance of the proposed sparse Bayesian technique compared to other existing regularization techniques.