Compressed sensing MRI based on the hybrid regularization by denoising and the epigraph projection

Abstract

Signal models play a paramount role in compressed sensing magnetic resonance imaging (CSMRI), which aims to accurately recover magnetic resonance (MR) images from highly undersampled measurements. In recent decade, lots of works exploit the sparsity and the low rank for CSMRI. However, there are some defects involving many finely-tuned parameters and pending to further improve the image reconstruction quality. In order to address the above issues, this paper proposes a hybrid regularization by denoising (HRED) constraint, in which we employ the weighting of two types of denoisers such as the BM3D and a fast flexible denoising convolutional neural network (FFDNet). Essentially, the HRED constraint exploits the complementarity of multifarious priors, including the non-local similarity and sparsity induced by BM3D, and the learning deep priors induced by FFDNet. We plug the proposed HRED constraint into CSMRI framework to construct a CSMRI algorithm dubbed HRED-MRI. Concretely, we leverage the HRED constraint to formulate a CSMRI problem, and then tackle the formulated CSMRI problem via the alternating projection implemented by the epigraph method. The epigraph method is equivalent to the gradient descent method whose step sizes are selected in an adaptive manner. Thereinto, epigraph sets of the HRED constraint and the data fidelity term are defined, and the two epigraph sets are all convex. The HRED-MRI relied on the HRED constraint and epigraph method, only has one parameter which needs to be tuned. Compared with the state-of-the-art CSMRI approaches, experiments validate that the HRED-MRI can achieve more excellent image reconstruction performance and better robustness to noise.