Compressed sensing MRI based on image decomposition model and group sparsity.

The image representation plays an important role in compressed sensing magnetic resonance imaging (CSMRI). However, how to adaptive sparsely represent images is a challenge for accurately reconstructing magnetic resonance (MR) images from highly undersampled data with noise. In order to further improve the reconstruction quality of the MR image, this paper first proposes tight frame-based group sparsity (TFGS) regularization that can capture the structure information of images appropriately, then TFGS regularization is employed to the image cartoon-texture decomposition model to construct CSMRI algorithm, termed cartoon-texture decomposition CSMRI algorithm (CD-MRI). CD-MRI effectively integrates the total variation and TFGS regularization into the image cartoon-texture decomposition framework, and utilizes the sparse priors of image cartoon and texture components to reconstruct MR images. Virtually, CD-MRI exploits the global sparse representations of image cartoon components by the total variation regularization, and explores group sparse representations of image texture components via the adaptive tight frame learning technique and group sparsity regularization. The alternating iterative method combining with the majorization-minimization algorithm is applied to solve the formulated optimization problem. Finally, simulation experiments demonstrate that the proposed algorithm can achieve high-quality MR image reconstruction from undersampled K-space data, and can remove noise in different sampling schemes. Compared to the previous CSMRI algorithms, the proposed approach can lead to better image reconstruction performance and better robustness to noise.