Compressive Sensing MRI with Wavelet Tree Sparsity

In Compressive Sensing Magnetic Resonance Imaging (CS-MRI), one can reconstruct a MR image with good quality from only a small number of measurements. This can significantly reduce MR scanning time. According to structured sparsity theory, the measurements can be further reduced to O(K + log n) for tree-sparse data instead of O(K + K log n) for standard K-sparse data with length n. However, few of existing algorithms have utilized this for CS-MRI, while most of them model the problem with total variation and wavelet sparse regularization. On the other side, some algorithms have been proposed for tree sparse regularization, but few of them have validated the benefit of wavelet tree structure in CS-MRI. In this paper, we propose a fast convex optimization algorithm to improve CS-MRI. Wavelet sparsity, gradient sparsity and tree sparsity are all considered in our model for real MR images. The original complex problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved with an iterative scheme. Numerous experiments have been conducted and show that the proposed algorithm outperforms the state-of-the-art CS-MRI algorithms, and gain better reconstructions results on real MR images than general tree based solvers or algorithms.