title: The benefit of tree sparsity in accelerated MRI.
abstract: The wavelet coefficients of a 2D natural image are not only approximately sparse with a large number of coefficients tend to be zeros, but also yield a quadtree structure. According to structured sparsity theory, the required measurement bounds for compressive sensing reconstruction can be reduced to O(K+log(N/K)) by exploiting the tree structure rather than O(K+Klog(N/K)) for standard K-sparse data. In this paper, we proposed two algorithms with convex relaxation to solve the tree-based MRI problem. They are based on FISTA and NESTA frameworks respectively to validate the benefit of tree sparsity in accelerated MRI, both of which have very fast convergence rate and low computational cost. These properties make them be comparable with the fastest algorithms with standard sparsity. Extensive experiments are conducted to validate how much benefit it can bring by tree sparsity. Experimental results show that the proposed methods can definitely improve existing MRI algorithms, although with gaps to the theory.
authors.affiliation: Department of Computer Science and Engineering, University of Texas at Arlington, 500 UTA Boulevard, Arlington, TX 76019, United States.
authors.forename: Chen
authors.initials: C
authors.lastname: Chen
authors.affiliation: Department of Computer Science and Engineering, University of Texas at Arlington, 500 UTA Boulevard, Arlington, TX 76019, United States. Electronic address: jzhuang@uta.edu.
authors.forename: Junzhou
authors.initials: J
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: Compressive sensing MRI; SparseMRI; Structured sparsity; Tree sparsity