Jiexun Xu1, Nicolas Pannetier2, Ashish Raj2. 1. Department of Computer Science, Cornell University, Ithaca, New York. 2. Department of Radiology, University of California, San Francisco, California.
Abstract
PURPOSE: Compressive sensing (CS)-based image reconstruction methods have proposed random undersampling schemes that produce incoherent, noise-like aliasing artifacts, which are easier to remove. The denoising process is critically assisted by imposing sparsity-enforcing priors. Sparsity is known to be induced if the prior is in the form of the Lp (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L1 norm, which may not exploit the full power of CS. An efficient, discrete optimization formulation is proposed, which works not only on arbitrary Lp -norm priors as some non-convex CS methods do, but also on highly non-convex truncated penalty functions, resulting in a specific type of edge-preserving prior. These advanced features make the minimization problem highly non-convex, and thus call for more sophisticated minimization routines. THEORY AND METHODS: The work combines edge-preserving priors with random undersampling, and solves the resulting optimization using a set of discrete optimization methods called graph cuts. The resulting optimization problem is solved by applying graph cuts iteratively within a dictionary, defined here as an appropriately constructed set of vectors relevant to brain MRI data used here. RESULTS: Experimental results with in vivo data are presented. CONCLUSION: The proposed algorithm produces better results than regularized SENSE or standard CS for reconstruction of in vivo data.
PURPOSE: Compressive sensing (CS)-based image reconstruction methods have proposed random undersampling schemes that produce incoherent, noise-like aliasing artifacts, which are easier to remove. The denoising process is critically assisted by imposing sparsity-enforcing priors. Sparsity is known to be induced if the prior is in the form of the Lp (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L1 norm, which may not exploit the full power of CS. An efficient, discrete optimization formulation is proposed, which works not only on arbitrary Lp -norm priors as some non-convex CS methods do, but also on highly non-convex truncated penalty functions, resulting in a specific type of edge-preserving prior. These advanced features make the minimization problem highly non-convex, and thus call for more sophisticated minimization routines. THEORY AND METHODS: The work combines edge-preserving priors with random undersampling, and solves the resulting optimization using a set of discrete optimization methods called graph cuts. The resulting optimization problem is solved by applying graph cuts iteratively within a dictionary, defined here as an appropriately constructed set of vectors relevant to brain MRI data used here. RESULTS: Experimental results with in vivo data are presented. CONCLUSION: The proposed algorithm produces better results than regularized SENSE or standard CS for reconstruction of in vivo data.
Authors: Mark A Griswold; Peter M Jakob; Robin M Heidemann; Mathias Nittka; Vladimir Jellus; Jianmin Wang; Berthold Kiefer; Axel Haase Journal: Magn Reson Med Date: 2002-06 Impact factor: 4.668