A dictionary-based graph-cut algorithm for MRI reconstruction.

Overview

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 L_p (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 L_p -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.