A dictionary‐based graph‐cut algorithm for MRI reconstruction

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 L p (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L 1 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 nonconvex 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. K E Y W O R D S compressive sensing, graph cuts, parallel imaging, SENSE 1 | INTRODUCTION Undersampled MRI acquisitions can speed up MRI scan time, but also introduce aliasing artifacts due to sub-Nyquist sampling in k-space, if reconstructed using a simple inverse FFT of zero-filled k-space data. Aliasing is removed during reconstruction using advanced methods such as parallel imaging (PI), which uses the redundancy provided by multiple receiver coils, and by compressive sensing (CS), which exploits the noise-like aliasing artifacts resulting from random acquisition schemes. Traditional PI reconstruction algorithms include sensitivity encoding (SENSE), 1-3 simultaneous acquisition of spatial harmonics (SMASH), 4,5 and generalized auto-calibrating partially parallel acquisitions (GRAPPA). 6 Although these methods can be adapted for the case of arbitrary undersampling patterns, their usual implementation is for uniform Cartesian undersampling. Such undersampling results in structured aliasing artifacts called image folding, whereby many shifted copies of the true image are folded on top of each other. Uniform Cartesian PI methods can allow for acceleration of up to two-to fourfold, but further acceleration is limited