Adaptive structured low rank algorithm for MR image recovery

Abstract: We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low rank property of the matrices to formulate a combined regularized optimization problem, which can be solved efficiently. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the previously proposed algorithms.