Adaptive structured low rank algorithm for MR image recovery

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.