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We introduce an adaptive structured low rank algorithm to recover MR imagesfrom their undersampled Fourier coefficients. The image is modeled as acombination 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 propertyof the matrices to formulate a combined regularized optimization problem, whichcan be solved efficiently. Numerical experiments indicate that the proposedalgorithm provides improved recovery performance over the previously proposedalgorithms.

Adaptive structured low rank algorithm for MR image recovery