  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.
