Patent ID: 7864999

Claim:
A method comprising: receiving a first set of data from a magnetic resonance image device; automatically applying a minimization algorithm to a pre-formulated functional that comprises a norm of a sparse representation of a trial image derived from said first set of data and a data fidelity term, said minimization algorithm comprising a conjugate gradient sub-algorithm and a Bregman iteration; at each iteration of a plurality of iterations of said Bregman iteration: updating said data fidelity term; and repeating said conjugate gradient sub-algorithm to iteratively update said trial image, said conjugate gradient sub-algorithm comprising: at each iteration of a plurality of iterations, finding an update direction of said trial image via: computing a sub-gradient of said norm of said sparse image representation and a gradient of said data fidelity term; applying a nonuniform Fourier transform of said trial image; subtracting said first set of data from said nonuniform Fourier transform; using an adjoint of said nonuniform Fourier transform to obtain said gradient of said data fidelity term; finding a step size in said update direction using a backtracking line search algorithm; updating said trial image based upon said update direction and said step size; and rendering a final image when said Bregman iteration is finished.