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We propose a novel deformation corrected compressed sensing (DC-CS) frameworkto recover dynamic magnetic resonance images from undersampled measurements. Weintroduce a generalized formulation that is capable of handling a wide class ofsparsity/compactness priors on the deformation corrected dynamic signal. Inthis work, we consider example compactness priors such as sparsity in temporalFourier domain, sparsity in temporal finite difference domain, and nuclear normpenalty to exploit low rank structure. Using variable splitting, we decouplethe complex optimization problem to simpler and well understood sub problems;the resulting algorithm alternates between simple steps of shrinkage baseddenoising, deformable registration, and a quadratic optimization step.Additionally, we employ efficient continuation strategies to minimize the riskof convergence to local minima. The proposed formulation contrasts withexisting DC-CS schemes that are customized for free breathing cardiac cineapplications, and other schemes that rely on fully sampled reference frames ornavigator signals to estimate the deformation parameters. The efficientdecoupling enabled by the proposed scheme allows its application to a widerange of applications including contrast enhanced dynamic MRI. Throughexperiments on numerical phantom and in vivo myocardial perfusion MRI datasets,we demonstrate the utility of the proposed DC-CS scheme in providing robustreconstructions with reduced motion artifacts over classical compressed sensingschemes that utilize the compact priors on the original deformationun-corrected signal.

Deformation corrected compressed sensing (DC-CS): a novel framework for accelerated dynamic MRI