arXiv subjects

Mathews Jacob

Publications and source records attributed to Mathews Jacob.

75 records · Page 5Linked to original sources

arXiv2015

Recovery of Piecewise Smooth Images from Few Fourier Samples

We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we show the Fourier transform coefficients of partial derivatives of the signal satisfy an annihilation relation. We present necessary and sufficient conditions for unique recovery of piecewise constant images using the above annihilation relation. We pose the recovery of the Fourier coefficients of the signal from the measurements as a convex matrix completion algorithm, which relies on the lifting of the Fourier data to a structured low-rank matrix; this approach jointly estimates the signal and the annihilating filter. Finally, we demonstrate our algorithm on the recovery of MRI phantoms from few low-resolution Fourier samples.

cs.CV↗

arXiv2014

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

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover dynamic magnetic resonance images from undersampled measurements. We introduce a generalized formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to minimize the risk of convergence to local minima. The proposed formulation contrasts with existing DC-CS schemes that are customized for free breathing cardiac cine applications, and other schemes that rely on fully sampled reference frames or navigator signals to estimate the deformation parameters. The efficient decoupling enabled by the proposed scheme allows its application to a wide range of applications including contrast enhanced dynamic MRI. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we demonstrate the utility of the proposed DC-CS scheme in providing robust reconstructions with reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation un-corrected signal.

cs.CV↗

arXiv2014

Iterative Non-Local Shrinkage Algorithm for MR Image Reconstruction

We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a global criterion. The proposed algorithm alternates between a non-local shrinkage step and a quadratic subproblem. We derive analytical shrinkage rules for several penalties that are relevant in non-local regularization. The redundancy in the searches used to evaluate the shrinkage steps are exploited using filtering operations. The resulting algorithm is observed to be considerably faster than current alternating non-local algorithms. The comparisons of the proposed scheme with state-of-the-art regularization schemes show a considerable reduction in alias artifacts and preservation of edges.

cs.CV↗