Exploiting sparsity and rank-deficiency in dynamic MRI reconstruction

Abstract

This work addresses the problem of dynamic MRI reconstruction from partially sampled K-space. When the frames of the dynamic MRI sequences are stacked as columns of a matrix, the resultant matrix is both sparse (in a transform domain) and rank-deficient. The dynamic MRI sequence is reconstructed by solving an optimization problem that minimizes a sum of sparsity and rank-deficiency penalties subject to data constraints (K-space data acquisition model). In this work, we propose a non-convex optimization problem for dynamic MRI reconstruction where the sparsity penalty is an l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm and the rank-deficiency penalty is the Schatten-q norm (0<;p,q≤1). There is no algorithm to solve this combined l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm and Schatten-q norm minimization problem; hence we derive a new algorithm based on the Majorization Minimization method. Our proposed method shows considerable improvement in reconstruction results over state-of-the-art techniques in dynamic MRI reconstruction.