Sampling and recovery of MRI data using low rank tensor models

In this paper we investigate the utility of several low-rank models for recovery of Magnetic Resonance Imaging (MRI) data from limited sampling in the k - t space for dynamic imaging. In particular, for 3D temporal (2D space + time) MRI data we employ several tensor factorization techniques and assess the degree of dimensionality reduction, or compressibility, that can be obtained. This algebraic approach is more data adaptive, in contrast to existing compressed sensing (CS) based methods that exploit sparsity in a transform domain, such as wavelets or total variation. Further, we compare these tensor factorization approaches in recovering temporal MRI data under limited sampling. Respecting traditional MRI data acquisition methods, the sampling process is restricted to be uniformly random along only one k space direction. Experimental results on synthetically sub-sampled MRI data show promise in using tensor factorization for sampling and recovery of MRI data.