Tensor Low Rank Column-Wise Compressive Sensing for Dynamic Imaging

Abstract

In recent work , we developed a fast, memory-efficient, and sample-efficient solution to the Low Rank column-wise Compressive Sensing (LRcCS) problem: recover an n × q LR matrix from m under-sampled linear projections of each of its columns. Here, undersampled means m ≪ n,q . The matrix LR model and the corresponding algorithms have two important limitations. First, for real image sequences, the required memory complexity is prohibitive. Secondly, for image or volume image sequences, it requires vectorizing the image or volume as one column of a matrix and this ignores the inherent 2D or 3D structure of the images or volumes. To address these limitations, in this work, we explore the use of a tensor LR model on the image sequence along with developing a fast and memory-efficient gradient descent (GD) based recovery algorithm and evaluating it experimentally.