Improvement of Recovery in Segmentation-Based Parallel Compressive Sensing

This paper extends the recently introduced 1-D Kronecker-based Compressive Sensing (CS) recovery technique to 2-D signals and images. Traditionally large sensing matrices are used while compressing images using CS. CS when applied to individual columns of the image instead of the entire image during the sensing phase, leads to smaller sensing matrices and reduction in computational complexity. For achieving further reduction in computational complexity, the column vectors are further segmented into smaller length segments and CS is applied to each of the smaller length segments. This segmentation process reduces quality of the recovered signal. To enhance the quality of the recovered signal, the entire column vector is recovered using the Kronecker-based CS recovery technique. Magnetic Resonance (MR) images from NCIGT database were used to demonstrate the superiority of the Kronecker-based recovery for 2-D images. Structural similarity and reconstruction error were used to compare the results obtained from Kronecker-based recovery technique with non-Kronecker-based repeated recovery applied to each segments individually. Kronecker-based recovery showed improvement over non-Kronecker-based individual recovery even at higher CR.