Improving Information Content in Compressed Sensing by Modifying the Random Re-Construction Matrices

Abstract

Background/Objectives: Compressed Sensing (CS) is an efficient sensing paradigm which guarantees reasonable reconstruction with less number of samples. We aim to increase the reconstruction quality of signals in CS. Methods/ Statistical Analysis: The behavior of random matrices is analyzed and an efficient method for improving the reconstruction quality is developed in CS based ECG reconstruction applications. The method is compared against Biorthogonal wavelet based approaches. Findings: Our analysis reveals that introduction of a modified column vector in the reconstruction matrix, which contains the sum of all columns of random matrix increases the reconstruction quality in CS applications. This idea was applied to different sparsifying domains and the results are very encouraging. We studied the effect of doing this on the singular values and both unitary matrices U and V. The first singular value (Σ) shot up making the condition number high, however there was not much change in the other singular values. The matrix U seems to remain random unitary matrix, where as matrix V has one value becoming unity in its rank space. Application/Improvements: Compared to wavelet based approaches the method shows reasonable improvement in Percentage Root Square Deviation (PRD).