Application of Compressed Sensing using a Reed Solomon (RS) code based Deterministic Measurement Matrix

Abstract

Compressed Sensing (CS) is an emerging technique in the field of acquiring and compressing signals as this technique allows for sampling a signal which is sparse in some domain with a rate well below the limit prescribed by the conventional Shannon-Nyquist sampling theorem. As a result, this new sensing paradigm is applicable to many fields like medical imaging, Data streaming, UWB-based communication systems, wireless sensor networks etc. A sensing matrix is one of the principal components in the architecture of compressed sensing. Traditionally, random sensing matrices have been used for CS but these matrices prove difficult for practical implementation and hence the development of deterministic sensing matrix have gathered recent momentum. In this paper, CS is applied to gray scale images using the deterministic sensing matrix based on Reed-Solomon (RS) code with asymptotically optimal coherence. The performance is compared with random measurement matrix for different reconstruction algorithms like Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP). The performance metrics considered for comparison of the original and reconstructed images are Structural Similarity Index (SSIM), PSNR, SNR and run time. Also, the role of the level of signal sparsity in CS is analyzed using simulation results.