Compressive Sensing CS - Sparse Representation Using Wavelet Transform

In this article, we explore concepts related to Compressive Sensing (CS), implementing a framework that utilizes wavelet transform for sparse representation, employs Gaussian random matrices as measurement matrices, and applies the IRLS algorithm for signal reconstruction. Using the classic Lena image as our test case, we investigate reconstruction performance between the original image and IRLS algorithm outputs at varying sampling ratios (0.74, 0.5, 0.3). Each configuration undergoes 50 independent runs to statistically compare algorithm performance through PSNR metrics and computational time analysis. The implementation involves several key components: wavelet decomposition using functions like wavedec2() for 2D sparse representation, random matrix generation via randn() for measurements, and iterative reweighted least squares optimization for reconstruction. We provide detailed explanations of CS fundamentals and associated algorithm principles, including sparse signal representation theory, measurement matrix properties, and convex optimization approaches, to help readers better understand and apply these techniques in practical scenarios. The code structure typically follows: image preprocessing → wavelet sparse transformation → random projection sampling → IRLS reconstruction → quality assessment. Performance evaluation includes calculating PSNR using psnr() function and tracking execution time with tic/toc commands to ensure comprehensive algorithm analysis.