Wavelet Transform-Based Image Compressive Sensing with Performance Analysis

This article explores wavelet transform-based image compressive sensing and conducts performance analysis using Orthogonal Matching Pursuit (OMP) reconstruction to evaluate how sampling rates affect compressive sensing efficiency. The wavelet transform serves as a powerful mathematical tool that decomposes images into distinct frequency subbands, enabling enhanced understanding of image structures and features through multi-resolution analysis. Compressive sensing represents an emerging signal processing technique that reconstructs complete signals from partial measurements, achieved via sparse signal representations and optimized sampling matrices. Our implementation combines these approaches by first applying discrete wavelet transforms (e.g., using Haar or Daubechies wavelets via MATLAB's wavedec2 function) to create sparse image representations, followed by random sampling using Gaussian or Bernoulli measurement matrices. The OMP algorithm (implemented with greedy iteration and residual updating) then reconstructs images by iteratively selecting the most correlated atoms from the sensing matrix. We analyze peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) metrics across varying sampling rates (e.g., 10%-50% of original data size), demonstrating trade-offs between compression efficiency and reconstruction quality. This comparative study provides insights into the method's advantages in storage reduction and computational efficiency, while addressing limitations such as reconstruction artifacts at low sampling rates and computational complexity in high-dimensional cases.