Simulation of 256×256 8-bit Grayscale Lena Image with Compressive Sensing

In this experiment, we conduct a simulation on a 256×256 8-bit grayscale Lena image. We employ sparse matrix representation for the image, specifically selecting the Discrete Cosine Transform (DCT) matrix as our sparse basis due to its excellent energy compaction properties for natural images. For image sampling, we utilize a Gaussian random matrix as our measurement matrix, which satisfies the Restricted Isometry Property (RIP) required for successful compressive sensing. The reconstruction process implements the Orthogonal Matching Pursuit (OMP) algorithm, an iterative greedy approach that selects the most correlated dictionary atoms at each step and solves a least-squares problem to update the signal approximation. The algorithm iterates until either reaching a predetermined sparsity level or meeting a residual error threshold. Through this simulation, we explore how sparse representation and compressive sensing theory can be applied to image reconstruction, while demonstrating the practical implementation and performance of the OMP algorithm in image recovery applications. The implementation typically involves MATLAB functions like dctmtx() for DCT matrix generation, randn() for Gaussian random matrix creation, and custom OMP algorithm coding with matrix operations for correlation computation and least-squares solution.