MATLAB Code Implementation for Compressed Sensing

This text discusses the fundamental concepts of compressed sensing and sparse representation in signal processing. Sparse representation utilizes wavelet basis functions to express signals as linear combinations of a small number of non-zero coefficients, enabling efficient signal compression. In compressed sensing implementation, random Gaussian matrices serve as the foundation for compression measurements, allowing signals to be reduced to smaller dimensions while preserving essential information. The reconstruction process employs the Orthogonal Matching Pursuit (OMP) algorithm to recover the original signal from compressed measurements. The OMP algorithm iteratively selects the most correlated atoms from the measurement matrix and solves a least-squares problem to approximate the sparse coefficients. Key implementation considerations include proper parameter selection for wavelet decomposition levels, Gaussian matrix dimensions matching the desired compression ratio, and OMP iteration thresholds to balance reconstruction accuracy and computational efficiency. MATLAB implementation typically involves functions like wavedec for wavelet decomposition, randn for generating Gaussian measurement matrices, and custom OMP algorithms that leverage matrix operations for efficient sparse recovery. Successful implementation requires careful tuning of sparsity constraints and stopping criteria to ensure accurate signal reconstruction while maintaining computational feasibility.