Compressed Sensing for Noisy Signals

Compressed Sensing (CS) has revolutionized the field of signal processing by enabling the acquisition and reconstruction of sparse signals from a remarkably small number of measurements, far below the traditional Nyquist sampling limit. This paper presents a comprehensive MATLAB based study on robust compressed sensing for noisy signals. We focus on two widely used reconstruction algorithms: Orthogonal Matching Pursuit (OMP) and Least Absolute Shrinkage and Selection Operator (LASSO). By systematically varying Signal-to-Noise Ratios (SNR = 30 dB, 20 dB, 10 dB) and measurement-to-signal-length ratios (M/N), we perform extensive simulations to benchmark their performance. Our results reveal critical insights into the trade-offs between sparsity, noise resilience, and computational efficiency. OMP demonstrates rapid and accurate reconstruction for high sparsity signals under moderate noise, whereas LASSO exhibits superior robustness in highly noisy scenarios. The findings have broad implications for practical applications, including wireless communications, biomedical imaging, and real-time sensor networks. This study also provides a versatile MATLAB framework that can be adapted for a wide range of CS experiments, enabling reproducible and scalable research.