Wavelet-Based Compressed Sensing Simulation Algorithm

The wavelet-based compressed sensing simulation algorithm is a signal processing method that integrates wavelet transform with compressed sensing theory, designed for efficient acquisition and reconstruction of sparse signals. This algorithm employs wavelet bases as sparse representation tools, utilizes random measurement matrices for dimension-reduced sampling during the signal acquisition phase, and applies the Orthogonal Matching Pursuit (OMP) algorithm for precise signal reconstruction during the recovery phase.

Core Concepts: Sparse Representation: Wavelet bases transform signals into sparse domains where most coefficients approach zero, leaving only a few significant components. This property makes signals suitable for compressed sensing processing under wavelet bases. Compressive Sampling: Sub-Nyquist sampling is achieved through random measurement matrices (e.g., Gaussian matrices), significantly reducing data acquisition volume. Orthogonal Matching Pursuit Recovery: The OMP algorithm iteratively selects the most relevant wavelet basis atoms, computes residuals, and updates the support set to achieve accurate signal reconstruction.

Advantages and Applications: Ideal for efficient compression and recovery of natural signals like images and audio. OMP algorithm demonstrates fast convergence and high reconstruction accuracy under wavelet bases. Maintains robust recovery performance even at low sampling rates, making it suitable for resource-constrained applications.

Potential extensions include exploring the impact of different wavelet bases (e.g., Haar, DB4) on reconstruction performance or combining with other optimization algorithms to further enhance recovery efficiency.