Compressive Sensing Simulation Algorithms in Wavelet Basis

In compressive sensing simulation algorithms using wavelet basis, the reconstruction algorithm employs orthogonal matching pursuit (OMP). This algorithm can accurately recover signals through a small number of linear measurements of the signal. Essentially, it enables signal reconstruction with minimal measurements, thereby reducing transmission and storage costs. The implementation typically involves iterative selection of the most correlated wavelet basis functions and solving least squares problems to approximate the sparse coefficients. In practical applications, this algorithm has been widely used in image and video compression, as well as speech and audio signal processing. The wavelet transform provides sparse representations for many natural signals, while OMP efficiently identifies the significant coefficients through greedy iteration. Key implementation aspects include designing measurement matrices, computing wavelet transforms, and optimizing the stopping criteria for the OMP iterations. Therefore, this approach holds broad application prospects in the field of signal processing, particularly for systems requiring efficient data acquisition and compression.