Compressive Sampling Matching Pursuit Algorithm in Compressed Sensing

In this document, we explore a highly valuable algorithm called Compressive Sampling Matching Pursuit (CoSaMP), which is designed for reconstructing sparse signals within compressed sensing frameworks. This algorithm achieves high-quality signal reconstruction while significantly reducing sampling rates, thereby conserving storage space and transmission bandwidth. The CoSaMP algorithm finds applications across signal processing, image processing, and communication systems, providing robust support for various technological implementations.

Specifically, the algorithm employs compressive sampling techniques to minimize the required sampling rate, then utilizes a matching pursuit mechanism to recover the original signal. The implementation leverages sparsity assumptions through iterative processes that identify the most significant signal components. Key algorithmic steps include: atom selection based on correlation metrics, support set expansion, signal estimation via least-squares approximation, and pruning of weak components. This approach ensures computational efficiency while maintaining reconstruction accuracy. Overall, CoSaMP demonstrates exceptional performance for sparse signal processing, substantially enhancing both processing efficiency and reconstruction fidelity in practical applications.