Signal Reconstruction Algorithms

In modern communication fields, signal reconstruction algorithms represent a critically important technology. Compressive sensing theory serves as the fundamental framework for these algorithms, enabling fast, efficient, and reliable signal reconstruction. Since the proposal of compressive sensing theory, numerous impactful research efforts have continuously emerged. Currently, various sparse signal reconstruction algorithms have been developed, primarily classified into three major categories: greedy algorithms, convex relaxation algorithms, and combinatorial algorithms. Among these, the Subspace Pursuit (SP) algorithm stands as a significant greedy approach. The SP algorithm reconstructs signals by iteratively selecting components with the largest projection coefficients through correlation calculations between the residual and measurement matrix columns. Its implementation typically involves maintaining a candidate support set, performing least-squares estimation for signal approximation, and updating residuals through orthogonal projections. The algorithm offers theoretical guarantees and strong practical advantages, including provable convergence under restricted isometry property conditions and computational efficiency through matrix operations. Consequently, in signal reconstruction research, the SP algorithm constitutes an indispensable component, particularly valuable for applications requiring balance between reconstruction accuracy and computational complexity.