Compressed Sensing Reconstruction Algorithms

In this article, we will explore Compressed Sensing Reconstruction Algorithms in detail. Compressed Sensing (CS) is an emerging interdisciplinary field between mathematics and information science that has gained significant attention in recent years. CS challenges traditional sampling and encoding techniques based on the Nyquist-Shannon sampling theorem. The fundamental principle involves reconstructing signals from fewer random measurements than traditionally required, thereby reducing sampling rates. Key algorithmic implementations typically involve solving underdetermined linear systems through L1-norm minimization techniques using optimization solvers like basis pursuit or greedy algorithms such as Orthogonal Matching Pursuit (OMP). This technology has found widespread applications in image processing, signal processing, communications, and continues to evolve with ongoing improvements. Therefore, deeper understanding of its principles and implementations is essential for effectively leveraging its advantages in practical applications.