Solving L1-Norm Minimization Using Linear Programming for Compressed Sensing Applications

In this article, we demonstrate how to solve L1-norm minimization problems using linear programming algorithms to achieve compressed sensing functionality. Compressed sensing represents an emerging signal processing technique for recovering original signals from high-dimensional data. By representing signals as sparse vectors, compressed sensing technology can reduce sampling rates while maintaining high accuracy, thereby lowering costs and complexity. Our discussion covers the fundamental concepts of compressed sensing and provides practical techniques for implementing compressed sensing using linear programming algorithms. We include code-level explanations of key implementations such as formulating the L1-minimization problem as a linear program using objective functions like min ||x||_1 subject to measurement constraints Ax = b. Additionally, we explore how to leverage existing compressed sensing libraries to streamline algorithm implementation and examine the application prospects of compressed sensing in artificial intelligence, machine learning, and image processing domains.