Signal Reconstruction Using L1-Norm Minimization and Orthogonal Matching Pursuit in Compressed Sensing

This article explores a critical application of compressed sensing technology: signal reconstruction. Compressed sensing is a methodology for acquiring signals through sparse sampling, widely applicable in domains such as image processing and signal analysis. Two prominent compressed sensing algorithms—L1-norm minimization and Orthogonal Matching Pursuit (OMP)—are examined for their capability to reconstruct original signals from compressed measurements. The L1-norm minimization approach reformulates signal recovery as a convex optimization problem, typically implemented using linear programming techniques or iterative thresholding algorithms. Orthogonal Matching Pursuit operates as a greedy iterative algorithm that selects the most correlated dictionary atoms in each iteration and orthogonalizes residuals through least-squares solutions. These algorithms can be implemented using optimization packages like CVX in MATLAB or custom Python implementations with NumPy/SciPy libraries. By employing these methods, high-quality signal reconstruction results can be achieved, making them instrumental across various practical applications including medical imaging and wireless communications.