MATLAB Implementation of Matching Pursuit (MP) Algorithm for Signal Sparse Decomposition

The Matching Pursuit (MP) algorithm implements signal sparse decomposition by employing a projection-based approach. This algorithm serves as a fundamental method for signal processing that achieves sparse signal representation through iterative matching pursuit. The core mechanism utilizes mathematical projection concepts where vectors are projected onto dictionary atoms to obtain residual approximations. In MATLAB implementation, the algorithm typically involves: - Initializing residual as the original signal - Iteratively selecting the dictionary atom with maximum inner product with current residual - Calculating projection coefficients through orthogonal projection operations - Updating residuals by subtracting projected components - Repeating until meeting sparsity criteria or error thresholds Key implementation aspects include: - Dictionary generation (often using Fourier/DCT bases or custom waveforms) - Inner product computation for atom selection (using dot product operations) - Residual update via vector subtraction operations - Stopping conditions based on iteration count or residual energy thresholds The projection methodology enables precise analysis of signal characteristics and structural decomposition, making it particularly valuable for sparse representation applications in signal compression and feature extraction.