MP-based Signal Sparse Decomposition Reference Implementation

This reference implementation demonstrates how to perform signal sparse decomposition using the Matching Pursuit (MP) algorithm. Sparse decomposition is a signal processing technique that represents signals as linear combinations of sparse coefficients. By expressing signals in sparse coefficient form, we can achieve signal compression, noise reduction, and various other signal processing applications. The core algorithm operates through iterative greedy selection: at each iteration, it identifies the dictionary atom that best matches the current signal residual, updates the coefficients, and subtracts the selected atom's contribution. Key implementation components include: - Dictionary initialization (typically using overcomplete basis sets) - Residual calculation and atom matching using correlation metrics - Coefficient update rules and stopping criteria (based on reconstruction error or sparsity constraints) This reference serves as an excellent starting point for learning sparse decomposition, providing clear insights into both algorithmic principles and practical implementation techniques. The code structure demonstrates proper handling of signal normalization, iterative optimization, and reconstruction validation.