Sparse Decomposition Signal Reconstruction

In this documentation, I will further elaborate on the operational principles of the sparse decomposition signal reconstruction program. This algorithm employs matching pursuit methodology to achieve signal reconstruction through iterative component matching. Specifically, the program first decomposes the input signal into a set of fundamental atom signals (typically represented as basis functions or dictionary elements). Through the matching pursuit approach, the algorithm systematically selects and combines these atoms to reconstruct the original signal. This methodology effectively reduces signal redundancy, enabling more accurate reconstruction results. The core implementation involves:

Algorithm workflow: The program iteratively identifies the atom that best matches the current signal residual, subtracts its contribution, and updates the residual until convergence criteria are met. Key functions include atom dictionary generation, correlation computation between residual and dictionary elements, and orthogonal projection operations.

Through this sparse decomposition reconstruction program, we obtain clearer and more precise signal reconstruction outcomes, thereby enhancing the quality and effectiveness of signal processing applications. The implementation typically involves optimization techniques for atom selection and weight calculation to maximize reconstruction accuracy while maintaining computational efficiency.