MATLAB Implementation of Sparse Methods Based on Gradient Projection Reconstruction

This program illustrates how to implement sparse reconstruction methods based on gradient projection using MATLAB. The approach utilizes gradient projection techniques that decompose images into frequency components and represent them as low-dimensional linear combinations to achieve image reconstruction. The key advantage of this method lies in its ability to reconstruct high-quality images using limited data while effectively reducing noise impact. The implementation involves optimization algorithms where gradient directions are projected onto constraint sets to enforce sparsity constraints. We provide detailed explanations with practical code examples, including demonstrations of key MATLAB functions such as gradient descent optimization, projection operators, and sparse representation techniques. These examples help users understand the underlying working principles, including how the algorithm handles frequency domain transformations and implements regularization for noise reduction.