Sparse Decomposition and Precise Reconstruction of Images using Matching Pursuit

The paper describes how we can employ the Matching Pursuit (MP) algorithm to perform sparse decomposition of images and achieve precise reconstruction using 2D Gabor (GA) atoms. Sparse decomposition is a methodology that represents images as sparse coefficients combined with atoms, where these atoms can locally represent different features within the image. Through the MP algorithm implementation, which iteratively selects the best matching atoms from a dictionary to approximate the signal, we can decompose an image into a set of sparse coefficients. These coefficients quantify the presence and intensity of different features in the image. The reconstruction process then utilizes 2D Gabor atoms, which are particularly effective for capturing texture and edge information due to their optimal joint resolution in both spatial and frequency domains. By combining these coefficients with the corresponding atoms through linear combination, we can reconstruct the image with high precision. The key implementation aspects include designing an appropriate dictionary of 2D Gabor atoms with varying scales, orientations, and frequencies, and implementing the greedy MP iteration that maximizes the inner product between the residual and dictionary atoms at each step. This approach of using MP algorithm with 2D GA atoms enables effective sparse decomposition and accurate reconstruction of images, thereby preserving and enhancing informational content and fine details.