Dictionary Properties for Sparse Representation: Implementation and Analysis

Background and Objective: Linear inverse problems emerge throughout the engineering and the mathematical sciences. Over the last two decades, sparsity constraints have emerged as a fundamental type of regularizer. This paper implements and assesses the role of dictionary miscellany in sparse representation for image processing prospective. Materials and Methods: A dictionary is formed by a linear basis using a mathematical model from the set of images referred as analytic dictionary or using a set of realizations of the images referred as trained dictionary. This study considers the problem of true sparsity formation and analyzes the two most commonly used algorithms-the Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) using analytical dictionaries. These methods were compared using diverse dictionaries formation for image restoration applications. Results: The results were validated using peak signal to noise ratio and mean square error of the sparse approximation for the images. The different dictionaries like-discrete wavelet dictionary, Discrete Cosine Transform and Kronecker Delta dictionary and Haar Wavelet Packets and DCT dictionary had been used for implementation of these two algorithms. Conclusion: This experiment showed that the discrete wavelet based dictionary performs best with orthogonal matching pursuit algorithm in terms of MSE and PSNR performances. The result also shows the out performance of OMP in comparison with MP. From the experiments, it has been observed that high number of iterations and small patch size proves to be advantageous.