Publication

Abstract : pWavelet Galerkin method (WGM) is an efficient numerical method for solving boundary value problems. In this paper we propose WGM in image processing and formulated the algorithm as a numerical solution of the total variation (TV) denoising method. The properties of the wavelets such as, regularity, vanishing moments, smoothness and the properties of Galerkin method which uses an algebraic formulation are very attractive for image processing. The necessary changes for adapting the WGM algorithm as a solution of total variation problem are derived. The performance of the proposed method in enhancing the noisy images against noise additions is compared with1, non-convex tight regularization algorithm and finite element method (FEM). The effectiveness of the proposed method is confirmed by the improved structural similarity index (SSIM) and peak signal to noise ratio (PSNR) based image quality metrics. A GMM based image classification system is developed for determining the efficiency of the proposed method based on accuracy of the classification. The improved classification accuracy of proposed method confirmed its effectiveness. Image classification is performed as a quality metric for analyzing the performance of proposed algorithm. For sparse reconstruction, the proposed method gives performance comparable to most of the algorithms used for comparison and has much reduced run time. © 2018 The Authors. Published by Elsevier B.V./p