Complementary Data Regularization for Nonlinear Matrix-Valued Image Denoising
Abstract
In this study, we present some findings from applying a complementary data regularization approach to a nonlinear image denoising model. The proposed method uses optimizing non-quadratic energy functionals with normalized data terms. This study aims to develop an image denoising technique that combines well-known robust diffusivity coefficients such as total variation regularization with normalized data term known as complementary data regularization. We apply our modified mathematical approach to the matrix-valued images, a challenging computational task. The primary purpose of the complementary regularization idea of data terms is to create a compatible connection and a reliable balance between diffusion and data terms. The standard finite difference scheme has been considered as a discretization method for the numerical solution of the partial differential equation obtained from the variational optimization of the modified energy function. The performance of the proposed model is demonstrated through numerous numerical experiments in terms of image quality analysis and computational time. Comparison of the results with some well-known classical methods such as Perona–Malik, total variation, and non-local mean methods in the literature is the heart of this work.
Keywords: image denoising, isotropic diffusion, complementary regularization, variational optimization.
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