Lipschitz energy functional for anisotropic diffusion applications

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Image denoising remains a key research problem because of its potential role as a pre-processing component in image processing, computer vision, and machine learning tasks. Of the available approaches for image denoising, those inspired by anisotropic diffusion processes have been a center of discussion for decades. Despite the efforts and promising results achieved by diffusion-inspired denoising methods, we noted insufficient attention on the design of energy functionals for anisotropic diffusion equations. Most researchers consider heuristic approaches to design diffusivity functionals, a practice that cannot provide mathematical explanations on why their approaches work. The current research presents a strictly convex and Lipschitz energy functional that guarantees a unique solution for an evolutionary process. Based on this functional, we derive an anisotropic diffusion equation for image denoising applications. Experimental results show that an algorithm corresponding to the proposed equation is computationally efficient, and generates informative and visually appealing images with competitive values of peak signal-to-noise ratio and structural similarity. Guided by the compelling properties of our energy functional, we provide an additional insight to describe quality of the results. Implementation codes and test datasets of the proposed approach are publicly accessible at the MATLAB File Exchange (https://www.mathworks.com/matlabcentral/fileexchange/160108-lipschitz-diffusion-inspired-energy-functional).