We propose an alternative framework for total variation based image denoising models. The model is based on the minimization of the total variation with a functional coefficient, where, in this case, the functional coefficient is a function of the magnitude of image gradient. We determine the considerations to bear on the choice of the functional coefficient. With the use of an example functional, we demonstrate the effectiveness of a model chosen based on the proposed consideration. In addition, for the illustrative model, we prove the existence and uniqueness of the minimizer of the variational problem. The existence and uniqueness of the solution associated evolution equation are also established. Experimental results are included to demonstrate the effectiveness of the selected model in image restoration over the traditional methods of Perona-Malik (PM), total variation (TV), and the D-α-PM method.
In this work, the authors have proposed a multi-frame super-resolution method that is based on the diffusion-driven regularization functional. The new regularizer contains a variable exponent that adaptively regulates its diffusion mechanism depending upon the local image features. In smooth regions, the method favors linear isotropic diffusion, which removes noise more effectively and avoids unwanted artifacts (blocking and staircasing). Near edges and contours, diffusion adaptively and significantly diminishes, and since noise is hardly visible in these regions, an image becomes sharper and resolute-with noise being largely reduced in flat regions. Empirical results from both simulated and real experiments demonstrate that our method outperforms some of the state-of-the-art classical methods based on the total variation framework.
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