An edge enhancement filter is proposed for denoising and enhancing images corrupted with data-dependent noise which is observed to follow a Gamma distribution. The filter is equipped with three terms designed to perform three different tasks. The first term is an anisotropic diffusion term which is derived from a locally adaptive p-laplacian functional. The second term is an enhancement term or a shock term which imparts a shock effect at the edge points making them sharp. The third term is a reactive term which is derived based on the maximum a posteriori (MAP) estimator and this term helps the diffusive term to perform a Gamma distributive data-dependent multiplicative noise removal from images. And moreover, this reactive term ensures that deviation of the restored image from the original one is minimum. This proposed filter is compared with the state-of-the-art restoration models proposed for data-dependent multiplicative noise. 1. Introduction Image restoration is an important activity in image processing. Many different kinds of degradation models have been discussed in the recent literature. The degradation due to an additive data independent noise was explored extensively in the image denoising literature; see [1–3] for details. Further the degradations due to the combined effect of random noise and linear shift invariant blur are also studied elaborately; see [4–7] for further details. Another category of degradation that is discussed in the recent literatures is the model with multiplicative data-dependent noise with linear shift-invariant blur. Nevertheless, a solution to data-dependent noise model should practically consider the noise distribution as well [8]. Different noise distributions considered under a multiplicative data-dependent noise set-up include Gamma, Poisson, and Gaussian distributions; refer to [8–10] for further details. 2. PDE Models for Multiplicative Noise A common representation for a multiplicative denoising model, found in the image processing literature (assuming a shift-invariant nature of the linear blurring operator), is where is a linear shift invariant blurring kernel, “ ” denotes a linear convolution operator, and is a multiplicative data-dependent noise. The distribution of the noise intensity varies with reference to the application under consideration. The first kind of model that was proposed for image restoration assuming a Gaussian multiplicative noise was RLO model by Lions et al. in [10]. The diffusion equation for the model is where and are the parameters which control the regularization and the data
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