An Adaptive Method for Recovering Image from Mixed Noisy Data

Abstract

In this paper, we present a new version of the famous Rudin-Osher-Fatemi (ROF) model to restore image.The key point of the model is that it could reconstruct images with blur and non-uniformly distributed noise. We develop this approach by adding several statistical control parameters to the cost functional, and these parameters could be adaptively determined by the given observed image. In this way, we could adaptively balance the performance of the fit-to-data term and the regularization term. The Numerical experiments have demonstrated the significant effectiveness and robustness of our model in restoring blurred images with mixed Gaussian noise or salt-and-pepper noise.

A well-balanced and adaptive variational model for the removal of mixed noise

“…The key point here is for each point x, the denoising occurs according to the estimated noise and the position of the point related to edges. The denoising will be stronger at point x further away from the edges, which means that the velocity of the denoising depends on the position of the point x in relation to the edges of the image, contrary to the method given in [20] where the smoothing process is the same for all points of the image regardless of their position with respect to the edges. Their approach can lead to loss of information at the edges.…”

“…In [16] the authors proposed a nonconvex model based on Bayes rule and Gama distribution to remove multiplicative noise. In [20], the authors use the statistical information of the noise to set the parameters of the models. Also in [20] two models were proposed: a Gauss-Total Variation model and a Gaussian Mixture-Total Variation model (GM-TV) based on statistical approaches.…”

“…In [20], the authors use the statistical information of the noise to set the parameters of the models. Also in [20] two models were proposed: a Gauss-Total Variation model and a Gaussian Mixture-Total Variation model (GM-TV) based on statistical approaches. In [21] the authors went on to use generalizations of these models to color images, and in [6,22], the split Bregman method is used to denoising and deblurring noisy images.…”

“…In [21] the authors went on to use generalizations of these models to color images, and in [6,22], the split Bregman method is used to denoising and deblurring noisy images. Inspired on [11,20], this paper goes on to propose a new approach which includes some statistical information of the noise as in [20] incorporating a well defined balance between the diffusion term, or regularized term, and the fitting term. This approach is based on two facts, first, the probability density function of the impulsive and/or mixed noise can be approximated as an additive noise with mixed Gaussian noise and, second, the balance between the fidelity term and the smooth term is adaptive and varies depending on the level of noise as well as, depending on the position of the noisy point x related to the edge points of the image.…”

Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise

“…Of course, the two-phase method cannot well handle mixed noise such as Gaussian mixture. In Liu et al (2009), a statistical method is employed to recover blurred grey scale images from mixed noisy data. Essentially, we include a L 2 -based weighting fidelity term in the cost functional, which has a superior performance in removing mixed noise, especially when the level of noise is high.…”