Cauchy noise, as a typical non-Gaussian noise, appears frequently in many important fields, such as radar, medical, and biomedical imaging. In this letter, we focus on image recovery under Cauchy noise. Instead of the celebrated total variation or low-rank prior, we adopt a novel deep-learning-based image denoiser prior to effectively remove Cauchy noise with blur. To preserve more detailed texture and better balance between the receptive field size and the computational cost, we apply the multi-level wavelet convolutional neural network (MWCNN) to train this denoiser. We use the forward-backward splitting (FBS) method to handle the proposed model, which can be implemented efficiently without introducing auxiliary variables. Moreover, the multi-noise-levels strategy is employed to train a series of denoisers to restore the image corrupted by Cauchy noise and blur. Numerical experiments demonstrate clearly that our method has better performance than the existing image restoration methods for removing Cauchy noise in terms of the quantitative index and visual quality.

The restoration of images degraded by blurring and noise is one of the most important tasks in image processing. In this paper, based on the total variation (TV) we propose a new variational method for recovering images degraded by Cauchy noise and blurring. In order to obtain a strictly convex model, we add a quadratic penalty term, which guarantees the uniqueness of the solution. Due to the convexity of our model, the primal dual algorithm is employed to solve the minimization problem. Experimental results show the effectiveness of the proposed method for simultaneously deblurring and denoising images corrupted by Cauchy noise. Comparison with other existing and well-known methods is provided as well.

In this paper, a new variational model for restoring blurred images with multiplicative noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized in order to obtain a strictly convex model under a mild condition, which guarantees the uniqueness of the solution and the stabilization of the algorithm. For solving the new convex variational model, a primal-dual algorithm is proposed, and its convergence is studied. The paper ends with a report on numerical tests for the simultaneous deblurring and denoising of images subject to multiplicative noise. A comparison with other methods is provided as well.

A two-phase image restoration method based upon total variation regularization combined with an L(1)-data-fitting term for impulse noise removal and deblurring is proposed. In the first phase, suitable noise detectors are used for identifying image pixels contaminated by noise. Then, in the second phase, based upon the information on the location of noise-free pixels, images are deblurred and denoised simultaneously. For efficiency reasons, in the second phase a superlinearly convergent algorithm based upon Fenchel-duality and inexact semismooth Newton techniques is utilized for solving the associated variational problem. Numerical results prove the new method to be a significantly advance over several state-of-the-art techniques with respect to restoration capability and computational efficiency.

Image restoration based on an $\ell^1$-data-fitting term and edge preserving total variation regularization is considered. The associated nonsmooth energy minimization problem is handled by utilizing Fenchel duality and dual regularization techniques. The latter guarantee uniqueness of the dual solution and an efficient way for reconstructing a primal solution, i.e., the restored image, from a dual solution. For solving the resulting primal-dual system, a semismooth Newton solver is proposed and its convergence is studied. The paper ends with a report on restoration results obtained by the new algorithm for salt-and-pepper or random-valued impulse noise including blurring. A comparison with other methods is provided as well.

The known median-based denoising methods tend to work well for restoring the images corrupted by random-valued impulse noise with low noise level but poorly for highly corrupted images. This letter proposes a new impulse detector, which is based on the differences between the current pixel and its neighbors aligned with four main directions. Then, we combine it with the weighted median filter to get a new directional weighted median (DWM) filter. Extensive simulations show that the proposed filter not only can provide better performance of suppressing impulse with high noise level but can preserve more detail features, even thin lines. As extended to restoring corrupted color images, this filter also performs very well

This paper proposes an image statistic for detecting random-valued impulse noise. By this statistic, we can identify most of the noisy pixels in the corrupted images. Combining it with an edge-preserving regularization, we obtain a powerful two-stage method for denoising random-valued impulse noise, even for noise levels as high as 60%. Simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection.