Is it possible to recover an image from its noisy version using convolutional neural networks? This is an interesting problem as convolutional layers are generally used as feature detectors for tasks like classification, segmentation and object detection. We present a new CNN architecture for blind image denoising which synergically combines three architecture components, a multi-scale feature extraction layer which helps in reducing the effect of noise on feature maps, an l_p regularizer which helps in selecting only the appropriate feature maps for the task of reconstruction, and finally a three step training approach which leverages adversarial training to give the final performance boost to the model. The proposed model shows competitive denoising performance when compared to the state-of-the-art approaches.
Non-local means algorithm @cite_14 modifies the averaging step to be a weighted averaging, where the weights are given by the similarity measure. BM3D @cite_9 uses collaborative filtering of all the similar patches to achieve superior results. Weighted Nuclear Norm Minimization @cite_22 exploits the fact that set of similar patches would be of low rank if they were noise free. Simply solving for a set which gives a lower weighted nuclear norm removes the noise from the data.
@cite_9 @cite_14 @cite_22
2048695508 2747056667 1860736741 2511551071
As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality. The nonsmooth and nonconvex regularization has many applications in imaging science and machine learning research due to its excellent recovery performance. A proximal iteratively reweighted nuclear norm algorithm has been proposed for the nonsmooth and nonconvex matrix minimizations. In this paper, we aim to investigate the convergence of the algorithm. With the Kurdyka–Łojasiewicz property, we prove the algorithm globally converges to a critical point of the objective function. The numerical results presented in this paper coincide with our theoretical findings. The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm-based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to use a family of nonconvex surrogates of @math -norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then, we propose to solve the problem by an iteratively reweighted nuclear norm (IRNN) algorithm. IRNN iteratively solves a weighted singular value thresholding problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that the IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low rank matrix recovery compared with the state-of-the-art convex algorithms. Non-local means filtering (NLM), has garnered a large amount of interest in the image processing community due to its capability to exploit image patch self-similarity in order to effectively filter noisy images. However, the computational complexity of non-local means filtering is the product of three different factors; namely, O(NDK), where K is the number of filter kernel taps (e.g. search window size), D is the number of patch taps, and N is number of pixels. We propose a fast approximation of non-local means filtering using the multiscale methodology of the pull-push scattered data interpolation method. By using NLM with a small filter kernel to selectively propagate filtering results and noise variance estimates from fine to coarse scales and back, the process can be used to provide comparable filtering capability to brute force NLM but with algorithmic complexity that is linear in the number of image pixels and the patch comparison taps, O(ND). In practical application, we demonstrate its denoising capability is comparable to NLM with much larger filter kernels, but at a fraction of the computational cost.