NERNet: Noise estimation and removal network for image denoising

A “Nonconvex+Nonconvex” approach for image restoration with impulse noise removal

This paper proposes multiscale structure-tensor total variation (MSTV) for image recovery. Gradient vectors in local patches usually have similar directions, and thus each local gradient matrix (the set of gradient vectors) tends to be low rank. STV introduces this property by calculating the sum of nuclear norms from all the 10-cal gradient matrices over the input image. By STV regularization, fine textures are recovered efficiently. However, since STV only considers differences of vertically and horizontally adjacent pixels, if neighboring samples are not reliable due to severe degradation, a latent image cannot be recovered efficiently. In this work, we assume that, for any two target pixels in a local patch, two vectors consisting of multiple differences not only between each target and adjacent pixels but also each target and further distant pixels exhibit a similar direction. According to this assumption, our MSTV firstly applies wavelet-based multiscale decomposition to vertical/horizontal gradient vectors and then evaluates the sum of nuclear norms of all the local wavelet coefficients. Experimental results show that the MSTV improves both numerical reconstruction error and subjective visual quality, compared with the conventional STV.

Multiscale Structure Tensor Total Variation for Image Recovery

A nonconvex nonsmooth regularization method with structure tensor total variation

This paper considers the distributed “nonsmooth+nonsmooth” composite optimization problems for which n agents collaboratively minimize the sum of their local objective functions over the directed networks. In particular, we focus on the scenarios where the sought solutions are desired to possess some structural properties, e.g., sparsity. However, to ensure the convergence, most existing methods produce an ergodic solution via the averaging schemes as the output, which causes the desired structural properties of the output to be destroyed. To address this issue, we develop a new decentralized stochastic proximal gradient method, termed DSPG, in which the nonergodic (last) iteration acts as the output. We also show that the DSPG method achieves the nonergodic convergence rate \(O(\log (T)/\sqrt{T})\) for generally convex objective functions and \(O(\log (T)/T)\) for strongly convex objective functions. When the structure-enhancing regularization is absent and the simple and suffix averaging schemes are used, the convergence rates of DSPG reach \(O(1/\sqrt{T})\) for generally convex objective functions and O(1/T) for strongly convex objective functions, showing improvement relative to the rates \(O(\log (T)/\sqrt{T})\) and \(O(\log (T)/T)\) provided by the existing methods. Simulation examples further illustrate the effectiveness of the proposed method.

Yichuan Dong

Papers

A nonconvex nonsmooth regularization method with structure tensor total variation

On the Non-ergodic Convergence Rate of the Directed Nonsmooth Composite Optimization.