An ELU Network with Total Variation for Image Denoising

In this paper, we propose a novel convolutional neural network (CNN) for image denoising, which uses exponential linear unit (ELU) as the activation function. We investigate the suitability by analyzing ELU's connection with trainable nonlinear reaction diffusion model (TNRD) and residual denoising. On the other hand, batch normalization (BN) is indispensable for residual denoising and convergence purpose. However, direct stacking of BN and ELU degrades the performance of CNN. To mitigate this issue, we design an innovative combination of activation layer and normalization layer to exploit and leverage the ELU network, and discuss the corresponding rationale. Moreover, inspired by the fact that minimizing total variation (TV) can be applied to image denoising, we propose a TV regularized L2 loss to evaluate the training effect during the iterations. Finally, we conduct extensive experiments, showing that our model outperforms some recent and popular approaches on Gaussian denoising with specific or randomized noise levels for both gray and color images.Comment: 10 pages, Accepted by the 24th International Conference on Neural Information Processing (2017

Regularizers for Vector-Valued Data and Labeling Problems in Image Processing

Дан обзор последних результатов в области регуляризаторов, основанных на полных вариациях, применительно к векторным данным. Результаты оказались полезными для хранения или улучшения мультимодальных данных и задач разметки на непрерывной области определения. Возможные регуляризаторы и их свойства рассматриваются в рамках единой модели.The review of recent developments on total variation-based regularizers is given with the emphasis on vector-valued data. These have been proven to be useful for restoring or enhancing data with multiple channels, and find particular use in relaxation techniques for labeling problems on continuous domains. The possible regularizers and their properties are considered in a unified framework.Наведено огляд останніх результатів у галузі регуляризаторів, що базуються на повних варіаціях, стосовно векторних даних. Результати виявилися корисними для зберігання та покращення мультимодальних даних і задач розмітки на неперервній області визначення. Можливі регуляризатори та їх властивості розглядаються в рамках єдиної моделі

An approach to vectorial total variation based on geometric measure theory

We analyze a previously unexplored generalization of the scalar total variation to vector-valued functions, which is motivated by geometric measure theory. A complete mathematical characterization is given, which proves important invariance properties as well as existence of solutions of the vectorial ROF model. As an important feature, there exists a dual formulation for the proposed vectorial total variation, which leads to a fast and stable minimization algorithm. The main difference to previous approaches with similar properties is that we penalize across a common edge direction for all channels, which is a major theoretical advantage. Experiments show that this leads to a significiantly better restoration of color edges in practice. 1