Fast and Interpretable Nonlocal Neural Networks for Image Denoising via Group-Sparse Convolutional Dictionary Learning

Nonlocal self-similarity within natural images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the $\ell 1$ sparsity prior of CDLNet to a weighted group-sparsity prior. From this formulation, we propose a novel sliding-window nonlocal operation, enabled by sparse array arithmetic. In addition to competitive performance with black-box nonlocal DNNs, we demonstrate the proposed sliding-window sparse attention enables inference speeds greater than an order of magnitude faster than its competitors.Comment: 11 pages, 8 figures, 6 table

Quenched zones and material structures at gears teeth

Gears are used in most types of machinery, including the automotive industry as a wide known application. Different types of gears are specified through many (inter)national standards, mainly their geometry, design specifications or requirements while the (micro) structures of gear's teeth are less known. In diagnostics of damage or rupture, when it is happened, the microstructure undergoes to investigation but this is usually too late. From that reason the (micro)structure and hardness of gear tooth should be known in advance and here is defined. In manufacturing of a gear many methods are available rather by cutting (milling, hobbing, shaving or grinding) than forging. Those cutting methods have no great influence on the structure. If the grinding was not performed correctly than the hardened surface may be softened, even with cracks. The main influences on the structure to be obtained lie in a kind of production techniques such as: casting, forging, rolling and finely by a kind of chemical heat-treating of gear teeth surface. Here are presented typical zones and microstructures realized through the chemical heat-treating of teeth, and those should be known, especially for providing an incoming control of a gear in industrial conditions. Those data are of a crucial importance for a gear life