Abstract

This talk addresses one of the fundamental problems of signal and image processing, the separation of noise and signal. It was already the key problem of Shannon’s foundational Mathematical Theory of Communication. This problem has uncountable applications for image formation, image and video post-production, and feature detection. Since the 70s, several denoising approaches have been identified and can be grouped in a handful of useful ‘denoising principles’ with notable progress, from Fourier analysis, wavelet theory to sparse decompositions and non-local methods. In 2016, neural denoisers have started outperforming (slightly) human made denoising algorithms. Their principles are quite different. Human algorithms adopt mathematical assumptions about the image structure to denoise them. Neural algorithms learn image structure from vast collections of images. We will explain the classical theories, the neural devices and demonstrate what perspectives and cross-fertilization this comparison yields.

Joint work with Pablo Arias and Gabriele Facciolo