Sparse image representation in nonlocal transform domain

Nonlocal methods have emerged during the past five years as one of the most promising developments in signal and image processing. These methods are based on the principle that natural signals, particularly images, are characterized by mutual self-similarity between patches of data found at different locations. In this talk we present the so-called grouping and collaborative filtering approach: mutually similar patches in an image or video are collected and jointly transformed using a higher-dimensional transform, sparsity is then enforced by shrinkage of the higher-dimensional spectrum. This approach has proved to be very successful, especially as the core element of denoising, deblurring, and other inverse filtering algorithms, including super-resolution and compressive-sensing reconstruction. We discuss various aspects related to the adaptivity of the transforms used in collaborative filtering, with particular emphasis on the geometrical adaptation and on the learning of basis elements from noisy data.
Alessandro Foi received the M.Sc. degree in Mathematics from the University degli Studi di Milano, Italy, in 2001, the Ph.D. degree in Mathematics from the Politecnico di Milano in 2005, and the D.Sc.Tech. degree in Signal Processing from Tampere University of Technology, Finland, in 2007. His research interests include mathematical and statistical methods for signal processing, functional and harmonic analysis, and computational modeling of the human visual system. Currently, he is Academy Research Fellow (Akatemiatutkija) with the Academy of Finland, at the Department of Signal Processing, Tampere University of Technology. His recent work focuses on spatially adaptive (anisotropic, nonlocal) algorithms for the restoration and enhancement of digital images, on noise modeling for imaging devices, and on the optimal design of statistical transformations for the stabilization, normalization, and analysis of random data. He is an Associate Editor for the IEEE Transactions on Image Processing.