**Time**: May 18, 2017, h. 14:00 - 15:00**Location**: Room Garda, Polo scientifico e tecnologico "Fabio Ferrari", Building Povo 1, via Sommarive 5, Povo (Trento)

### Speaker

Prof. **Alessandro Foi**, Tampere University of Technology, Finland

### Abstract

Signal-dependent noise is characteristic of many imaging modalities and its removal is of fundamental importance for many applications, such as low-light and ultra-fast photography and low-dose non-invasive imaging. Low-energy imaging involves significant variations of the noise standard deviation, up to a degree where the signal of interest is overwhelmed by noise. Hence, the premise of signal-dependent image restoration is very different from the case of additive white Gaussian noise with constant variance typically assumed by common signal processing filters. Variance-stabilizing transformations (VSTs) are nonlinear mappings which can be employed in order to reduce a signal corrupted by signal-dependent noise to a signal where the noise variance is constant and that can be thus processed by common filters. Being often based on large-value asymptotics, the use of VSTs for the low-energy case is subject to various complications.

In this talk we review the VST approach, from its fundamentals to its recent advances, emphasizing the benefits and the intrinsic limitations of this classical method. The Poisson and Rice distributions typical of photon-limited and MR imaging are used as leading examples. We then introduce an iterative framework for progressively improving the effectiveness of VST through iterated combinations of the noisy observations with the filtered estimate from the previous iteration. Its application to denoising and de-blurring results in very fast and stable algorithms that yield significantly better quality, particularly at low and extremely low signal-to-noise ratio (e.g., less than a count per pixel), outperforming much costlier state-of-the-art alternatives.

### About the Speaker

**Alessandro Foi** received the M.Sc. degree in Mathematics from the Università 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. He is an Associate Professor of Signal Processing at Tampere University of Technology. His research interests include mathematical and statistical methods for signal processing, functional and harmonic analysis, and computational modeling of the human visual system. His 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 a Senior Member of the IEEE, Member of the Image, Video, and Multidimensional Signal Processing Technical Committee of the IEEE Signal Processing Society, and an Associate Editor for the IEEE Transactions on Computational Imaging and for the SIAM Journal on Imaging Sciences.

**Contact Person**: Giulia Boato - giulia.boato [at] unitn.it