S3P 2015 Tutorial 2
Since the 1990s, modeling signals as sparse in a proper domain has emerged as an important tool in signal processing. Sparse signal representations are at the heart of many successful signal processing applications such as for example signal compression and denoising. From a mathematical point of view, the notion of sparse representation is deeply connected to wavelet theory, approximation theory and more in general harmonic analysis. However, there would not have been that much interest in the topic, had sparse signal representation not had a big impact in applications such as image restoration and more recently in sampling.
This tutorial will cover both the theoretical as well as the applied aspects of sparse signal processing. We will review basic concepts in wavelet theory and fundamental results on reconstructing signals which are sparse in overcomplete dictionaries. We will then discuss recent new algorithms for sparsity recovery, new multi-dimensional sparsity models and we will then highlight some applications where sparsity has been successful.
The second part of the tutorial will focus on sampling driven by sparsity models. We will discuss the difference between discrete-time and continuous-time sparsity. We will highlight how the knowledge of the acquisition device used for sampling allows the mapping of discrete samples to continuous-time information. We will then show how to reconstruct exactly non-bandlimited signals. Finally, applications of sparse sampling in super-resolution imaging, image resolution enhancement, neuroscience and sensor networks will be presented.
Pier Luigi Dragotti is Professor of Signal Processing in the Electrical and Electronic Engineering Department at Imperial College, London. He received the Laurea Degree (summa cum laude) in Electronic Engineering from the University Federico II, Naples, Italy, in 1997; the Master degree in Communications Systems from the Swiss Federal Institute of Technology of Lausanne (EPFL), Switzerland in 1998; and PhD degree from EPFL, Switzerland, in April 2002. He has held several visiting positions. Specifically, he was a visiting student at Stanford University, Stanford, CA in 1996, a summer researcher in the Mathematics of Communications Department at Bell Labs, Lucent Technologies, Murray Hill, NJ in 20
Dr Dragotti was Technical Co-Chair for the European Signal Processing Conference in 2012, Associate Editor of the IEEE TRANSACTIONS ON IMAGE PROCESSING from 2006 to 2009 and an Elected Member of the IEEE Image, Video and Multidimensional Signal Processing Technical Committee. He is currently a member of the IEEE Signal Processing Theory and Methods Technical Committee and a recipient of an ERC Starting investigator Award for the project RecoSamp. His research interests include sampling theory, wavelet theory and its applications, image processing and image super-resolution, image-based rendering. 00 and a visiting scientist at Massachusetts Institute of Technology (MIT) in 2011. Before joining Imperial College in November 2002, he was a senior researcher at EPFL working on distributed signal processing for sensor networks for the Swiss National Competence Center in Research on Mobile Information and Communication Systems.