Sampling and Reconstruction Driven by Sparsity Models: Theory and Applications
Speaker: Professor Pier Luigi Dragotti
Faculty Host: Professor Ivan W Selesnick
The problem of reconstructing or estimating partially observed or sampled signals is an important one that finds application in many areas of signal processing and communications. Traditional acquisition and reconstruction approaches are heavily influences by classical Shannon sampling theory which gives an exact sampling and interpolation formula for bandlimited signals. Recently, the classical Shannon sampling framework has been extended to classes of non-bandlimited structured signals, which we call signals with Finite Rate of Innovation.
The main aim of this talk is to give an overview of these new exciting findings in sampling theory. The fundamental theoretical results will be reviewed and constructive algorithms will be presented, both for 1-D and 2-D signals. We also discuss the effect of noise on the sampling and reconstruction of sparse signals. In this context, a variation of an iterative algorithm due to Cadzow is proposed and shown to perform close to optimal over a wide range of signal to noise ratios. Finally a diverse set of applications of these new concepts will be presented to emphasize the importance and far reaching implications of these new theories.
About the Speaker
Pier Luigi Dragotti is currently a Reader (Associate Professor) in the Electrical and Electronic Engineering Department at Imperial College, London. He received the Laurea Degree (summa cum laude) in Electrical 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. In 1996, he was a visiting student at Stanford University, Stanford, CA, and, from July to October 2000, he was a summer researcher in the Mathematics of Communications Department at Bell Labs, Lucent Technologies, Murray Hill, NJ. Dr Dragotti is an associate editor of the IEEE Transactions on Image Processing and a member of the IEEE Image, Video and MultiDimensional Signal Processing (IVMSP) Technical Committee. His research interests include: Wavelet and Sampling Theory, Image Compression, Image Super-resolution and Image Based Rendering.