Thierry Blu, Pier-Luigi Dragotti, Pina Marziliano, Martin Vetterli
Signal acquisition and reconstruction is at the heart of signal processing and communications, and sampling theorems provide the bridge between the continuous and the discrete-time worlds. The most celebrated and widely used sampling theorem is often attributed to Shannon, and gives a sufficient condition, namely bandlimitedness, for an exact sampling and interpolation formula. Recently, this framework has been extended to classes of non-bandlimited signals. The way around Shannon classical sampling theorem resides in a parametric approach, where the prior that the signal is sparse in a basis or in a parametric space is put to contribution. This leads to new exact reconstruction formulas and fast algorithms that achieve such reconstructions.
The aim of this tutorial is to give an overview of these recent exciting findings in sampling theory. The fundamental theoretical results will be reviewed and constructive algorithms will be presented. Finally, a diverse set of applications will be presented so as to demonstrate the tangibility of the theoretical concepts.
Thierry Blu received the “Diplôme d’ingénieur” from École Polytechnique, France, in 1986 and the Ph.D. from Télécom Paris,in 1996. His main field of research is approximation, interpolation, sampling theory and wavelets. He was with the Biomedical Imaging Group at the Swiss Federal Institute of Technology, Lausanne, and is now with the Department of Electronic Engineering, the Chinese University of Hong Kong. He received two best paper awards from the IEEE Signal Processing Society (2003 and 2006).
Pier-Luigi Dragotti is a senior lecturer (associate professor) in the Electrical and Electronic Engineering Department at Imperial College London. He received the laurea degree in electrical engineering from the University Federico II, Naples, Italy, in 1997 and the master’s and Ph.D. degrees from the École Polytechnique Federale de Lausanne, in 1998 and 2002, respectively. He was a visiting student at Stanford University and a summer researcher in the Mathematics of Communications Department at Bell Labs, Lucent Technologies. His research interests include wavelet theory, sampling and approximation theory, image and video processing, and compression. He is an associate editor of IEEE Transactions on Image Processing.
Pina Marziliano received the B.Sc. in applied mathematics and the M.Sc. in computer science from the Université de Montréal, Canada, in 1994 and 1996, respectively. In 2001, she completed the Ph.D from the Écôle Polytechnique Fédérale de Lausanne, Switzerland. She joined Genimedia in 2002 as a research engineer where she developed no reference perceptual quality metrics for images and video. Since 2003, she has been an assistant professor in the School of Electrical and Electronic Engineering at the Nanyang Technological University in Singapore. She received IEEE Signal Processing Society 2006 Best Paper Award. Her research interests include sampling theory and applications in communications and biomedical engineering, watermarking, and perceptual quality metrics for multimedia.
Martin Vetterli received the Dipl. El.-Ing. degree from ETH Zurich (ETHZ), Switzerland, in 1981, the MS degree from Stanford University in 1982, and the Doctorat ès Sciences degree from EPF Lausanne (EPFL), Switzerland, in 1986.
He was a Research Assistant at Stanford and EPFL, and has worked for Siemens and AT&T Bell Laboratories. In 1986, he joined Columbia University in New York, where he was last an Associate Professor of Electrical Engineering and co-director of the Image and Advanced Television Laboratory. In 1993, he joined the University of California at Berkeley, where he was a Professor in the Department of Electrical Engineering and Computer Sciences until 1997, and now holds an Adjunct Professor position.
Since 1995, he is a Professor of Communication Systems at EPF Lausanne, Switzerland, where he chaired the Communications Systems Division (1996/97), and heads the Audiovisual Communications Laboratory. From 2001 to 2004 he directed the National Competence Center in Research on mobile information and communication systems. He is also a Vice-President for International Affairs at EPFL since October 2004. He has held visiting positions at ETHZ (1990) and Stanford (1998).
He is a fellow of the IEEE, a member of SIAM, and was the Area Editor for Speech, Image, Video, and Signal Processing of the IEEE Transactions on Communications. He is also on the editorial boards of Annals of Telecommunications, Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Application.
He received the Best Paper Award of EURASIP in 1984 for his paper on multidimensional subband coding, the Research Prize of the Brown Bovery Corporation (Switzerland) in 1986 for his doctoral thesis, the IEEE Signal Processing Society's Senior Awards in 1991 and in 1996 (for papers with D. LeGall and K. Ramchandran, respectively). He won the Swiss National Latsis Prize in 1996, the SPIE Presidential award in 1999, and the IEEE Signal Processing Technical Achievement Award in 2001. He was a member of the Swiss Council on Science and Technology until Dec. 2003.
He was a plenary speaker at various conferences (e.g. 1992 IEEE ICASSP) and is the co-author, with J. Kovacevic, of the book Wavelets and Subband Coding (Prentice-Hall, 1995). He has published about 85 journal papers on a variety of topics in signal/image processing and communications and holds 7 patents.
His research interests include sampling, wavelets, multirate signal processing, computational complexity, signal processing for communications, digital video processing and joint source/channel coding.