Abstract

Classical sampling theorem states that by using an anti-aliased low-pass filter at the Nyquist rate, one can transmit and retrieve the filtered signal. This approach, which has been used for decades in signal processing, is not good for high quality speech, image and video signals where the actual signals are not low-pass but rather sparse. The traditional sampling theorems do not work for sparse signals. Modern approach, developed by statisticians at Stanford (Donoho and Candes), give some lower bounds for the minimum sampling rate such that a sparse signal can be retrieved with high probability. However, their approach, using a sampling matrix called compressive matrix, has certain drawbacks: Compressive matrices require the knowledge of all the samples, which defeats the whole purpose of compressive sampling! 

Moreover, for real signals, one does not need a compressive matrix and we shall show in this seminar that random sampling performs as good as or better than compressive sampling. In addition, we show that greedy methods such as Orthogonal Matching Pursuit (OMP) are too complex with inferior performance compared to IMAT and other iterative methods. Furthermore, we shall compare IMAT to OMP and other reconstruction methods in terms of complexity and show the advantages of IMAT. Various applications such as image and speech recovery from random or block losses, salt&  pepper noise, OFDM channel estimation, MRI, and finally spectral estimation will be discussed and simulated.

Biography

Dr Marvasti received his BS, Ms and PhD degrees all from Rensselaer Polytechnic Institute in 1970, 1971 and 1973, respectively. He has worked, consulted and taught in various industries and academic institutions since 1972. Among which are Bell Labs, University of California Davis, Illinois Institute of Technology, University of London, King's College. He was one of the editors and associate editors of IEEE Trans on Communications and Signal Processing from 1990-1997. He has about 100 Journal publications and has written several reference books; he has also several international patents. His last book is on Nonuniform Sampling: Theory and Practice by Springer in 2001. He was also a guest editor on Special Issue on Nonuniform Sampling for the Sampling Theory & Signal and Image Processing journal, May 2008.  Besides being the co-founders of two international conferences (ICT's and SampTA's), he has been the organizer and special session chairs of many IEEEE conferences including ICASSP conferences. Recently, he was the Lead editor on "Sparse Signal Processing" for the Special Issue of Eurasip J on Advanced in Signal Processing. Dr Marvasti is currently a professor at Sharif University of Technology and the director Advanced Communications Research Institute (ACRI) and a former head of Center for Multi-Access Communications Systems. He is presently spending his sabbatical leave at the Communications and Information Systems Group of University College London (UCL).

Future C4DM seminars:

Shelley Katz, University of Surrey: Symphonova virtual orchestra
Wed 23rd January 2012