Is it possible to reconstruct a signal or an image accurately from a number of samples much smaller than what is predicted by the Nyquist-Shannon theorem? Recently, compressed sensing (CS) has emerged as a new paradigm that, under some conditions, gives a positive answer to this question. The main idea is to exploit the fact that many real-world signals are sparse or compressible, in the sense that they contain many coefficients close or equal to zero, when represented in an appropriate basis. To date, the main body of research in CS has been driven by contributions from the fields of signal processing, statistics and computer science. In contrast, CS has strong ties to coding and information theory. While the connections between coding and CS have been investigated in recent papers, these contributions remain limited. Important but largely unsolved questions in CS theory concern the existence of a) tight bounds on the number of measurements to recover the signal in the presence of noise; b) low-complexity algorithms for CS reconstruction; c) small practical sensing matrices that support such schemes. This project is aimed at fundamental contributions to address these challenges, exploiting the links between CS, error correcting coding, source coding and information theory. Contributions from these fields are crucial to harvest the potential gains of CS in practical systems, and will have a significant impact in applications such as medical imaging and sensor networks.
Professor at Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems
Funding Chalmers participation during 2012–2015