Mathematics Colloquia and Seminars
Compressed Sensing Meets Information TheoryPDE and Applied Math Seminar
|Speaker:||Dror Baron, Menta Capital|
|Start time:||Thu, Jun 5 2008, 11:00AM|
Sensors, signal processing hardware, and algorithms are under increasing pressure to accommodate ever larger data sets; ever faster sampling and processing rates; ever lower power consumption; and radically new sensing modalities. Fortunately, there have been enormous increases in computational power. This progress has motivated Compressed Sensing (CS), an emerging field based on the revelation that a sparse signal can be reconstructed from a small number of linear measurements. The implications of CS are promising, and enable the design of new kinds of cameras and analog-to-digital converters.
Information theory has numerous insights to offer CS; I will describe several investigations along these lines. First, unavoidable analog measurement noise dictates the minimum number of measurements required to reconstruct the signal. Second, we leverage the remarkable success of LDPC channel codes to design low-complexity CS reconstruction algorithms. Third, distributed compressed sensing (DCS) provides new distributed signal acquisition algorithms that exploit both intra- and inter-signal correlation structures in multi-signal ensembles. DCS is immediately applicable in sensor networks.
Linear measurements play a crucial role not only in compressed sensing but in disciplines such as finance, where numerous noisy measurements are needed to estimate various statistical characteristics. Indeed, many areas of science and engineering seek to extract information from linearly derived measurements in a computationally feasible manner. Advances toward a unified theory of linear measurement systems will enable us to effectively process the vast amounts of data being generated in our dynamic world.