Thursday, 18.9.2008, 11:30
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.