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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY:Toward Sparse and Structured Projections for Compr
essed Sensing - Prof Hayder Radha\, Department of
Electrical and Computer Engineering Michigan State
University
DTSTART;TZID=Europe/London:20090730T141500
DTEND;TZID=Europe/London:20090730T151500
UID:TALK19310AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/19310
DESCRIPTION:The problem of finding the unique (sparsest) solut
ion (/x/) to an underdetermined system: /y/ = /Px/
\, is at the core of many problems in signal proce
ssing\, including compressed sensing. The required
methods for solving this profound problem are sig
nificantly influenced by the choice of the project
ion/measurement matrix /P/. Consequently\, the not
ion of categorizing projection matrices\, with com
mon attributes\, into an ensemble /A/ have been em
ployed in an effort to develop better understandin
g of the influence of projection matrices on the a
forementioned problem. Popular matrix ensembles\,
which are quite simple to construct and which have
been studied thoroughly\, include the Gaussian en
semble and partial Fourier ensemble. In this semin
ar\, two new directions in the design of projectio
n ensembles for compressed sensing will be outline
d. First\, we show that new designs that are spars
e in nature provide significant reductions in comp
utational complexity. It can be shown that certai
n class of random sparse projections\, when operat
ing on a /k/-sparse signal of length /n/\, require
s /m/ = O(/Ck/)/ /compressive samples for perfect
recovery\, where /C/ is independent of /n/. More i
mportantly\, the decoder complexity is lower than
the complexity of greedy algorithms. Second\, we p
resent another class of projections where the ense
mbles are designed with some underlying structure
imposed on random sparse matrices. These matrices
are known as Complex Randomness-in-Structured Proj
ection (CRISP) ensembles. CRISP matrices recover a
sparse signal with significantly less compressive
samples at the expense of a slight increase in so
lver complexity relative to unstructured random sp
arse projections. Our simulation results demonstra
te the CRISP framework's ability to recover a sign
al in situations where the rather-complex Basis Pu
rsuit approach fails to do so\, and meanwhile\, th
e required time for recovery is less than the time
required by Orthogonal Matching Pursuit\, a well
known greedy algorithm. \nThese new design example
s highlight the importance of pursuing sparse and
structured projection ensembles for compressed sen
sing.\n
LOCATION:LR5\, Engineering\, Department of
CONTACT:Rachel Fogg
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