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SUMMARY:Toward Sparse and Structured Projections for Compressed Sensing - 
 Prof Hayder Radha\, Department of Electrical and Computer Engineering Mich
 igan State University
DTSTART:20090730T131500Z
DTEND:20090730T141500Z
UID:TALK19310@talks.cam.ac.uk
CONTACT:Rachel Fogg
DESCRIPTION:The problem of finding the unique (sparsest) solution (/x/) to
  an underdetermined system: /y/ = /Px/\, is at the core of many problems i
 n signal processing\, including compressed sensing. The required methods f
 or solving this profound problem are significantly influenced by the choic
 e of the projection/measurement matrix /P/. Consequently\, the notion of c
 ategorizing projection matrices\, with common attributes\, into an ensembl
 e /A/ have been employed in an effort to develop better understanding of t
 he influence of projection matrices on the aforementioned problem. Popular
  matrix ensembles\, which are quite simple to construct and which have bee
 n studied thoroughly\, include the Gaussian ensemble and partial Fourier e
 nsemble. In this seminar\, two new directions in the design of projection 
 ensembles for compressed sensing will be outlined. First\, we show that ne
 w designs that are sparse in nature provide significant reductions in comp
 utational complexity.  It can be shown that certain class of random sparse
  projections\, when operating on a /k/-sparse signal of length /n/\, requi
 res /m/ = O(/Ck/)/ /compressive samples for perfect recovery\, where /C/ i
 s independent of /n/. More importantly\, the decoder complexity is lower t
 han the complexity of greedy algorithms. Second\, we present another class
  of projections where the ensembles are designed with some underlying stru
 cture imposed on random sparse matrices. These matrices are known as Compl
 ex Randomness-in-Structured Projection (CRISP) ensembles. CRISP matrices r
 ecover a sparse signal with significantly less compressive samples at the 
 expense of a slight increase in solver complexity relative to unstructured
  random sparse projections. Our simulation results demonstrate the CRISP f
 ramework's ability to recover a signal in situations where the rather-comp
 lex Basis Pursuit approach fails to do so\, and meanwhile\, the required t
 ime for recovery is less than the time required by Orthogonal Matching Pur
 suit\, a well known greedy algorithm. \nThese new design examples highligh
 t the importance of pursuing sparse and structured projection ensembles fo
 r compressed sensing.\n
LOCATION:LR5\, Engineering\, Department of
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