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SUMMARY:Compressed sensing in the real world - The need for a new theory -
  Hansen\, A (University of Cambridge)
DTSTART:20140212T090000Z
DTEND:20140212T094500Z
UID:TALK50818@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Compressed sensing is based on the three pillars: sparsity\, i
 ncoherence and uniform random subsampling. In addition\, the concepts of u
 niform recovery and the Restricted Isometry Property (RIP) have had a grea
 t impact. Intriguingly\, in an overwhelming number of inverse problems whe
 re compressed sensing is used or can be used (such as MRI\, X-ray tomograp
 hy\, Electron microscopy\, Reflection seismology etc.) these pillars are a
 bsent. Moreover\, easy numerical tests reveal that with the successful sam
 pling strategies used in practice one does not observe uniform recovery no
 r the RIP. In particular\, none of the existing theory can explain the suc
 cess of compressed sensing in a vast area where it is used. In this talk w
 e will demonstrate how real world problems are not sparse\, yet asymptotic
 ally sparse\, coherent\, yet asymptotically incoherent\, and moreover\, th
 at uniform random subsampling yields highly suboptimal results. In additio
 n\, we will present easy arguments explaining why unif orm recovery and th
 e RIP is not observed in practice. Finally\, we will introduce a new theor
 y that aligns with the actual implementation of compressed sensing that is
  used in applications. This theory is based on asymptotic sparsity\, asymp
 totic incoherence and random sampling with different densities. This theor
 y supports two intriguing phenomena observed in reality: 1. the success of
  compressed sensing is resolution dependent\, 2. the optimal sampling stra
 tegy is signal structure dependent. The last point opens up for a whole ne
 w area of research\, namely the quest for the optimal sampling strategies.
 \n
LOCATION:Seminar Room 1\, Newton Institute
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