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SUMMARY:Breaking the coherence barrier - A new theory for compressed sensi
 ng
DTSTART:20141017T141500
DTSTAMP:20260925T090716Z
UID:56616bdcc47fb03711b687a3175d993843ceba2736a7e10b41b7084a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Anders Hansen\, University of Cambridge\nCompressed sensin
 g is based on the three pillars: sparsity\, incoherence and uniform random
  subsampling. In addition\, the concepts of uniform recovery and the Restr
 icted Isometry Property (RIP) have had a great impact. Intriguingly\, in a
 n overwhelming number of inverse problems where compressed sensing is used
  or can be used (such as MRI\, X-ray tomography\, Electron microscopy\, Re
 flection seismology etc.) these pillars are absent. Moreover\, easy numeri
 cal tests reveal that with the successful sampling strategies used in prac
 tice one does not observe uniform recovery nor the RIP. In particular\, no
 ne of the existing theory can explain the success of compressed sensing in
  a vast area where it is used. In this talk we will demonstrate how real w
 orld problems are not sparse\, yet asymptotically sparse\, coherent\, yet 
 asymptotically incoherent\, and moreover\, that uniform random subsampling
  yields highly suboptimal results.\nSubsequently\, we will introduce a new
  theory that aligns with the actual implementation of compressed sensing t
 hat is used in applications. This theory is based on asymptotic sparsity\,
  asymptotic incoherence and multilevel sampling. This theory supports two 
 intriguing phenomena observed in reality: 1. the success of compressed sen
 sing is resolution dependent\, 2. the optimal sampling strategy is signal 
 structure dependent. The last point opens up for a whole new area of resea
 rch\, namely the quest for the optimal sampling strategies.\nFinally\, we 
 will show that by using multilevel sampling\, which exploits the structure
  of the signal\, one can outperform random Gaussian/Bernoulli sampling eve
 n when the classical $l^1$ recovery algorithm is replaced by modified algo
 rithms which aim to exploit structure such as model based or Bayesian comp
 ressed sensing or approximate message passing.\nBio: Dr. Hansen completed 
 his PhD at Cambridge and then moved to Caltech as von Karman Fellow\, befo
 re returning to Cambridge as a Research Fellow of Homerton College. His re
 search is in computational mathematics and includes applied harmonic analy
 sis\, mathematical signal processing with emphasis on sampling theory and 
 compressed sensing as well as spectral theory\, computability theory\, com
 plexity theory and numerical analysis: a rapidly growing area of mathemati
 cs with enormous applications ranging from medical imaging to signal proce
 ssing.
LOCATION:BC 420 https://plan.epfl.ch/?room==BC%20420
STATUS:CONFIRMED
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