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SUMMARY:Fast and sample efficient algorithms for the sparse Fourier transf
 orm
DTSTART:20160722T140000
DTEND:20160722T160000
DTSTAMP:20260407T095719Z
UID:c6662560b5ddb1ccb0cd0967655f869d4971e323d10ba9355ce6c34a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Amir Zandieh\nEDIC Candidacy Exam\nExam President: Prof. Ola S
 vensson\nThesis Director: Prof. Mikhail Kapralov\nCo-examiner: Prof. Volka
 n Cevher\nBackground papers:Nearly Optimal Sparse Fourier Transform\, by H
 . Hassanieh\, P. Indyk\, D. Katabi\, E. Price.The Restricted Isometry Prop
 erty of Subsampled Fourier Matrices\, by I. Haviv\, O. Regev.Super-resolut
 ion\, Extremal Functions and the Condition Number of Vandermonde Matrices\
 , by A. Moitra.Abstract\nThe Fourier transform appears in many theoretical
 \,\nalgorithmic\, and practical problems. It has a wide range of\napplicat
 ions in digital and analog signal processing. Although\nmost of the signal
 s in real world are continuous\, because\nprocessing tools are all digital
 \, they have to be converted to\ndigital eventually. Once a signal is digi
 tized\, we need fast\nalgorithms for computing its Fourier transform. Fort
 unately\, in\nmany applications signals are also sparse and this enables u
 s to\ncompute sparse Fourier transform in sub-linear time. We review\nthe 
 techniques and algorithms for doing so. The sparsity leverage\,\nalso enab
 les accurate reconstruction of the signals from a very\nlimited number of 
 measurements. It reduces the cost of analog to\ndigital conversion conside
 rably. The techniques for such sample\nefficient signal acquisition\, whic
 h are known as “compressed\nsensing”\, rely on the restricted isometry
  property (RIP) of the\nsensing matrix. We explain this property and repre
 sent one of\nthe best known result on the RIP of Fourier sensing matrices.
 \nThe procedure of sampling analog signals works very nicely\nwhen the har
 dware is able to sample at a sufficient rate\, i.e.\, the\ngap between two
  consecutive samples are small enough. But there\nare some cases where we 
 want to extract structure of a sparse\ncontinuous signal from coarse grain
 ed measurements (because\nof some physical limitations). This problem is k
 nown as ”Super\nresolution”. In these cases the digitized signal is no
 t sparse even\nthough the analog signal is such and we need to develop dif
 ferent\ntechniques.
LOCATION:BC 129 https://plan.epfl.ch/?room==BC%20129
STATUS:CONFIRMED
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