Somantika Datta's February 2nd, 2011 Talk

  • Title: Spiral Sampling and Signal Reconstruction by Fourier Frames

  • Abstract: Given a spiral in 

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    , a sequence of points 
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    can be chosen on the spiral such that every finite energy signal with support in 
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    can be reconstructed from the samples of their frequencies at the points in S. This is useful in dealing with certain medical data like that obtained in MRI. The reconstruction is by means of a frame reconstruction algorithm. This is due to work by J. J. Benedetto, A. Powell and H-C Wu. However, the set S in the given spiral is an infinite set and for practical purposes one has to truncate the reconstruction formula to a finite sum. We will discuss such implementation issues and how the error in truncation depends on properties of the signal like its smoothness etc.