Exact Reconstruction using Beurling Minimal Extrapolation

Abstract : We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the Laplace transform, the Stieltjes transformation, etc.). Generalized minimal extrapolation shares related geometric properties with the basis pursuit approach of Chen, Donoho and Saunders [CDS98]. Indeed we also extend some standard results of compressed sensing (the dual polynomial, the nullspace property) to the signed measure framework. We express exact reconstruction in terms of a simple interpolation problem. We prove that every nonnegative measure, supported by a set containing s points, can be exactly recovered from only 2s + 1 generalized moments. This result leads to a new construction of deterministic sensing matrices for compressed sensing.
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Contributor : Yohann de Castro <>
Submitted on : Wednesday, January 30, 2013 - 1:17:46 PM
Last modification on : Friday, April 12, 2019 - 4:22:50 PM

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  • HAL Id : hal-00678423, version 1
  • ARXIV : 1103.4951

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Yohann de Castro, Fabrice Gamboa. Exact Reconstruction using Beurling Minimal Extrapolation. Journal of Mathematical Analysis and Applications, Elsevier, 2012, 395 (1), pp.Pages 336-354. ⟨hal-00678423⟩

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