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Reconstructing Signals with Finite Rate of Innovation from Noisy Samples

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Abstract

A signal is said to have finite rate of innovation if it has a finite number of degrees of freedom per unit of time. Reconstructing signals with finite rate of innovation from their exact average samples has been studied in Sun (SIAM J. Math. Anal. 38, 1389–1422, 2006). In this paper, we consider the problem of reconstructing signals with finite rate of innovation from their average samples in the presence of deterministic and random noise. We develop an adaptive Tikhonov regularization approach to this reconstruction problem. Our simulation results demonstrate that our adaptive approach is robust against noise, is almost consistent in various sampling processes, and is also locally implementable.

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Authors and Affiliations

  1. Department of Scientific Computing and Computer Applications, Sun Yat-Sen University, Guangzhou, 510275, China

    Ning Bi

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    M. Zuhair Nashed & Qiyu Sun

Authors
  1. Ning Bi
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  2. M. Zuhair Nashed
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  3. Qiyu Sun
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Corresponding author

Correspondence to Ning Bi.

Additional information

Research of the first author was supported in part by NSFC #10631080, and the Science Foundation of Guangdong Province #04205407 and #2007B090400091.

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Bi, N., Nashed, M.Z. & Sun, Q. Reconstructing Signals with Finite Rate of Innovation from Noisy Samples. Acta Appl Math 107, 339–372 (2009). https://doi.org/10.1007/s10440-009-9474-9

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  • DOI: https://doi.org/10.1007/s10440-009-9474-9

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