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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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