Reconstructing Signals with Finite Rate of Innovation from Noisy Samples

    Authors

    N. Bi; M. Z. Nashed;Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    Acta Appl. Math.

    Keywords

    Sampling; Signals with finite rate of innovation; Regularized least; squares; Mean squared error; Wiener filter; SHIFT-INVARIANT SPACES; SHANNON; REGULARIZATION; Mathematics, Applied

    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.

    Journal Title

    Acta Applicandae Mathematicae

    Volume

    107

    Issue/Number

    1-3

    Publication Date

    1-1-2009

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    339

    Last Page

    372

    WOS Identifier

    WOS:000266918300019

    ISSN

    0167-8019

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