NONUNIFORM AVERAGE SAMPLING AND RECONSTRUCTION OF SIGNALS WITH FINITE RATE OF INNOVATION

    Authors

    Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    SIAM J. Math. Anal.

    Keywords

    average sampling; ideal sampling; signals with finite rate of; innovation; shift-invariant spaces; Mathematics, Applied

    Abstract

    From an average (ideal) sampling/reconstruction process, the question arises whether the original signal can be recovered from its average (ideal) samples and, if so, how. We consider the above question under the assumption that the original signal comes from a prototypical space modeling signals with a finite rate of innovation, which includes finitely generated shift-invariant spaces, twisted shift-invariant spaces associated with Gabor frames and Wilson bases, and spaces of polynomial splines with nonuniform knots as its special cases. We show that the displayer associated with an average (ideal) sampling/reconstruction process, which has a well-localized average sampler, can be found to be well-localized. We prove that the reconstruction process associated with an average (ideal) sampling process is robust, locally behaved, and finitely implementable, and thus we conclude that the original signal can be approximately recovered from its incomplete average (ideal) samples with noise in real time. Most of our results in this paper are new even for the special case when the original signal comes from a finitely generated shift-invariant space.

    Journal Title

    Siam Journal on Mathematical Analysis

    Volume

    38

    Issue/Number

    5

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    1389

    Last Page

    1422

    WOS Identifier

    WOS:000208471400002

    ISSN

    0036-1410

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