Error analysis of frame, reconstruction from noisy samples

    Authors

    A. Aldroubi; C. Leonetti;Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Signal Process.

    Keywords

    frames; reconstruction from averages; sampling; SHIFT-INVARIANT SPACES; WAVELET SUBSPACES; THEOREM; Engineering, Electrical & Electronic

    Abstract

    This paper addresses the problem of reconstructing a continuous function defined on R-d from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance sigma(2). We sample the continuous function f on the uniform lattice (1/m)Z(d), and show for large enough m that the variance of the error between the frame reconstruction f(epsilon,m) from noisy samples of f and the function f satisfy var(f(epsilon,m)(x) - f(x))approximate to Z (sigma(2)/m(d))C-x where C-x is the best constant for every x is an element of R-d. We also prove a similar result in the case that our data are weighted-average samples of f corrupted by additive noise.

    Journal Title

    Ieee Transactions on Signal Processing

    Volume

    56

    Issue/Number

    6

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    2311

    Last Page

    2325

    WOS Identifier

    WOS:000256153800013

    ISSN

    1053-587X

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