Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces

    Authors

    A. Aldroubi; Q. Y. Sun;W. S. Tang

    Comments

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    Abbreviated Journal Title

    J. Fourier Anal. Appl.

    Keywords

    irregular sampling; Calderon resolution; frames; wavelets; amalgam; spaces; RECONSTRUCTION; SUBSPACES; THEOREMS; FRAMES; Mathematics, Applied

    Abstract

    In this article, we study three interconnected inverse problems in shift invariant spaces: 1) the convolution/deconvolution problem; 2) the uniformly sampled convolution and the reconstruction problem; 3) the sampled convolution followed by sampling on irregular grid and the reconstruction problem. In all three cases, we study both the stable reconstruction as well as ill-posed reconstruction problems. We characterize the convolutors for stable deconvolution as well as those giving rise to ill-posed deconvolution. We also characterize the convolutors that allow stable reconstruction as well as those giving rise to ill-posed reconstruction from uniform sampling. The connection between stable deconvolution, and stable reconstruction from samples after convolution is subtle, as will be demonstrated by several examples and theorems that relate the two problems.

    Journal Title

    Journal of Fourier Analysis and Applications

    Volume

    11

    Issue/Number

    2

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    215

    Last Page

    244

    WOS Identifier

    WOS:000228171400005

    ISSN

    1069-5869

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