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  • 1.
    Ericsson, Stefan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Irregular sampling in shift invariant spaces of higher dimensions2008In: International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, E-ISSN 1793-690X, Vol. 6, no 1, p. 121-136Article in journal (Refereed)
    Abstract [en]

    We consider irregular sampling in shift invariant spaces V of higher dimensions. The problem that we address is: find epsilon so that given perturbations (lambda(k)) satisfying sup vertical bar lambda(k)vertical bar < epsilon, we can reconstruct an arbitrary function f of V as a Riesz basis expansions from its irregular sample values f(k+lambda(k)). A framework for dealing with this problem is outlined and in which one can explicitly calculate sufficient limits epsilon for the reconstruction. We show how it works in two concrete situations.

  • 2. Ericsson, Stefan
    et al.
    Grip, Niklas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    An analysis method for sampling in shift-invariant spaces2005In: International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, E-ISSN 1793-690X, Vol. 3, no 3, p. 301-319Article in journal (Refereed)
    Abstract [en]

    A subspace V of L2(ℝ) is called shift-invariant if it is the closed linear span of integer-shifted copies of a single function.As a complement to classical analysis techniques for sampling in such spaces, we propose a method which is based on a simple interpolation estimate of a certain coefficient mapping. Then we use this method to derive both new results and relatively simple proofs of some previously known results. Among these are some results of rather general nature and some more specialized results for B-spline wavelets. The main problem under study is to find a shift x0 and an upper bound δ such that any function f ∈ V can be reconstructed from a sequence of sample values (f(x0 + k + δk))k∈ℤ, either when all δk = 0 or in the irregular sampling case with an upper bound supk|δk| < δ.

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