Local reconstruction for sampling in shift-invariant spaces

13 years 4 months ago

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The local reconstruction from samples is one of most desirable properties for many applications in signal processing, but it has not been given as much attention. In this paper, we will consider the local reconstruction problem for signals in a shiftinvariant space. In particular, we consider finding sampling sets X such that signals in a shift-invariant space can be locally reconstructed from their samples on X. For a locally finite-dimensional shift-invariant space V we show that signals in V can be locally reconstructed from its samples on any sampling set with sufficiently large density. For a shift-invariant space V (1, . . . , N ) generated by finitely many compactly supported functions 1, . . . , N , we characterize all periodic nonuniform sampling sets X such that signals in that shift-invariant space V (1, . . . , N ) can be locally reconstructed from the samples taken from X. For a refinable shift-invariant space V () generated by a compactly supported refinable function , we...

Qiyu Sun

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