Residue and Sampling Techniques in Deconvolution

  • Stephen Casey
  • David Walnut
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this chapter we will study techniques for solving the following general problem, which we will refer to as the Multisensor Deconvolution Problem or MDP: Given a collection of compactly supported distributions, \(\{ {\mu _i}\} _{i = 1}^m \subseteq \mathcal{E}\prime ({\mathbb{R}^d})\) how can we recover an arbitrary function \(f \in {C^\infty }({\mathbb{R}^d})\) from the data \(\left\{ {{S_i}} \right\}_{i = 1}^m = \left\{ {f*{\mu _i}} \right\}_{i = 1}^m?\) The solution technique that we consider involves the construction of deconvolvers. These come in a variety of types but are essentially a collection of distributions which (1) depend only on the convolvers \(\left\{ {{\mu _i}} \right\}_{i = 1}^m\) and (2) allow for the solution of the MDP with only simple linear operations on the data \(\left\{ {{\mu _i}} \right\}_{i = 1}^m\)


Gabor Frame Approximate Identity Holder Space Dilation Factor Deconvolution Problem 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Stephen Casey
  • David Walnut

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