Abstract
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 \(\left\{ {{\mu _i}} \right\}_{i = 1}^m\)
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© 2001 Springer Science+Business Media New York
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Casey, S., Walnut, D. (2001). Residue and Sampling Techniques in Deconvolution. In: Benedetto, J.J., Ferreira, P.J.S.G. (eds) Modern Sampling Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0143-4_9
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DOI: https://doi.org/10.1007/978-1-4612-0143-4_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6632-7
Online ISBN: 978-1-4612-0143-4
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