Modern Sampling Theory pp 193-218 | Cite as

# Residue and Sampling Techniques in Deconvolution

## 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 \(\left\{ {{\mu _i}} \right\}_{i = 1}^m\)

## Keywords

Gabor Frame Approximate Identity Holder Space Dilation Factor Deconvolution Problem## Preview

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