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Inverse Problems

  • Paul Fieguth
Chapter
Part of the Information Science and Statistics book series (ISS)

Abstract

An understanding of forward and inverse problems [12, 301] lies at the heart of any large estimation problem. Abstractly, most physical systems can be defined or parametrized in terms of a set of attributes, or unknowns, from which other attributes, or measurements, can be inferred. In other words, the quantities \(\underline{m}\) which we measure are some mathematical function
$$\underline{m} = f(\underline{Z})$$
(2.1)
of other, more basic, underlying quantities \(\underline{z},\) where f may be deterministic or stochastic. In the special case when f is linear, a case of considerable interest to us, then (2.1) may be expressed as
$$\underline{m} = C\underline{Z} \quad {\rm or} \quad \underline{m} = C\underline{Z} + \underline{v}$$
(2.2)
for the deterministic or stochastic cases, respectively. Normally \(\underline{z},\) is an ideal, complete representation of the system: detailed, noise-free, and regularly structured (e.g.,pixellated), whereas the measurements \(\underline{m},\) are incomplete and approximate: possibly noise-corrupted, irregularly structured, limited in number, or somehow limited by the physics of the measuring device.

Keywords

Inverse Problem Condition Number Data Fusion Prior Model Forward Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2011

Authors and Affiliations

  1. 1.Department of Systems Design Engineering Faculty of EngineeringUniversity of WaterlooWaterlooCanada

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