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Proceedings Paper

Trade-offs between measurement residual and reconstruction error in inverse problems with prior information
Author(s): Paul Hughett
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Paper Abstract

In many inverse problems with prior information, the measurement residual and the reconstruction error are two natural metrics for reconstruction quality, where the measurement residual is defined as the weighted sum of the squared differences between the data actually measured and the data predicted by the reconstructed model, and the reconstruction error is defined as the sum of the squared differences between the reconstruction and the truth, averaged over some a priori probability space of possible solutions. A reconstruction method that minimizes only one of these cost functions may produce unacceptable results on the other. This paper develops reconstruction methods that control both residual and error, achieving the minimum residual for any fixed error or vice versa. These jointly optimal estimators can be obtained by minimizing a weighted sum of the residual and the error; the weights are determined by the slope of the tradeoff curve at the desired point and may be determined iteratively. These results generalize to other cost functions, provided that the cost functions are quadratic and have unique minimizers; some results are obtained under the weaker assumption that the cost functions are convex.

Paper Details

Date Published: 9 October 1995
PDF: 12 pages
Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224154
Show Author Affiliations
Paul Hughett, Lawrence Berkeley National Lab. (United States)


Published in SPIE Proceedings Vol. 2570:
Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications
Randall Locke Barbour; Mark J. Carvlin; Michael A. Fiddy, Editor(s)

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