Tradeoffs between measurement residual and reconstruction error in inverse problems with prior information

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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 ... continued below

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12 p.

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Hughett, P. June 1, 1995.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

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  • Hughett, P. Lawrence Berkeley Lab., CA (United States). Life Sciences Div.

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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. This paper applies these results to a model problem from biomagnetic source imaging and exhibits the tradeoff curve for this problem.

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12 p.

Notes

OSTI as DE96000120

Source

  • Experimental and numerical methods for solving ill-posed problems, San Diego, CA (United States), 9-14 Jul 1995

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  • Other: DE96000120
  • Report No.: LBL--37402
  • Report No.: CONF-9507171--1
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/106621 | External Link
  • Office of Scientific & Technical Information Report Number: 106621
  • Archival Resource Key: ark:/67531/metadc621005

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  • June 1, 1995

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  • June 16, 2015, 7:43 a.m.

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  • April 5, 2016, 12:10 p.m.

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Hughett, P. Tradeoffs between measurement residual and reconstruction error in inverse problems with prior information, report, June 1, 1995; California. (digital.library.unt.edu/ark:/67531/metadc621005/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.