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- W4292719328 abstract "In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of information is familiar when discussing key questions such as which parts of the function can be inferred accurately and which cannot. For example, it is generally understood that we can identify system parameters accurately only close to detectors, or along ray paths between sources and detectors, because we have the most information for these places. Although referenced in many publications, the information that is invoked in such contexts is not a well understood and clearly defined quantity. Herein, we present a definition of information density that is based on the variance of coefficients as derived from a Bayesian reformulation of the inverse problem. We then discuss three areas in which this information density can be useful in practical algorithms for the solution of inverse problems, and illustrate the usefulness in one of these areas -- how to choose the discretization mesh for the function to be reconstructed -- using numerical experiments." @default.
- W4292719328 created "2022-08-23" @default.
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- W4292719328 date "2022-08-18" @default.
- W4292719328 modified "2023-09-24" @default.
- W4292719328 title "Estimating and using information in inverse problems" @default.
- W4292719328 doi "https://doi.org/10.48550/arxiv.2208.09095" @default.
- W4292719328 hasPublicationYear "2022" @default.
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