Heidelberg 1999 – scientific programme

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KY: Kybernetik

KY 3: Datenerfassung | Datenanalyse

KY 3.4: Talk

Tuesday, March 16, 1999, 14:45–15:30, ZO 3

The adaptive resolution concept in form-free distribution estimation — •R. Fischer — Max-Planck-Institut für Plasmaphysik, EURATOM Association, POB 1533, D-85740 Garching

The ubiquitous ill-posed inverse problem of estimating a form-free distribution and the respective reliability given a set of noisy or incomplete data is solved with Bayesian probability theory by exploiting prior information. The method applies to problems where we do not have enough information to be able to characterize the distribution by a specific type of functional model or do not have enough confidence in functions with a few specific parameters. The price for the flexibility to allow for any conceivable solution is a large number of variables.

One important ingredient in form-free reconstruction is the prior information of the existence of different length scales intrinsic to all natural distributions. To incorporate a multi-length-scale concept into the calculation a multi-variate spatial correlation approach is used to account for local smoothness in the distribution. We present an adaptive-kernel approach which allows for the highest resolution while noise-fitting due to redundant degrees-of-freedom is avoided.

The adaptive resolution method is applied to different types of problems such as determination of an apparatus transfer function and its deconvolution, reconstruction of depth profiles from Rutherford backscattering measurements, reconstruction of electron energy distributions in plasmas and density estimation.