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Statistical regularization of inverse problems
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DOI：10.1137/S0036144500358232.png)
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In experimental sciences we often need to solve inverse problems. That is, we want to obtain information about the internal structure of a physical system from indirect noisy observations. Often the problem is not whether a solution exists; on the contrary, there are too many solutions that fit the data to a chosen tolerance level. The goal is to use prior information to determine a physically meaningful solution. Here, we present some of the basic questions that arise. We describe methods that call be used to find inversion estimates as well as ways to assess their performance.
Keyword:
Fredholm integral equations
Backus-Gilbert method
reproducing kernels
Tikhonov regularization
splines
cross-validation
wavelets
minimax estimation
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6.1
论文数:
888
被引数:
1.2W
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