Application of the kernel method to the inverse geosounding problem
Neural Networks - 2003 Special issue: Neural network analysis of complex scientific data: Astronomy and geosciences
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Counter-examples for Bayesian MAP restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Designing Optimal Spectral Filters for Inverse Problems
SIAM Journal on Scientific Computing
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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 can be used to find inversion estimates as well as ways to assess their performance.