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Bayesian methods for non-linear blind inverse problems

Agentura: 
GACR
Identifikační číslo: 
GA20-27939S
Zahájení: 
01.01.2020
Ukončení: 
31.12.2022
Zaměření projektu.: 
teoretický
Typ projektu (EU): 
other
Abstrakt: 
Blind inverse problems (i.e. inverse problems with unknown parameters of the forward model) are well studied for models with uniform grids, such as blind image deconvolution or blind signal separation. Recently, new methods of learning of non-linear problems with differentiable nonlinearities (i.e. neural networks) have been proposed, however they rely on supervised learning on a training set. The aim of this project is to develop methods of blind inverse problems with a general observation operator (such as irregular grids) and general parametric structure that can be learned from a single sample. The main challenge is to find suitable regularization structure. We propose to use the Bayesian approach defining regularization using prior distribution and novel methods of distribution representation developed in machine learning such as variational autoencoders. The proposed methods will be validated in specialized models for: i) determination of a source term of an atmospheric release, and ii) adaptive measurement grid refinement in environmental electron microscopy.
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20.04.2020 - 12:40