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Neural network based solution to inverse problems
Description
The well-posedness of problems is not always guaranteed in inverse problems, unlike in forward problems. Thus, a number of methods for giving well-posedness have been studied in mathematical fields. In the field of neural networks, the network inversion method for solving inverse problems was proposed; it is useful but does not remove the ill-posedness of inverse problems. To overcome the difficulty, we propose the answer-in-weights scheme to provide the network with a priori given knowledge. We compare the performance of answer-in-weights network with the one of an inversion network in solving the ill-posed inverse problem arising in the Fredholm integral equation of the first kind. Furthermore, we compare the expression of the a priori knowledge inherent to the problem, by using two kinds of models.
Journal
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- 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227)
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1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227) 3 2471-2476, 2002-11-27
IEEE