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Complex-Valued Neural Network and Inverse Problems

Complex-Valued Neural Network and Inverse Problems
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Author(s): Takehiko Ogawa (Takushoku University, Japan)
Copyright: 2009
Pages: 29
Source title: Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters
Source Author(s)/Editor(s): Tohru Nitta (National Institute of Advanced Industrial Science and Technology, Japan)
DOI: 10.4018/978-1-60566-214-5.ch002

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Abstract

Network inversion solves inverse problems to estimate cause from result using a multilayer neural network. The original network inversion has been applied to usual multilayer neural networks with real-valued inputs and outputs. The solution by a neural network with complex-valued inputs and outputs is necessary for general inverse problems with complex numbers. In this chapter, we introduce the complex-valued network inversion method to solve inverse problems with complex numbers. In general, difficulties attributable to the ill-posedness of inverse problems appear. Regularization is used to solve this ill-posedness by adding some conditions to the solution. In this chapter, we also explain regularization for complex-valued network inversion.

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