Quaternion network inversion for solving inverse problems

Recently, the neural network model for handling the high dimensional numbers including a complex number has been proposed and studied in the field of artificial neural networks. Especially, the quaternion is focused in a number of fields such as computer graphics, because we easily express the algebra in three-dimensional space using quaternion. On the other hand, the problem which searches for a cause from an observed result is called an inverse problem, and has been studied in various fields. The network inversion has been studied as a neural network based solution for inverse problems. Recently, the extension to complex-valued neural network has been proposed. In this study, we propose the extension of the network inversion method to the quaternion neural networks.