Convolutional neural networks in phase space and inverse problems
This work addresses inverse problems in wave propagation for applications like medical imaging or geophysics, but it appears incremental as it applies existing CNN methods to a specific domain.
The paper tackles the inverse problem of determining medium properties from wave responses by constructing a deep convolutional neural network to classify and reconstruct coefficients of nonlinear wave equations, achieving quantitative relationships between network depth/units and medium complexity for given accuracy.
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to classify and reconstruct the coefficients of nonlinear wave equations that model the medium properties. Furthermore, for given approximation accuracy, we obtain the depth and number of units of the network and their quantitative dependence on the complexity of the medium.