With many physical problems, measurement of spectral distribution, cosmic radiation, aerial and satellite imaging indirect sensing/recording devices are used. In many of these cases, the recording systems can be modeled by a Fredholm integral equation of the first kind. An inversion of the kernel representing a system, in the presence of noise, is an ill-posed problem. The direct inversion often yields an unacceptable solution. In this paper, we suggest an artificial neural network (ANN) architecture to solve certain kinds of ill-posed problems. The weights in the model are initialized using eigen-vectors and eigen-values of the kernel matrix that characterize the recording system. We assume the solution to be a sample function of a wide sense stationary process with a known auto-correlation function. As an illustration, we consider two problems: a well known Phillips' problem and problem of restoration of a degraded image.
['Arun D. Kukarni']
Solving ill-posed problems with artificial neural networks