The algebraic eigenvalue problem
The algebraic eigenvalue problem
Neural networks and natural intelligence
Neural networks and natural intelligence
Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Statistical Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind
Journal of the ACM (JACM)
On Solving Fredholm Integral Equations of the First Kind
Journal of the ACM (JACM)
Combining artificial neural networks and statistics for stock-market forecasting
CSC '93 Proceedings of the 1993 ACM conference on Computer science
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No imaging system in practice is perfect, in fact the recorded images are always distorted or of finite resolution. An image recording system can be modeled by a Fredholm integral equation of the first kind. An inversion of the kernel representing the 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 ill posed problems in the presence of noise. We use two types of neuron like processing units: the units that use the weighted sum and the units that use the weighted product. The weights in the model are initialized using the eigen vectors of the kernel matrix that characterizes 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 images that are degraded by motion blur.