By Peter W. Hawkes (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 87
Because of the nature of this network inversion method, a suitable inverse can be obtained even without allowing the network to fully settle. This is due to the iterative minimization of the energy function defining the network. The solution path proceeds along an n-dimensional contour towards a global minimum. This tends to overcome round-off errors inherent in numerical methods for matrix inversion. C . Properties of the Neural Matrix Inverse An objective in the development of the neural matrix-inversion method was to obviate the need for an explicit regularization parameter.
12. Here, as the regularization parameter, ,8, is decreased, the mapping approaches the behavior of the 1/a function. The differences between the regularized SVD and neural network matrix inverses can be examined from their singular value spectra. The singular values of a set of regularized SVD matrix inverses, for a representative example, can be seen in Fig. 13. Figure 14 shows the singular values for a set of neural network inverses for differing values of settling accuracies. Note that the neural network inverses generally have larger condition numbers than their regularized SVD counterparts, but a larger number of the singular values are much smaller.
It has been found that, even for low settling accuracies, matrix inverses are obtained that provide image restorations with significantly enhanced resolution. There may be some additional property associated with the neural inverse matrix that improves its properties in this context; this observation merits further investigation. It should also be noted that low settling accuracies greatly reduce the computational time required, which could be still further reduced by fully parallel implementation in appropriate hardware.
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