Download Advances in Electronics and Electron Physics, Vol. 87 by Peter W. Hawkes (Ed.) PDF

By Peter W. Hawkes (Ed.)

ISBN-10: 0120147297

ISBN-13: 9780120147298

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Extra resources for Advances in Electronics and Electron Physics, Vol. 87

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J . (1980). “Coherent optical extrapolation of 2-D band-limited signals: Processor theory,” Appl. Opt. 19, 1670-1672. IMAGE RESTORATION O N T H E HOPFIELD NEURAL NETWORK 47 Marks, R. J. (1981). “Gerchberg’s extrapolation algorithm in two dimensions,” App. Opt. 20, 1815-1820. Marks, R . , and Smith, D. K . (1980). “Iterative coherent processor for bandlimited signal extrapolation,” Proc. SPIE 231, 106- 1 1 1. , Rosenbluth, A. , Rosenbluth, M. , Teller, A. , and Teller, E. (1953). “Equation of state calculations by fast computing machines,” J .

O a FIGURE 12. y vs. 01 for the regularized SVD inverses. C . Discussion It has been shown that the neural network calculates a somewhat different matrix inverse than that calculated by regularized SVD. Given the relationship between the a and the singular values y of the inverse matrix for regularized SVD, where Y= +P), together with some evaluation criterion, one can deduce an effective regularassociated with a specific settling ization parameter 0,normalized to accuracy. This relationship defines a mapping of the singular values of the matrix into those of its regularized inverse, which can be seen in Fig.

Recognizable and improved) reconstruction occurring at low accuracies (values over 20% have been successfully used). Figures 10 and 11 are graphs demonstrating the processing times (on an Apollo DN IOOOO) needed for the matrix inversion. Figure 10 shows the increase in processing time with matrix size. 974. Although the neural inverse takes significantly longer to compute, it does yield a usable inverse without the need to optimize a regularization parameter. The second graph (Figure 11) shows the processing times needed for differing values of settling accuracies.

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