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

By Peter W. Hawkes (Ed.)

ISBN-10: 0120147297

ISBN-13: 9780120147298

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

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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. It is important to note that the algorithm tends to settle fairly quickly to an approximate solution; hence, one can reduce the amount of processing time and still obtain a good reconstruction. This is an attractive feature of the inverse derived by minimizing an energy function.

Jones, L. , and Trutzer, V. (1990). “On extending the orthogonality property of minimum norm solutions in Hilbert space to general methods for linear inverse problems,” Inverse problems 6, 379-388. , and Gualtieri, J. A. (1992). “Solving inversion problems with neural networks,” Proc. IJCNN ’92, Baltimore, Vol. 111, p. 955. , New Jersey. , ed. (1991). Neural Networks for Signal processing, Prentice-Hall, Englewood Cliffs, New Jersey. Kyuma, K. (1991). “Optical neural networks: a review,” Nonlinear Optics I, 39-49.

26) The grey-scale mapping we are considering associates a specific neuron with one and only one image pixel. Hence the columns of S each contain only one element, and it is found that the diagonal elements of T take the form Tkk = - 2 s $ ( A T A f (27) where sjk is the nonzero element of the kth column of S. negative, since the diagonal elements of A T A are positive and quantity. Hence we can rewrite Eq. (26) in the form Tkk is always 0 is a positive AEk = -Ak[(Tv+b)k-iITkklAklr (28) and thus A E k will be negative provided where This condition will be met if lAvkI < (Akl and sgn(Avk) = sgn(Ak).

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


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