By Peter W. Hawkes (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 87
These iterations can be terminated when some prescribed settling accuracy, defined by Eq. (45), is achieved. As the settling accuracy increases, the neural inverse should, and indeed does, tend toward an unregularized inverse. , 1993; Steriti and Fiddy, 1993). The properties of the inverse are very well conditioned for a wide range of settling accuracies, and the iterative procedure requires no action on the part of the user except for the selection of the stopping point through this parameter.
This expression can be rewritten in the form + E = vTATAv - 2gTAv + gTg PvTv, (19) where the term gTg can be ignored since it represents a total offset for E. Comparing this expression for E with that of the Hopfield network gives T = -2(ATA +,LIZ), b = 2ATg. Thus, superresolution performed by this procedure can be mapped simply and directly onto a Hopfield network. The regularization parameter, P, which sets a bound on the norm of the final estimatef, determines the Tmatrix from elements of the A-matrix, which encodes information about the imaging system and prior information about the object.
Nashed, M. , and Wahba, G. (1974). “Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations,” SIAM J . Math. Anal. 5,974-987. Owechko, Y. (1989a).