By Peter W. Hawkes (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 87
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. It is found that the matrix inverse obtained from a Hopfield-based implementation can indeed be regularized by truncating the number of network iterations. 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.
Iteration can be achieved via hybrid methods or the use of optical elements such as photorefractives which inject gain into the optical processor. If the connection matrix is to be refined or redefined, an adaptive optical interconnection element is required. With a digital frame store or a dynamic volume holographic storage element, the joint transform correlator architecture could be used as a trainable neural network. The input and output planes would incorporate a number of neurons equal to the number of pixels in the SLMs used.
Using too small a settling accuracy for the image restoration problem, on the other hand, is counterproductive, because of both the decreasing regularization and the increased computational time. VII. NEWRESTORATION APPROACHES We have described how the Hopfield model for a neural network can be used for solving an optimization problem that arises in signal and image recovery, namely superresolution or image restoration. There is a practical advantage in implementing such a procedure in this way.