#### Technical Report USC-SIPI-112

“Image Restoration Using a Neural Network”

by Yi-Tong Zhou, B. Keith Jenkins, and Rama Chellappa

A new approach for restoration of grey level images degraded by a known shift invariant blur function and additive noise is presented using a neural computational network. A neural network model is employed to represent a possibly nonstationary image whose gray level function is the simple sum of the neuron state variables. The restoration procedure consists of two stages: estimation of the parameters of the neural network model and reconstruction of images. During the first stage, the parameters are estimated by comparing the energy function of the neural network with a constrained error function. The nonlinear restoration method is then carried out iteratively in the second stage by using a dynamic algorithm to minimize the energy function of an appropriate neural network. Owing to the model's fault-tolerant nature and computation capability, a high quality image is obtained using this approach. A practical algorithm with reduced computational complexity is also presented. Several computer simulation examples involving synthetic and real images are given to illustrate the usefulness of our method. The choice of the boundary values to reduce the ringing effect is discussed and comparisons with other restoration methods such as the SVD pseudoinverse filter, minimum mean square error (MMSE) filter and modified MMSE filter using Gaussian Markov random field model are given.

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