Adaptive regularization in image restoration by unsupervised learning

We present a neural network based image restoration approach which makes use of multiple regularization parameters within the same image to achieve adaptive regularization. We derived an unsupervised learning scheme that estimates the appropriate parameter value for each pixel site based on information provided by the dynamics of the neural network. This scheme is based on the principle of adopting small regularization parameters for the highly textured regions to emphasize the details, while using large regularization parameters for the smooth regions to suppress the more visible noise and ringing in those regions. A secondary parameter update process is incorporated after the primary image gray values update process, to determine the appropriate local parameter at each image pixel. The variables required in the adaptation equations of the auxiliary neuron arise as byproducts of computational results of the primary neuron. As a result, the determination of the regularization parameter only involves local computation and no explicit evaluation of the underlying cost function is required. The current algorithm was applied to a number of real world images. The results correspond closely to our original expectation in that the algorithm automatically adopts small regularization parameters for the highly textured regions while maintaining high parameters for smooth regions, thus resulting in an overall pleasing appearance for the restored images. (C) 1998 SPIE and IS&T. [S1017-9909(98)01801-7].