<title>Adaptive regularization in image restoration using a model-based neural network</title>

Abstract

The determination of the regularization parameter is an important sub-problem in optimizing the performances of image restoration systems. The parameter controls the relative weightings of the data-conformance and model- conformance terms in the restoration cost function. A small parameter value would lead to noisy appearances in the smooth image regions due to over-emphasis of the data term, while a large parameter results in blurring of the textured regions due to dominance of the model term. Based on the principle of adopting small parameter values for the highly textured regions for detail emphasis while using large values for noise suppression in the smooth regions, a spatially adaptive regularization scheme was derived in this paper. An initial segmentation based on the local image activity was performed and a distinct regularization parameter was associated with each segmented component. The regional value was estimated by viewing the parameter as a set of learnable neuronal weights in a model-based neural network. A stochastic gradient descent algorithm based on the regional spatial characteristics and specific functional form of the neuronal weights was derived to optimize the regional parameter values. The efficacy of the algorithm was demonstrated by our observation of the emergence of small parameter values in textured regions and large values in smooth regions.