Image Restoration using Nonlocal Regularized Variational Model with Spatially Adapted Regularization Parameter

Abstract

Restoration of blurred images corrupted with impulse noise has attracted increasing attention due to its great potential toward practical applications. To guarantee the noisy image deblurring performance, total variation (TV), one of the most popular regularizers, has been extensively exploited in the literature. This local regularizer is known for its capability of preserving edges and penalizing oscillations but not sharp discontinuities. However, TV regularized variational models commonly suffer from undesirable staircase-like artifacts in homogeneous regions. The reason behind this phenomenon is that TV regularizer favors solutions that are piecewise constant in numerical experiments. To overcome the model-dependent deficiency, we proposed to replace the commonly used local regularizer by its nonlocal extension, i.e., nonlocal total variation (NLTV) regularizer. By taking advantage of the high degree of self-similarity within images, the proposed nonlocal variational model is able to remove both blurring and impulse noise while preserving meaningful image details. To guarantee solution stability and efficiency, the resulting nonsmooth image restoration problem was effectively dealt with using an alternating optimization algorithm. In addition, to further enhance the image quality, a local variance estimator-based automatic method was introduced to calculate the spatially adapted regularization parameters during image restoration. Extensive experiments have demonstrated that the proposed method could achieve superior imaging performance compared with several state-of-the-art image restoration methods.