Efficient schemes for joint isotropic and anisotropic total variation minimization for deblurring images corrupted by impulsive noise

Total variation (TV) model is a classical image restoration model. The introduction of this model is revolutionary, since TV can preserve discontinuities (edges) while removing other unwanted fine scale details. Lots of efficient methods have been successfully devised and applied to image restoration. However, many of them are sensitive to numerical errors. In this paper, we will first introduce a robust TV based model, which regularizes the restoration using joint isotropic and anisotropic total variation to suppress numerical errors, then present an efficiently iterative algorithm using augmented Lagrangian method. By separating the problem into three sub-problems, the algorithm can be solved efficiently either via fast Fourier transform (FFT) or closed form solution in each iteration. Finally, we use metric Q which is based upon singular value decomposition of local image gradient matrix to effectively measure true image content. Extensive numerical experiments demonstrate that our proposed model has better performance than several state-of-the-art algorithms in terms of signal-noise ratio and recovered image quality. (C) 2013 Elsevier Ltd. All rights reserved.