Research On Image Restoration’s Algorithms Based On Total Variation

Images are produced to record or display useful information. Due to the imper-fections in the imaging and capturing process, however, the final image invariably rep-resents a degraded version of the original scene. The undoing of these imperfections, i.e., image restoration, is critical to many of the subsequent image processing tasks. Therefore, image restoration (sometimes referred to as image deblurring or image de-convolution) becomes a very important research subject.Total variation (TV) model is a classical image restoration model. The introduc-tion of this model is revolutionary, since TV can preserve discontinuities (edges) while removing other unwanted fine scale details. Lots of efficient methods have been suc-cessfully devised and applied to image restoration. However, many of them are sensitive to numerical errors.In this paper, we will first study classical image restoration models and corre-sponding algorithms by analyzing the advantages and disadvantages, and design new TV-based model, which regularizes the restoration using joint isotropic and anisotropic total variation to suppress numerical errors, to address the problems found. Then, we present an efficiently iterative algorithm using augmented Lagrangian method. By sep-arating 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.Although our model has better performance than classical FTVd and ALM models in terms of signal-noise-ratio and recovered images’quality, the algorithm designed ac-cording to our model does not take the structure of an image into account and is stopped at the wrong time. This is because MSE is used as the metric for measuring the closeness of two variables and determines when to stop the algorithm. Therefore, we redesign our algorithm by replacing MSE with a new metric Q, which is based upon singular value decomposition of local image gradient matrix to effectively measure true image con-tend and is properly correlated with noise level, sharpness and intensity contrast of the structured regions of an image.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, and our improved algorithm runs almost as fast as them.