Image Restoration Methods And Applications Based On Augmented Lagrangian Method

Image restoration aims to reconstruct the original image with high quality fromthe degraded image. Restoration quality and speed are always the major targets ofimage restoration research. As the preprocessing step of image processing, imagerestoration is of vary importance to make image segmentation, target identification，and image understanding easier.The Total variation (TV) minimization model has got lots of attention in imagerestoration due to its capability in preserving the edges of image. However,TV-based image restoration is a classic nonsmooth optimization problem, and thusfast optimization algorithms are required to be developed. Augmented Lagrangianmethod (ALM) is one class of promising methods among the fast optimization al-gorithms. Due to the clear theoretical framework and simple calculation, ALM pro-vides a way to solve total variation image restoration efficiently. In this paper, weanalyze TV-based image restoration model, variable splitting (VS), and classicALM algorithms. Based on these methods and models, we discuss the TV imagerestoration based on ALM and the situation when the image restoration model ownsmore regularization terms. We propose a new TV image restoration model based ondata fidelity variable splitting (DFVS) and give a fast algorithm to solving thismodel based on ALM. In the experiments, We further discuss the influence of imagerestoration with different variable splitting methods and augmented Lagrangianmethods based on the performance indicators of CPU time, peak signal to noise ra-tio (PSNR), objective function value and image quality assessment by conductingcomparative experiments. We give a detailed correlation about the quality of re-stored image and the performance of DFVS algorithm. The difference of ADMMand IALM are also concluded by experiments using algorithm SALSA and FTVd. Gradient vector flow active contour model (GVF Snake) is fact a problem ofimage restoration. Due to the ability to getting continuous single edge of the object,Snake has achieved a great success in image segmentation, object tracking and etc.Gradient vector flow (GVF) Snake and generalized GVF has become the importantresearch direction in Snake research, because of its new external force field owningthe ability to solve the problems of original Snake model which is sensitive to theinitial position of the contour and could not detect the concave edges of the image.In this paper, we analyze the fast GVF algorithm and GGVF algorithm based onALM. The experiments on different sizes of images showed the performance dif-ferences of GVF, GGVF algorithms based on ALM, multigrid method and the orig-inal algorithm.