Image restoration is one of the essential tasks in image processing. In order to restore images from blurs and noise while also preserving their edges, one often applies total variation (TV) minimization. Cauchy noise, which frequently appears in engineering applications, is a kind of impulsive and non-Gaussian noise. Removing Cauchy noise can be achieved by solving a nonconvex TV minimization problem, which is difficult due to its nonconvexity and nonsmoothness. In this paper, we adapt recent results in the literature and develop a specific alternating direction method of multiplier to solve this problem. Theoretically, we establish the convergence of our method to a stationary point. Experimental results demonstrate that the proposed method is competitive with other methods in visual and quantitative measures. In particular, our method achieves higher PSNRs for 0.5 dB on average.
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Canny Arithmetic Operator has been proved to be a traditional operator possessing a better detective effect in the common usage of edge detection algorithm currently. However, Canny Operator also has certain deficiencies, such as choices of dimensions and Threshold Limit Values. When the dimension is bigger, effect of noise to the edge is smaller, but the locating accuracy will be lost. Whereas, when the dimension is smaller, the locating accuracy will be high, but the ratio of Signal-to-Noise of output image will be lower. In the meantime, using a same Threshold Limit Values (TLV) in the whole image would also influence the edge detection in dissimilar districts. This paper presents an improved algorithm to the edge detection, which uses image pyramid theories to improve the Canny Operator. It is also demonstrated in this study that this method can rectify the shortage perfectly, and obtain a more ideal edge image.
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