In order to remove speckle noise while preserving image features, a novel variational model for image restoration based on total curvature is proposed in this paper. Due to the characteristics of nonlinear, non-convex, and non-smooth, the proposed variational model is transformed into an alternating optimization problem through introducing a series of auxiliary variables and using the alternating direction method of multipliers. In each loop of optimization, the Fast Fourier Transform is employed to solve the involved partial differential equations numerically, and the generalized soft thresholding formula is used to solve the involved algebra equations analytically. Moreover, the projection method is applied to fulfill some related inequality constraints simply for different sub-problems, thus the computational efficiency is improved totally. The numerous experiments on synthetic and real cases are implemented to demonstrate the advantages of the proposed model in image edge and corner preserving, and to indicate the high computation efficiency of the designed algorithm through comparison with other fast algorithms. INDEX TERMS Speckle noise, curvature-dependent, alternating direction method of multipliers, discrete Fourier transform.

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