A Fast Augmented Lagrangian Method for Euler's Elastica Model

In this paper, a fast algorithm for Euler's elastica functional is proposed, in which the Euler's elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of sub-problems. To tackle the nonlinear constraints arising in the model, a novel fixed-point-based approach is proposed so that all the sub-problems either are linear problems or have closed form solutions. Numerical examples are provided to demonstrate the performance of the proposed method.