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Register a new userA Preconditioned Alternating Direction Method of Multipliers for the TV-$L^1$ Optical Flow via Dual Approach
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This work introduces a preconditioned dual optimization framework with the alternating direction method of multipliers (ADMM) to the optical flow estimates. By introducing efficient preconditioners with the multiscale pyramid, our preconditioned algorithms give competitive optical flow estimates under appropriate variational functional frameworks. We propose a novel preconditioned alternating direction methods of multipliers (ADMM) with convergenceguarantee for the total variation regularized optical flow problem through optimizing the dual problems. The numerical tests show the proposed preconditioned ADMM algorithms are very efficient for the total variation regularized optical flow estimates.
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In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The optimization algorithm that we develop not only gives the cartoon part and the texture part of an image but also gives the restored image (cartoon part + texture part). We also present the global convergence and the local linear convergence rate for the algorithm under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the dual ADMM (dADMM). Furthermore, we can obtain relatively higher signalto-noise ratio (SNR) comparing to other algorithms. It shows that the choice of the algorithm is also important even for the same model.
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to improve the performance of the method, such as the inertial technique. By studying the geometric properties of ADMM, we discuss the limitations of current inertial accelerated ADMM and then present and analyze an adaptive acceleration scheme for the method. Numerical experiments on problems arising from image processing, statistics and machine learning demonstrate the advantages of the proposed acceleration approach.
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