Jintao Song

Jintao Song, Wenqi Lu, Yunwen Lei et al.

The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameters, including both the associated penalty and relaxation parameters, often relies on empirical approaches tailored to specific problem domains and contextual scenarios. Incorrect parameter selection can significantly hinder ADMM's convergence rate. To address this challenge, in this paper we first propose a general approach to optimize the value of penalty parameter, followed by a novel closed-form formula to compute the optimal relaxation parameter in the context of linear quadratic problems (LQPs). We then experimentally validate our parameter selection methods through random instantiations and diverse imaging applications, encompassing diffeomorphic image registration, image deblurring, and MRI reconstruction.

Huizhu Pan, Jintao Song, Wanquan Liu et al.

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snake model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model (GAC). The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform (FFT) or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

Jintao Song, Huizhu Pan, Wuanquan Liu et al.

In order to completely separate objects with large sections of occluded boundaries in an image, we devise a new variational level set model for image segmentation combining the Chan-Vese model with elastica and landmark constraints. For computational efficiency, we design its Augmented Lagrangian Method (ALM) or Alternating Direction Method of Multiplier (ADMM) method by introducing some auxiliary variables, Lagrange multipliers, and penalty parameters. In each loop of alternating iterative optimization, the sub-problems of minimization can be easily solved via the Gauss-Seidel iterative method and generalized soft thresholding formulas with projection, respectively. Numerical experiments show that the proposed model can not only recover larger broken boundaries but can also improve segmentation efficiency, as well as decrease the dependence of segmentation on parameter tuning and initialization.