Bo Han

Jing Wang, Wei Wang, Bo Han

In this paper, we discuss the construction, analysis and implementation of a novel iterative regularization scheme with general convex penalty term for nonlinear inverse problems in Banach spaces based on the homotopy perturbation technique, in an attempt to detect the special features of the sought solutions such as sparsity or piecewise constant. By using tools from convex analysis in Banach spaces, we provide a detailed convergence and stability results for the presented algorithm. Numerical simulations for one-dimensional and two-dimensional parameter identification problems are performed to validate that our approach is competitive in terms of reducing the overall computational time in comparison with the existing Landweber iteration with general convex penalty.

Jing Wang, Bo Han, Wei Wang

Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to preserve local smoothness, and the current L1-norm can enforce the sparsity to preserve sharp edges. Considering the fact that L2-norm penalty always makes the solution overly smooth and L1-norm penalty always makes the solution too sparse, elastic-net regularization approach with a convex combination term of L1-norm and L2-norm emerges for fully nonlinear EIT inverse problems. Our aim is to combine the strength of both terms: sparsity in the transform domain and smoothness in the physical domain, in an attempt to improve the reconstruction resolution and robustness to noise. Nonlinearity and non-smoothness of the generated composite minimization problem make it challenging to find an efficient numerical solution. Then we develop one simple and fast numerical optimization scheme based on the split Bregman technique for the joint penalties regularization. The method is validated using simulated data for some typical conductivity distributions. Results indicate that the proposed inversion model with an appropriate parameter choice achieves an efficient regularization solution and enhances the quality of the reconstructed image.

Wei Yao, Zhanke Zhou, Zhicong Li et al.

It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the concerned fairness definition and solve a constrained optimization problem. However, it is intriguing in previous work that such fairness surrogate functions may yield unfair results and high instability. In this work, in order to deeply understand them, taking a widely used fairness definition--demographic parity as an example, we show that there is a surrogate-fairness gap between the fairness definition and the fairness surrogate function. Also, the theoretical analysis and experimental results about the gap motivate us that the fairness and stability will be affected by the points far from the decision boundary, which is the large margin points issue investigated in this paper. To address it, we propose the general sigmoid surrogate to simultaneously reduce both the surrogate-fairness gap and the variance, and offer a rigorous fairness and stability upper bound. Interestingly, the theory also provides insights into two important issues that deal with the large margin points as well as obtaining a more balanced dataset are beneficial to fairness and stability. Furthermore, we elaborate a novel and general algorithm called Balanced Surrogate, which iteratively reduces the gap to mitigate unfairness. Finally, we provide empirical evidence showing that our methods consistently improve fairness and stability while maintaining accuracy comparable to the baselines in three real-world datasets.

Bo Han, Heqing Zou, Haoyang Li et al.

Text-based talking-head video editing aims to efficiently insert, delete, and substitute segments of talking videos through a user-friendly text editing approach. It is challenging because of \textbf{1)} generalizable talking-face representation, \textbf{2)} seamless audio-visual transitions, and \textbf{3)} identity-preserved talking faces. Previous works either require minutes of talking-face video training data and expensive test-time optimization for customized talking video editing or directly generate a video sequence without considering in-context information, leading to a poor generalizable representation, or incoherent transitions, or even inconsistent identity. In this paper, we propose an efficient cascaded conditional diffusion-based framework, which consists of two stages: audio to dense-landmark motion and motion to video. \textit{\textbf{In the first stage}}, we first propose a dynamic weighted in-context diffusion module to synthesize dense-landmark motions given an edited audio. \textit{\textbf{In the second stage}}, we introduce a warping-guided conditional diffusion module. The module first interpolates between the start and end frames of the editing interval to generate smooth intermediate frames. Then, with the help of the audio-to-dense motion images, these intermediate frames are warped to obtain coarse intermediate frames. Conditioned on the warped intermedia frames, a diffusion model is adopted to generate detailed and high-resolution target frames, which guarantees coherent and identity-preserved transitions. The cascaded conditional diffusion model decomposes the complex talking editing task into two flexible generation tasks, which provides a generalizable talking-face representation, seamless audio-visual transitions, and identity-preserved faces on a small dataset. Experiments show the effectiveness and superiority of the proposed method.