Jingzhi Li

Jingzhi Li, Hongyu Liu, Zaijiu Shang et al.

We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave. The multiple scatterers could be extremely general with an unknown number of components, and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content. The second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting EM wavelength. The number of the obstacle components is not required to be known in advance, but the shape of each component must be from a certain known admissible class. The admissible class may consist of multiple different reference obstacles. The second scheme could also be extended to include the medium components if a certain generic condition is satisfied. Both schemes are based on some novel indicator functions whose indicating behaviors could be used to locate the scatterers. No inversion will be involved in calculating the indicator functions, and the proposed methods are every efficient and robust to noise. Rigorous mathematical justifications are provided and extensive numerical experiments are conducted to illustrate the effectiveness of the imaging schemes.

Deyue Zhang, Yukun Guo, Jingzhi Li et al.

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.

Jingzhi Li, Zongwei Wu, Eduard Zamfir et al.

Accurate 3D objects relighting in diverse unseen environments is crucial for realistic virtual object placement. Due to the albedo-lighting ambiguity, existing methods often fall short in producing faithful relights. Without proper constraints, observed training views can be explained by numerous combinations of lighting and material attributes, lacking physical correspondence with the actual environment maps used for relighting. In this work, we present ReCap, treating cross-environment captures as multi-task target to provide the missing supervision that cuts through the entanglement. Specifically, ReCap jointly optimizes multiple lighting representations that share a common set of material attributes. This naturally harmonizes a coherent set of lighting representations around the mutual material attributes, exploiting commonalities and differences across varied object appearances. Such coherence enables physically sound lighting reconstruction and robust material estimation - both essential for accurate relighting. Together with a streamlined shading function and effective post-processing, ReCap outperforms all leading competitors on an expanded relighting benchmark.

Jingzhi Li, Changjiang Luo, Ruoyu Chen et al.

Recent advances in multimodal large language models (MLLMs) have demonstrated strong capabilities in understanding general visual content. However, these general-domain MLLMs perform poorly in face perception tasks, often producing inaccurate or misleading responses to face-specific queries. To address this gap, we propose FaceInsight, the versatile face perception MLLM that provides fine-grained facial information. Our approach introduces visual-textual alignment of facial knowledge to model both uncertain dependencies and deterministic relationships among facial information, mitigating the limitations of language-driven reasoning. Additionally, we incorporate face segmentation maps as an auxiliary perceptual modality, enriching the visual input with localized structural cues to enhance semantic understanding. Comprehensive experiments and analyses across three face perception tasks demonstrate that FaceInsight consistently outperforms nine compared MLLMs under both training-free and fine-tuned settings.

Guan Wang, Fuming Ma, Yukun Guo et al.

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

Jingzhi Li, Xiaofei Li, Hongyu Liu

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties of the so-called interior transmission eigenfunctions, we develop a novel inverse scattering scheme. The proposed method can efficiently capture the cusp singularities of the support of the inhomogeneous medium. If further a priori information is available on the support of the medium, say, it is a convex polyhedron, then one can actually recover its shape. Both theoretical analysis and numerical experiments are provided. Our reconstruction method is new to the literature and opens up a new direction in the study of inverse scattering problems.

Yukun Guo, Jingzhi Li, Hongyu Liu et al.

This paper is concerned with the mathematical design of a novel input/instruction device using a moving emitter. The emitter generates a point source and can be installed on a digit pen or worn on the finger of the human being who wants to interact/communicate with the computer. The input/instruction can be recognized by identifying the motion trajectory of the emitter performed by the human being from the collected wave field data. The identification process is modelled as an in- verse source problem where one intends to identify the trajectory of a moving point source. There are several salient features of our study which distinguish our result from the existing ones in the literature. First, the point source is moving in an inhomogeneous background medium, which models the human body. Second, the dynamical wave field data are collected in a limited aperture. Third, the recon- struction method is independent of the background medium, and it is totally direct without any matrix inversion. Hence, it is efficient and robust with respect to the measurement noise. Both theoretical justifications and computational experiments are presented to verify our novel findings.

Huangxin Chen, Jingzhi Li, Weifeng Qiu

We propose a robust a posteriori error estimator for the hybridizable discontinuous Galerkin (HDG) method for convection-diffusion equations with dominant convection. The reliability and efficiency of the estimator are established for the error measured in an energy norm. The energy norm is uniformly bounded even when the diffusion coefficient tends to zero. The estimators are robust in the sense that the upper and lower bounds of error are uniformly bounded with respect to the diffusion coefficient. A weighted test function technique and the Oswald interpolation are key ingredients in the analysis. Numerical results verify the robustness of the proposed a posteriori error estimator. In numerical experiments, optimal convergence is observed.

Huangxin Chen, Guosheng Fu, Jingzhi Li et al.

We present and analyze a first order least squares method for convection dominated diffusion problems, which provides robust L2 a priori error estimate for the scalar variable even if the given data f in L2 space. The novel theoretical approach is to rewrite the method in the framework of discontinuous Petrov - Galerkin (DPG) method, and then show numerical stability by using a key equation discovered by J. Gopalakrishnan and W. Qiu [Math. Comp. 83(2014), pp. 537-552]. This new approach gives an alternative way to do numerical analysis for least squares methods for a large class of differential equations. We also show that the condition number of the global matrix is independent of the diffusion coefficient. A key feature of the method is that there is no stabilization parameter chosen empirically. In addition, Dirichlet boundary condition is weakly imposed. Numerical experiments verify our theoretical results and, in particular, show our way of weakly imposing Dirichlet boundary condition is essential to the design of least squares methods - numerical solutions on subdomains away from interior layers or boundary layers have remarkable accuracy even on coarse meshes, which are unstructured quasi-uniform.