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Yidong Luo

Yidong Luo appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.NANumerical AnalysisComputer Vision

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Published work

4 published item(s)

preprint2026arXiv

PolarVSR: A Unified Framework and Benchmark for Continuous Space-Time Polarization Video Reconstruction

Polarimetric imaging captures surface polarization characteristics, such as the Degree of Linear Polarization (DoLP) and the Angle of Polarization (AoP). In mainstream Division of-Focal-Plane (DoFP) color polarization imaging, recovering polarization parameters from captured mosaic arrays remains a challenging inverse problem. Existing DoFP cameras also face hardware bottlenecks and often cannot support high-frame-rate acquisition, limiting polarimetric imaging in dynamic video tasks. These limitations motivate joint spatial and temporal enhancement. To this end, we propose the first space-time polarization video reconstruction architecture. The method jointly models polarization directions in space and time and uses a polarization-aware implicit neural representation for continuous, high-fidelity upsampling. By analyzing temporal variations in polarization parameters, we further introduce a flow-guided polarization variation loss to supervise polarization dynamics. We also establish the first large-scale color DoFP polarization video benchmark to support this research direction. Extensive experiments on this benchmark demonstrate the effectiveness of the method.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A non-conditional divergence criteria of Petrov-Galerkin method for bounded linear operator equation

Petrov-Galerkin methods are always considered in numerical solutions of differential and integral equations $ Ax=b $. It is common to consider the convergence and error analysis when $ b \in \mathcal{R}(A) $ which make the equation solvable. However, the case when $ b \notin \mathcal{R}(A) $ is always ignored. In this paper, we consider the numerical behavior of Petrov-Galerkin methods when $ b \notin \mathcal{R}(A) $. It is a natural guess that when $ b \in \mathcal{R}(A) $, the corresponding approximate solution constructed by Petrov-Galerkin methods with arbitrary basis will diverge to infinity. We prove this conjecture for bounded linear operator equation with dense range $ \mathcal{R}(A) $ and give a more general divergence result for bounded linear operator equation with not necessarily dense range $ \mathcal{R}(A) $. Several applications show its power.

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preprint2020arXiv

Numerical analysis on boundary integral equation to exterior Dirichlet problem of Laplace equation

This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with trigonometric basis for the induced modified Symm's integral equation of the first kind on analytic boundary. Besides, utilizing the composite trapezial quadrature formula and trigonometric interpolation to handle the singularity in modified logarithmic kernel, we establish the numerical procedure for implementation. On these numerical examples, we compare the effect and efficiency of different Petrov-Galerkin and Galerkin-Collocation methods.

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preprint2020arXiv

Unified analysis on Petrov-Galerkin method into Symm's integral of the first kind

On bounded and simply connected planar analytic domain $ Ω$, by $ 2π$ periodic parametric representation of boundary curve $ \partial Ω$, Symm's integral equation of the first kind takes form $ K Ψ= g $, where $ K $ is seen as an operator mapping from $ L^2(0,2π) $ to itself. The classical result show complete convergence and error analysis in $ L^2 $ setting for least squares, dual least squares, Bubnov-Galerkin methods with Fourier basis when $ g \in H^r(0,2π), \ r \geq 1 $. In this paper, weakening the boundary $ \partial Ω$ from analytic to $ C^3 $ class, we maintain the convergence and error analysis from analytic case. Besides, it is proven that, when $ g \in H^r(0,2π), \ 0 \leq r < 1 $, the least squares, dual least squares, Bubnov-Galerkin methods with Fourier basis will uniformly diverge to infinity at first order. The divergence effect and optimality of first order rate are confirmed in an example.

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