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Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We establish the general form of a geometric comparison principle for $n$-fold convolutions of certain singular measures in $\mathbb{R}^d$ which holds for arbitrary $n$ and $d$. This translates into a pointwise inequality between the…
In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
We present a variational approach for directed polymers in $D$ transversal dimensions which is used to compute the corrections to the mean field theory predictions with broken replica symmetry. The trial function is taken to be a…
The recently developed quadrature by expansion (QBX) technique accurately evaluates the layer potentials with singular, weakly or nearly singular, or even hyper singular kernels in the integral equation reformulations of partial…
We present a new perspective on the weak approximation conjecture of Hassett and Tschinkel: formal sections of a rationally connected fibration over a curve can be approximated to arbitrary order by regular sections. The new approach…
In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane…
Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plane curve. Our solutions are complex contour integral…
In this work, we address specular appearance in inverse rendering using 2D Gaussian splatting with deferred shading and argue for a refinement stage to improve specular detail, thereby bridging the gap with reconstruction-only methods. Our…
We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…
Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general…