Related papers: Paraxial diffusion-field retrieval
Conditional random fields (CRFs) are popular discriminative models for computer vision and have been successfully applied in the domain of image restoration, especially to image denoising. For image deblurring, however, discriminative…
The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
We study the sampling of spatial fields using sensors that are location-unaware but deployed according to a known statistical distribution. It has been shown that uniformly distributed location-unaware sensors cannot infer bandlimited…
The structure of the diffusion regions in antiparallel magnetic reconnection is investigated by means of a theory and a Vlasov simulation. The magnetic diffusion is considered as relaxation to the frozen-in state, which depends on a…
Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Dark-field images are formed by small-angle scattering of x-ray photons. The small-angle scattering signal is particularly sensitive to structural variations and density fluctuation on a length scale of several ten to hundred nanometers,…
We propose a diffusion model for the recently discovered diffusion-induced Ramsey narrowing arising when atoms diffuse in a buffer-gas cell in the laser radiation field. The diffusion equation for the coherence of metastable states coupled…
The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices…
We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are…
An overview is provided over the physics of dielectric microcavities with non-paraxial mode structure; examples are microdroplets and edge-emitting semiconductor microlasers. Particular attention is given to cavities in which two spatial…
The parabolic approximation is developed for high energy charged particles scattering in a bent crystal with variable curvature. The general form of parabolic equation is received for atomic chains located along coordinate axis of…
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
Consider a scalar reflected diffusion $(X_t:t\geq 0)$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for…
While a few methods for the determination of depth-resolved strain distributions each with inherent limitations are available, tomographic reconstruction has been applied to this problem in only a limited sense. One of the challenges was…
The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop…