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Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
We analyze multi-bounce propagation of light in an unknown hidden volume and demonstrate that the reflected light contains sufficient information to recover the 3D structure of the hidden scene. We formulate the forward and inverse theory…
This paper aims to recover object materials from posed images captured under an unknown static lighting condition. Recent methods solve this task by optimizing material parameters through differentiable physically based rendering. However,…
The calculation of the underground density field from measured gravity data has been done by a variety of methods of varied types. The use of the vector gravity components is here addressed in order to develop one accurate gravity inversion…
This paper summarizes the known physics of turbulent jets observed in laboratory experiments. The formula, which gives the power released in turbulence describes the concentration of turbulence/relativistic particles in each point of the…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
The transverse coherence functions (TCFs) of phase and amplitude fluctuations of a seismic wave are powerful to estimate the spatial distribution, length scales, and strength of random heterogeneities. However, TCFs have been formulated for…
It is shown that the evolution of an axially and reflection symmetric fluid distribution, satisfying the Tolman condition for thermal equilibrium, is not accompanied by the emission of gravitational radiation. This result, which was…
In this work, we summarize the current state of understanding of lateral displacement and angular deviations of an optical beam propagating through dielectric blocks. In part I, the analytical formulas, found for critical incidence, are…
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray…
Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of…
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
We consider the lateral shift of a light beam reflecting from a dielectric slab backed by a metal. It is found that the lateral shift of the reflected beam can be negative while the intensity of reflected beam is almost equal to the…
A planewave incident on an active etalon with net roundtrip gain may be expected to diverge in field amplitude, yet Maxwell's equations admit only a convergent solution. By examining a Gaussian beam obliquely incident on such a cavity, we…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…