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We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$…

Inverse path tracing has recently been applied to joint material and lighting estimation, given geometry and multi-view HDR observations of an indoor scene. However, it has two major limitations: path tracing is expensive to compute, and…

The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…

We present a novel ray acceleration structure for radiative transfer outside of local thermodynamic equilibrium (non-LTE), leveraging techniques from computer graphics to improve computational efficiency. By applying mipmapping (local…

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…

Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…

We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number…

The nonlinear eigen-problem $ Ax+F(x)=\lambda x$ is studied where $A$ is an $n\times n$ irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the…

We present a general method to solve radiative transfer problems including scattering in the continuum as well as in lines in 3D configurations with periodic boundary conditions. he scattering problem for line transfer is solved via means…

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…

In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…

This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation…

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU$(2)$-nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional…

The techniques and software tools developed for the reduction and analysis of ISO-CAM/PHOT data with the LARI method are presented. The method, designed for the detection of faint sources in ISO raster observations, is based on the…

Here we report on the characterization of one of the large-volume LaBr$_{3}$:Ce detectors for the ELIGANT project at ELI-NP. The main focus of this work is the response function for high-energy $\gamma$ rays of such detectors. In…