相关论文: Emission tomography with a multi-bang assumption o…

The throughout knowledge of a X-ray beam spectrum is mandatory to assess the quality of its source device. Since the techniques to directly measurement such spectra are expensive and laborious, the X-ray spectrum reconstruction using…

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…

Deformable image registration is a standard engineering problem used to determine the distortion experienced by a body by comparing two images of it in different states. This study introduces two new DIR methods designed to capture…

Multi-exposure fusion (MEF) is a technique for combining different images of the same scene acquired with different exposure settings into a single image. All the proposed MEF algorithms combine the set of images, somehow choosing from each…

Semantic Image Segmentation facilitates a multitude of real-world applications ranging from autonomous driving over industrial process supervision to vision aids for human beings. These models are usually trained in a supervised fashion…

We investigate the inverse problem of recovering an initial source for the wave equation with fractional attenuation, motivated by photoacoustic tomography (PAT). The attenuation is modeled by a Caputo fractional derivative of order…

Atmospheric tomography, the problem of reconstructing atmospheric turbulence profiles from wavefront sensor measurements, is an integral part of many adaptive optics systems. It is used to enhance the image quality of ground-based…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…

We demonstrate spectroscopy of incoherent light with sub-diffraction resolution. In a proof-of-principle experiment we analyze the spectrum of a pair of incoherent point-like sources whose separation is below the diffraction limit. The two…

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…

Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…

Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple…

We consider the problem of two-photon cooperative emission in systems of two-level atoms. Two physically distinct regimes are analyzed. First, we investigate the case of a small number of atoms. We study the evolution of two-photon super-…

Stimulated emission tomography is a powerful and successful technique to both improve the resolution and experimentally simplify the task of determining the modal properties of biphotons. In the present manuscript we provide a theoretical…

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^n$. We consider two different geometries for the cone…

The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…

The production of single photons using rephased amplified spontaneous emission is examined. This process produces single photons on demand with high efficiency by detecting the spontaneous emission from an atomic ensemble, then applying a…

We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…