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Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
21cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a…
Accurate and robust wavefront reconstruction methods for pyramid wavefront sensors are in high demand as these sensors are planned to be part of many instruments currently under development for ground based telescopes. The pyramid sensor…
Nonlinear processes lie at the heart of many technologies such as frequency converters and entangled photon sources. Historically, observation and manipulation of these processes, for instance through nanostructures, has been limited to…
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear…
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard…
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…
The validity of two approximative linear tensor models to be used for grating based X-ray or neutron dark-field tensor tomography is investigated in a simulation study. While the dark-field contrast originating from anisotropic microscopic…
We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
The translation of an early (1957), Russian article on the development of x-ray computed tomography is provided. The article demonstrates a principle possibility of determining the local attenuation coefficient in every element of a…
The development of new techniques to improve measurements is crucial for all sciences. By employing quantum systems as sensors to probe some physical property of interest allows the application of quantum resources, such as coherent…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…