Related papers: Single pixel X-ray transform and related inverse p…

We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…

In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens…

In this paper, we propose a technique named reflection F-scan or RF-scan, that can be used to measure the nonlinear-refractive index n_2 of thin-film semiconductors. In this technique, a p-polarized Gaussian beam is focused using an…

Materials exposed to intense femtosecond X-ray pulses with energies above their K-shell absorption edge can enter an extremely ionized state, which could give rise to nonlinear phenomena, such as saturable absorption and reverse saturable…

X-ray dark-field imaging creates a representation of the sample where contrast is generated by subresolution features within the volume under inspection. These are detected by a local measurement of the radiation field's angular…

This paper considers the problem of undersampled MRI reconstruction. We propose a novel Transformer-based framework for directly processing signal in k-space, going beyond the limitation of regular grids as ConvNets do. We adopt an implicit…

In this article we study uniqueness and nonuniqueness for potential reconstruction from one boundary measurement in quantum fields, associated with the steady state Schr\"{o}dinger equation. It is an extension of our recent work…

We demonstrate single-pixel imaging in the spectral domain by encoding Fourier probe patterns onto the spectrum of a superluminescent laser diode using a programmable optical filter. As a proof-of-concept, we measure the…

We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…

3D image reconstruction from a set of X-ray projections is an important image reconstruction problem, with applications in medical imaging, industrial inspection and airport security. The innovation of X-ray emitter arrays allows for a…

In this paper, a new phase-retrieval algorithm from an X-ray schlieren image is proposed. The schlieren method allows phase-contrast imaging with an objective lens and a knife-edge filter placed at the back focal plane of the objective.…

Single Pixel Imaging is an emerging imaging technique that employs a bucket detector (photodiode) to sample a spatially modulated light field, rather than measuring the spatial distribution with an array of detectors. This approach provides…

In this paper we reverse engineer the Sony IMX219PQ image sensor, otherwise known as the Raspberry Pi Camera v2.0. We provide a visual reference for pixel non-uniformity by analysing variations in transistor length, microlens optic system…

While it is well known that X-ray tomography using a polychromatic source is non-linear, as the linear attenuation coefficient depends on the wavelength of the X-rays, tomography using near monochromatic sources are usually assumed to be a…

This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…

Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension.…

Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…

Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our…

A Radon-type transform called a cone transform that assigns to a given function its integral over various sets of cones has arisen in the last decade in the context of the study of Compton cameras used in Single Photon Emission Computed…