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Three-dimensional electron tomography is used to understand the structure and properties of samples in chemistry, materials science, geoscience, and biology. With the recent development of high-resolution detectors and algorithms that can…
Lost image areas with different size and arbitrary shape can occur in many scenarios such as error-prone communication, depth-based image rendering or motion compensated wavelet lifting. The goal of image reconstruction is to restore these…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce…
Dielectric tensor tomography is an imaging technique for mapping three-dimensional distributions of dielectric properties in transparent materials. This work introduces an enhanced illumination strategy employing a micro-electromechanical…
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…
The nucleation of quasicrystals remains a fundamental puzzle, primarily due to the absence of a periodic translational template. Here, we demonstrate that phasons - hidden degrees of freedom unique to quasiperiodic order - drive diverse…
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and…
Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution…
In this letter, we investigate the coherent tunneling process of photons between a defected circular resonator and a waveguide based on the recently developed discrete coordinate scattering methods (L. Zhou et al., Phys. Rev. Lett. 101,…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from…
Single-shot wide-angle diffraction imaging is a widely used method to investigate the structure of non-crystallizing objects such as nanoclusters, large proteins or even viruses. Its main advantage is that information about the…
Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
Computed tomography (CT) has become an essential part of modern science and medicine. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source, a detector captures X-rays…
Fourier Ptychographic Microscopy (FPM) is a computational imaging method that is able to super-resolve features beyond the diffraction-limit set by the objective lens of a traditional microscope. This is accomplished by using synthetic…