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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…
Optical aberrations prevent telescopes from reaching their theoretical diffraction limit. Once estimated, these aberrations can be compensated for using deformable mirrors in a closed loop. Focal plane wavefront sensing enables the…
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…
Deformable image registration is one of the fundamental tasks in medical imaging. Classical registration algorithms usually require a high computational cost for iterative optimizations. Although deep-learning-based methods have been…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
Large-scale text-to-image models have demonstrated amazing ability to synthesize diverse and high-fidelity images. However, these models are often violated by several limitations. Firstly, they require the user to provide precise and…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Ptychography is a promising phase retrieval technique for visible light, X-ray and electron beams. Conventional ptychography reconstructs the amplitude and phase of an object light from a set of the diffraction intensity patterns obtained…
Human has an incredible ability to effortlessly perceive the viewpoint difference between two images containing the same object, even when the viewpoint change is astonishingly vast with no co-visible regions in the images. This remarkable…
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
Ptychography, a coherent diffraction imaging technique, has become an indispensable tool in materials characterization, biological imaging, and nanostructure analysis due to its capability for high-resolution, lensless reconstruction of…
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…
Curved refractive objects are common in the human environment, and have a complex visual appearance that can cause robotic vision algorithms to fail. Light-field cameras allow us to address this challenge by capturing the view-dependent…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…