Related papers: Regularized Newton Methods for X-ray Phase Contras…
New lensless diffractive X-ray technic for micro-scale imaging of biological tissue is based on quantitative phase retrieval schemes. By incorporating refraction, this method yields improved contrast compared to purely absorption-based…
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…
Imaging with hard x-rays is an invaluable tool in medicine, biology, materials science, and cultural heritage. Propagation-based x-ray phase-contrast imaging and tomography have been mostly used to resolve micrometer-scale structures inside…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
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…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the exact same image. Most current deterministic inversion techniques operate by approximately solving…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…
Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…
Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the…
Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…
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…
Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Paganin's method for image reconstruction in propagation-based phase-contrast X-ray imaging and tomography has enjoyed broad acceptance in recent years, with over one thousand publications citing its use. The present paper discusses…