Related papers: The Broken Ray Transform: Additional Properties an…
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…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events…
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…
The paper studies various properties of the V-line transform (VLT) in the plane and conical Radon transform (CRT) in $\mathbb{R}^n$. VLT maps a function to a family of its integrals along trajectories made of two rays emanating from a…
Here we introduce a new forward model and imaging modality for Bragg Scattering Tomography (BST). The model we propose is based on an X-ray portal scanner with linear detector collimation, currently being developed for use in airport…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in…
We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…
The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity…
In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image…
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…