Related papers: Torus computed tomography
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
We study the breakdown of rotational invariant tori in 2D and 4D standard maps by implementing three different methods. First, we analyze the domains of analyticity of a torus with given frequency through the computation of the Lindstedt…
We investigate aspects of Kauffman bracket skein algebras of surfaces and modules of 3-manifolds using quantum torus methods. These methods come in two flavors: embedding the skein algebra into a quantum torus related to quantum Teichmuller…
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from…
This paper is devoted to a Radon-type transform arising in a version of Photoacoustic Tomography that uses integrating circular detectors. We show that the transform can be decomposed into the spherical Radon transform and the…
Since X-ray tomography is now widely adopted in many different areas, it becomes more crucial to find a robust routine of handling tomographic data to get quality reconstructed images. Though there are several existing techniques, it seems…
Computed tomography (CT) is a non-destructive technique for observing internal images and has proven highly valuable in medical diagnostics. Recent advances in quantum computing have begun to influence tomographic reconstruction techniques.…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
To reduce the x-ray dose in computerized tomography (CT), many constrained optimization approaches have been proposed aiming at minimizing a regularizing function that measures lack of consistency with some prior knowledge about the object…
Topo-Tomography (TT) is a synchrotron-based X-ray diffraction imaging technique used to characterize grain shape and crystal orientation in polycrystalline samples. This work aims to provide a decisive and fundamental understanding of 3D…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
Since the Radon transform (RT) consists in a line integral function, some modeling assumptions are made on Computed Tomography (CT) system, making image reconstruction analytical methods, such as Filtered Backprojection (FBP), sensitive to…
Chest computed tomography (CT) imaging adds valuable insight in the diagnosis and management of pulmonary infectious diseases, like tuberculosis (TB). However, due to the cost and resource limitations, only X-ray images may be available for…
A 2-torus manifold is a closed connected smooth n-manifold with a non-free effective smooth $\mathbb{Z}^n_2$-action. In this paper, we prove that a 2-torus manifold is equivariantly formal if and only if the $\mathbb{Z}^n_2$-action is…
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…
Computed tomography (CT) scans offer a detailed, three-dimensional representation of patients' internal organs. However, conventional CT reconstruction techniques necessitate acquiring hundreds or thousands of x-ray projections through a…