Related papers: The Radon transform and the Hough transform: a uni…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
Computer vision tasks require processing large amounts of data to perform image classification, segmentation, and feature extraction. Optical preprocessors can potentially reduce the number of floating point operations required by computer…
Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…
With the rapidly growing population of resident space objects (RSOs) in the near-Earth space environment, detailed information about their condition and capabilities is needed to provide Space Domain Awareness (SDA). Space-based sensing…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
It is convenient to calibrate time-of-flight cameras by established methods, using images of a chequerboard pattern. The low resolution of the amplitude image, however, makes it difficult to detect the board reliably. Heuristic detection…
This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is…
Using integral transforms to the end of lines detection in images with complex background, makes the detection a hard task needing additional processing to manage the detection. As an integral transform, the Scale Space Radon Transform…
Digital in-line holography is commonly used to reconstruct 3D images from 2D holograms for microscopic objects. One of the technical challenges that arise in the signal processing stage is removing the twin image that is caused by 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…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the…
In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions…
Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions…
A ridge is a function that is characterized by a one-dimensional profile (activation) and a multidimensional direction vector. Ridges appear in the theory of neural networks as functional descriptors of the effect of a neuron, with the…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…