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We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in…

Classical Analysis and ODEs · Mathematics 2016-05-13 Loukas Grafakos , Allan Greenleaf , Alex Iosevich , Eyvindur Palsson

Discrete Wavelet Transform (DWT) has been widely explored to enhance the performance of image superresolution (SR). Despite some DWT-based methods improving SR by capturing fine-grained frequency signals, most existing approaches neglect…

Computer Vision and Pattern Recognition · Computer Science 2025-11-05 Peng Du , Hui Li , Han Xu , Paul Barom Jeon , Dongwook Lee , Daehyun Ji , Ran Yang , Feng Zhu

Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…

Neural and Evolutionary Computing · Computer Science 2025-06-10 Raoof HojatJalali , Edmondo Trentin

For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…

Functional Analysis · Mathematics 2025-08-26 I. V. Anikin

Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…

Numerical Analysis · Mathematics 2021-02-19 Alexander Katsevich

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…

Numerical Analysis · Mathematics 2016-07-19 Markus Haltmeier , Sunghwan Moon

The core problem of Magnetic Resonance Imaging (MRI) is the trade off between acceleration and image quality. Image reconstruction and super-resolution are two crucial techniques in Magnetic Resonance Imaging (MRI). Current methods are…

Image and Video Processing · Electrical Eng. & Systems 2021-12-16 Chun-Mei Feng , Yunlu Yan , Huazhu Fu , Li Chen , Yong Xu

We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is…

Functional Analysis · Mathematics 2018-05-09 Santiago Córdova , Daniel Vera

Effectively parsing the facade is essential to 3D building reconstruction, which is an important computer vision problem with a large amount of applications in high precision map for navigation, computer aided design, and city generation…

Computer Vision and Pattern Recognition · Computer Science 2021-06-03 Hantang Liu , Wentong Li , Jianke Zhu

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…

Computer Vision and Pattern Recognition · Computer Science 2017-03-02 Renata Khasanova , Pascal Frossard

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of…

Symbolic Computation · Computer Science 2014-09-04 R. Bradford , C. Chen , J. H. Davenport , M. England , M. Moreno Maza , D. Wilson

The advent of enhanced technologies in radio interferometry and the perspective of the SKA telescope bring new challenges in image reconstruction. One of these challenges is the spatio-spectral reconstruction of large (Terabytes) data cubes…

Instrumentation and Methods for Astrophysics · Physics 2016-03-07 Jérémy Deguignet , André Ferrari , David Mary , Chiara Ferrari

For conventional computed tomography (CT) image reconstruction tasks, the most popular method is the so-called filtered-back-projection (FBP) algorithm. In it, the acquired Radon projections are usually filtered first by a ramp kernel…

Medical Physics · Physics 2018-07-06 Yongshuai Ge , Qiyang Zhang , Zhanli Hu , Jianwei Chen , Wei Shi , Hairong Zheng , Dong Liang

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

Increasingly in medical imaging has emerged an issue surrounding the reconstruction of noisy images from raw measurement data. Where the forward problem is the generation of raw measurement data from a ground truth image, the inverse…

Image and Video Processing · Electrical Eng. & Systems 2020-03-24 Adam Peace

An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…

Functional Analysis · Mathematics 2015-09-24 Fatma Terzioglu

Deep learning has significantly advanced medical imaging analysis, yet variations in image resolution remain an overlooked challenge. Most methods address this by resampling images, leading to either information loss or computational…

Computer Vision and Pattern Recognition · Computer Science 2025-03-14 Ashay Patel , Michela Antonelli , Sebastien Ourselin , M. Jorge Cardoso

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Wenqi Lu , Jinming Duan , David Orive-Miguel , Lionel Herve , Iain B Styles

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky