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Related papers: Detectable singularities from dynamic Radon data

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Let X be an open subset of R^2. We study the dynamic operator, A, integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be…

Analysis of PDEs · Mathematics 2018-11-12 Siamak RabieniaHaratbar

We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $\mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by…

Analysis of PDEs · Mathematics 2015-10-27 Jürgen Frikel , Eric Todd Quinto

We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…

Mathematical Physics · Physics 2018-09-11 Basil Grammaticos , Alfred Ramani , Ralph Willox , Takafumi Mase

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Machine Learning · Computer Science 2023-06-16 Julius von Rohrscheidt , Bastian Rieck

We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic…

Analysis of PDEs · Mathematics 2015-01-22 Jürgen Frikel , Eric Todd Quinto

A number of practically important imaging problems involve inverting the generalized Radon transform (GRT) $\mathcal R$ of a function $f$ in $\mathbb R^3$. On the other hand, not much is known about the spatial resolution of the…

Numerical Analysis · Mathematics 2019-08-29 Alexander Katsevich

The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and…

Robotics · Computer Science 2022-06-17 Isiah Zaplana , Hugo Hadfield , Joan Lasenby

Due to the robustness in sensing, radar has been highlighted, overcoming harsh weather conditions such as fog and heavy snow. In this paper, we present a novel radar-only place recognition that measures the similarity score by utilizing…

Robotics · Computer Science 2023-07-11 Hyesu Jang , Minwoo Jung , Ayoung Kim

In this paper we study reconstruction of a function $f$ from its discrete Radon transform data in $\mathbb R^3$ when $f$ has jump discontinuities. Consider a conventional parametrization of the Radon data in terms of the affine and angular…

Numerical Analysis · Mathematics 2019-03-21 Alexander Katsevich

Singularities of the Radon transform of a piecewise smooth function $f(x)$, $x\in R^n$, $n\geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $f(x)$ are…

Classical Analysis and ODEs · Mathematics 2008-02-03 Alexander G. Ramm , Alexander I. Zaslavsky

In many imaging applications it is important to assess how well the edges of the original object, $f$, are resolved in an image, $f^\text{rec}$, reconstructed from the measured data, $g$. In this paper we consider the case of image…

Statistics Theory · Mathematics 2025-06-23 Anuj Abhishek , Alexander Katsevich , James W. Webber

In this article, we consider a generalized Radon transform that comes up in ultrasound reflection tomography. In our model, the ultrasound emitter and receiver move at a constant distance apart along a circle. We analyze the microlocal…

Analysis of PDEs · Mathematics 2011-10-20 Gaik Ambartsoumian , Venky P. Krishnan , Eric Todd Quinto

We study the integral transform over a general family of broken rays in $\mathbb{R}^2$. It is natural for broken rays to have conjugate points, for example, when they are reflected from a curved boundary. If there are conjugate points, we…

Analysis of PDEs · Mathematics 2018-03-02 Yang Zhang

Radiography is often used to probe complex, evolving density fields in dynamic systems and in so doing gain insight into the underlying physics. This technique has been used in numerous fields including materials science, shock physics,…

High-energy X-ray diffraction methods can non-destructively map the 3D microstructure and associated attributes of metallic polycrystalline engineering materials in their bulk form. These methods are often combined with external stimuli…

We present a paradigm for characterization of artifacts in limited data tomography problems. In particular, we use this paradigm to characterize artifacts that are generated in reconstructions from limited angle data with generalized Radon…

Analysis of PDEs · Mathematics 2014-09-16 Jürgen Frikel , Eric Todd Quinto

Unprecedented atomic-scale measurement resolution has recently been demonstrated in single-shot optical localization metrology based on deep-learning analyses of diffraction patterns of topologically structured light scattered from objects.…

The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…

Classical Analysis and ODEs · Mathematics 2016-09-07 Michael Christ , Alexander Nagel , Elias M. Stein , Stephen Wainger

We tackle the problem of exploiting Radar for perception in the context of self-driving as Radar provides complementary information to other sensors such as LiDAR or cameras in the form of Doppler velocity. The main challenges of using…

Computer Vision and Pattern Recognition · Computer Science 2020-07-29 Bin Yang , Runsheng Guo , Ming Liang , Sergio Casas , Raquel Urtasun

Change detection in heterogeneous multitemporal satellite images is a challenging and still not much studied topic in remote sensing and earth observation. This paper focuses on comparison of image pairs covering the same geographical area…

Computer Vision and Pattern Recognition · Computer Science 2017-02-13 Luigi Tommaso Luppino , Stian Normann Anfinsen , Gabriele Moser , Robert Jenssen , Filippo Maria Bianchi , Sebastiano Serpico , Gregoire Mercier
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