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A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

Numerical Analysis · Mathematics 2017-08-08 Heikki Haario , Aki Kallonen , Marko Laine , Esa Niemi , Zenith Purisha , Samuli Siltanen

This paper deals with a method of tomographic reconstruction of radially symmetric objects from a single radiograph, in order to study the behavior of shocked material. The usual tomographic reconstruction algorithms such as generalized…

Optimization and Control · Mathematics 2007-05-23 Isabelle Abraham , Romain Abraham , Maitine Bergounioux

We propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality.…

Optimization and Control · Mathematics 2025-01-13 Geunyeong Byeon , Minseok Ryu , Zichao Wendy Di , Kibaek Kim

Deconvolving COMPTEL gamma-ray data into images presents a major methodological challenge. We developed a new algorithm called Multiresolution Regularized Expectation Maximization (MREM), which explicitly accounts for spatial correlations…

With the availability of more powerful computers, iterative reconstruction algorithms are the subject of an ongoing work in the design of more efficient reconstruction algorithms for X-ray computed tomography. In this work, we show how two…

Computer Vision and Pattern Recognition · Computer Science 2017-03-14 D. Trinca , Y. Zhong

In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision to other system parts or high attenuation at certain tilting angles. Image reconstruction…

Image and Video Processing · Electrical Eng. & Systems 2020-01-09 Yixing Huang , Shengxiang Wang , Yong Guan , Andreas Maier

Revealing the structure of complex biological macromolecules, such as proteins, is an essential step for understanding the chemical mechanisms that determine the diversity of their functions. Synchrotron based x-ray crystallography and…

X-ray fluorescence (XRF) enables element-specific, nondestructive imaging, but conventional raster scanning scales poorly with sample size, particularly for tomography, because measurements must be repeated at every projection angle and…

Optics · Physics 2026-04-14 A. Ben-Yehuda , A. Rack , S. Shwartz , N. Viganò

Single-pixel imaging, originally developed in light optics, facilitates fast three-dimensional sample reconstruction, as well as probing with light wavelengths undetectable by conventional multi-pixel detectors. However, the spatial…

Atmospheric tomography, the problem of reconstructing atmospheric turbulence profiles from wavefront sensor measurements, is an integral part of many adaptive optics systems used for enhancing the image quality of ground-based telescopes.…

Numerical Analysis · Mathematics 2025-02-06 Lukas Weissinger , Simon Hubmer , Bernadett Stadler , Ronny Ramlau

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…

Numerical Analysis · Mathematics 2016-02-24 Jae Kyu Choi , Bin Dong , Xiaoqun Zhang

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…

Statistical Mechanics · Physics 2012-06-07 Florent Krzakala , Marc Mézard , François Sausset , Yifan Sun , Lenka Zdeborová

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…

Data Analysis, Statistics and Probability · Physics 2018-03-13 Masamichi J. Miyama , Koji Hukushima

In the paper, we introduce an unconstrained analysis model based on the $\ell_{1}-\alpha \ell_{2}$ $(0< \alpha \leq1)$ minimization for the signal and image reconstruction. We develop some new technology lemmas for tight frame, and the…

Information Theory · Computer Science 2021-12-30 Peng Li , Huanmin Ge , Pengbo Geng

Imaging structures at the molecular level is a fast developing interdisciplinary research field that spans across the boundaries of physics and chemistry. High spatial resolution images of molecules can be obtained with photons or ultrafast…

Atomic Physics · Physics 2016-09-01 R. Puthumpally-Joseph , J. Viau-Trudel , M. Peters , T. T. Nguyen-Dang , O. Atabek , E. Charron

Scene reconstruction in the presence of high-speed motion and low illumination is important in many applications such as augmented and virtual reality, drone navigation, and autonomous robotics. Traditional motion estimation techniques fail…

Computer Vision and Pattern Recognition · Computer Science 2023-09-08 Sacha Jungerman , Atul Ingle , Mohit Gupta

We present a Machine Learning-based method for tomographic reconstruction of dense layered objects, with range of projection angles limited to $\pm $10$^\circ$. Whereas previous approaches to phase tomography generally require two steps,…

Image and Video Processing · Electrical Eng. & Systems 2020-01-08 Alexandre Goy , Girish Rughoobur , Shuai Li , Kwabena Arthur , Akintunde I. Akinwande , George Barbastathis

Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale three-dimensional data demands new mathematical tools…

Numerical Analysis · Mathematics 2016-08-15 Nikolay Koshev , Elias S. Helou , Eduardo X. Miqueles

Many imaging technologies rely on tomographic reconstruction, which requires solving a multidimensional inverse problem given a finite number of projections. Backprojection is a popular class of algorithm for tomographic reconstruction,…

Image and Video Processing · Electrical Eng. & Systems 2020-06-03 Xueqing Liu , Paul Sajda

The MARS scanner is designed for the x-ray spectroscopic study of samples with the aid of computer tomography methods. Computer tomography allows the reconstruction of slices of an investigated sample using a set of shadow projections…

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