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Related papers: Shape recovery from sparse tomographic X-ray data

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Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization…

Computer Vision and Pattern Recognition · Computer Science 2023-08-01 Yuxin Zhang , Clément Huneau , Jérôme Idier , Diana Mateus

The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-05 Yushan Gao , Thomas Blumensath

We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear…

Computer Vision and Pattern Recognition · Computer Science 2013-12-02 Joseph Shtok , Michael Zibulevsky , Michael Elad

This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…

Functional Analysis · Mathematics 2013-03-04 Alireza Aghasi , Justin Romberg

We introduce single-shot X-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Ajinkya Kadu , Tristan van Leeuwen , K. Joost Batenburg

X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…

Image and Video Processing · Electrical Eng. & Systems 2022-01-25 Attila Juhos

This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational…

Graphics · Computer Science 2024-02-19 Hua Li , Lu Zhang , Ruoxi Guo , Zushang Xiao , Rui Guo

This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries.This regularity often carries crucial…

Numerical Analysis · Mathematics 2024-01-26 Babak Maboudi Afkham , Nicolai André Brogaard Riis , Yiqiu Dong , Per Christian Hansen

We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…

Numerical Analysis · Mathematics 2025-11-18 Markus Harju , Suvi Anttila , Teemu Tyni

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…

Computational Geometry · Computer Science 2024-10-08 Diana Marin , Filippo Maggioli , Simone Melzi , Stefan Ohrhallinger , Michael Wimmer

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

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…

Numerical Analysis · Mathematics 2018-01-17 Zenith Purisha , Juho Rimpeläinen , Tatiana Bubba , Samuli Siltanen

Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…

Image and Video Processing · Electrical Eng. & Systems 2022-07-28 Sayantan Bhadra , Umberto Villa , Mark A. Anastasio

Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…

In computed tomography, data consist of measurements of the attenuation of X-rays passing through an object. The goal is to reconstruct the linear attenuation coefficient of the object's interior. For each position of the X-ray source,…

We propose a direct reconstruction algorithm for Computed Tomography, based on a local fusion of a few preliminary image estimates by means of a non-linear fusion rule. One such rule is based on a signal denoising technique which is…

Computer Vision and Pattern Recognition · Computer Science 2010-04-27 Joseph Shtok , Michael Zibulevsky , Michael Elad

Computed Tomography (CT) is a technology that reconstructs cross-sectional images using X-ray images taken from multiple directions. In CT, hundreds of X-ray images acquired as the X-ray source and detector rotate around a central axis, are…

Image and Video Processing · Electrical Eng. & Systems 2024-12-05 Shin Kim

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…

Computer Vision and Pattern Recognition · Computer Science 2026-02-11 Chuyang Wu , Samuli Siltanen

We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…

Image and Video Processing · Electrical Eng. & Systems 2022-06-28 Icíar Lloréns Jover , Thomas Debarre , Shayan Aziznejad , Michael Unser

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…

Analysis of PDEs · Mathematics 2018-09-20 Henrik Garde , Stratos Staboulis