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Terahertz (THz) tomography is a rather novel technique for nondestructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from…

Numerical Analysis · Mathematics 2016-01-19 Jens Tepe , Thomas Schuster , Benjamin Littau

We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryo-EM dataset. The dataset contains noisy tomographic projections of the electrostatic potential of the…

Image and Video Processing · Electrical Eng. & Systems 2023-02-08 Carlos Esteve-Yagüe , Willem Diepeveen , Ozan Öktem , Carola-Bibiane Schönlieb

We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…

Computer Vision and Pattern Recognition · Computer Science 2013-09-19 Gilles Puy , Pierre Vandergheynst

In ultrasound nondestructive testing, a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using…

Signal Processing · Electrical Eng. & Systems 2020-12-09 Jan Kirchhof , Sebastian Semper , Christoph W. Wagner , Eduardo Pérez , Florian Römer , Giovanni Del Galdo

Recent research in tomographic reconstruction is motivated by the need to efficiently recover detailed anatomy from limited measurements. One of the ways to compensate for the increasingly sparse sets of measurements is to exploit the…

Computer Vision and Pattern Recognition · Computer Science 2017-12-08 Preeti Gopal , Ritwick Chaudhry , Sharat Chandran , Imants Svalbe , Ajit Rajwade

We propose a noise-resilient deep reconstruction algorithm for X-ray tomography. Our approach shows strong noise resilience without obtaining noisy training examples. The advantages of our framework may further enable low-photon tomographic…

Image and Video Processing · Electrical Eng. & Systems 2022-11-29 Zhen Guo , Zhiguang Liu , Qihang Zhang , George Barbastathis , Michael E. Glinsky

Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…

Materials Science · Physics 2014-08-26 Jason F. Panzarino , Timothy J. Rupert

A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter…

Statistics Theory · Mathematics 2013-11-18 Yoshio Komori , Hideo Hirose

Optical projection tomography (OPT) is a powerful tool for biomedical studies. It achieves 3D visualization of mesoscopic biological samples with high spatial resolution using conventional tomographic-reconstruction algorithms. However,…

Computer Vision and Pattern Recognition · Computer Science 2023-10-02 Yan Liu , Jonathan Dong , Thanh-An Pham , Francois Marelli , Michael Unser

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…

Numerical Analysis · Mathematics 2016-11-23 Markus Haltmeier , Thomas Berer , Sunghwan Moon , Peter Burgholzer

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Mathematical Physics · Physics 2023-05-03 M. H. Ding , H. Y. Liu , G. H. Zheng

Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our…

Quantum Physics · Physics 2019-08-14 Martin Kliesch , Richard Kueng , Jens Eisert , David Gross

In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after…

Image and Video Processing · Electrical Eng. & Systems 2021-04-20 Daniel Otero Baguer , Johannes Leuschner , Maximilian Schmidt

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption…

Numerical Analysis · Mathematics 2016-01-20 Antti Hannukainen , Lauri Harhanen , Nuutti Hyvönen , Helle Majander

Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…

Computer Vision and Pattern Recognition · Computer Science 2016-06-21 Atishay Jain

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

Statistical Mechanics · Physics 2012-08-20 Florent Krzakala , Marc Mézard , François Sausset , Yifan Sun , Lenka Zdeborová

We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear…

Numerical Analysis · Mathematics 2012-09-20 Stefania Petra , Christoph Schnörr , Andreas Schröder

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction…

Image and Video Processing · Electrical Eng. & Systems 2022-01-12 Lauren Partin , Daniele E. Schiavazzi , Carlos A. Sing Long

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…

Mathematical Physics · Physics 2015-06-17 Paolo Facchi , Marilena Ligabò , Sergio Solimini