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Reconstructing images from downsampled and noisy measurements, such as MRI and low dose Computed Tomography (CT), is a mathematically ill-posed inverse problem. We propose an easy-to-use reconstruction method based on Expectation…

Image and Video Processing · Electrical Eng. & Systems 2022-08-29 Robert G. Aykroyd , Kehinde Olobatuyi

Electrical tomography techniques have been widely employed for multiphase-flow monitoring owing to their non invasive nature, intrinsic safety, and low cost. Nevertheless, conventional reconstructions struggle to capture fine details, which…

Image and Video Processing · Electrical Eng. & Systems 2025-12-23 Wejian Yan

This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…

Numerical Analysis · Mathematics 2025-07-22 Kai Li , Kwancheol Shin , Zhi Zhou

The recent years have seen a surge of interest in methods for imaging beyond the direct line of sight. The most prominent techniques rely on time-resolved optical impulse responses, obtained by illuminating a diffuse wall with an ultrashort…

Computer Vision and Pattern Recognition · Computer Science 2020-01-30 Javier Grau Chopite , Matthias B. Hullin , Michael Wand , Julian Iseringhausen

We review a resistor network approach to the numerical solution of the inverse problem of electrical impedance tomography (EIT). The networks arise in the context of finite volume discretizations of the elliptic equation for the electric…

Mathematical Physics · Physics 2015-06-03 Liliana Borcea , Vladimir Druskin , Fernando Guevara Vasquez , Alexander V. Mamonov

This work examines two ways of using proper orthogonal decomposition (POD) to enhance the prior work of EITPose, a device which uses electrical impedance tomography (EIT) to detect posture by way of a band of electrodes on the forearm.…

Human-Computer Interaction · Computer Science 2024-12-12 Jessie Sheflin

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…

Analysis of PDEs · Mathematics 2015-05-20 Peter Kuchment , Leonid Kunyansky

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous…

Optimization and Control · Mathematics 2019-02-20 Bolaji James Adesokan , Bjørn Jensen , Bangti Jin , Kim Knudsen

Electron tomography is a powerful tool for understanding the morphology of materials in three dimensions, but conventional reconstruction algorithms typically suffer from missing-wedge artifacts and data misalignment imposed by experimental…

Image and Video Processing · Electrical Eng. & Systems 2025-12-10 Cedric Lim , Corneel Casert , Arthur R. C. McCray , Serin Lee , Andrew Barnum , Jennifer Dionne , Colin Ophus

The inverse problem in Acousto-Electric tomography concerns the reconstruction of the electric conductivity in a domain from knowledge of the power density function in the interior of the body. This interior power density results from…

Numerical Analysis · Mathematics 2020-01-09 Changyou Li , Mirza Karamehmedovic , Ekaterina Sherina , Kim Knudsen

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis…

Numerical Analysis · Mathematics 2016-01-20 Henrik Garde , Kim Knudsen

We demonstrate live-updating ptychographic reconstruction with ePIE, an iterative ptychography method, during ongoing data acquisition. The reconstruction starts with a small subset of the total data, and as the acquisition proceeds the…

Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction…

In the Reverse Engineering and Hardware Assurance domain, a majority of the data acquisition is done through electron microscopy techniques such as Scanning Electron Microscopy (SEM). However, unlike its counterparts in optical imaging,…

Image and Video Processing · Electrical Eng. & Systems 2020-04-30 Ronald Wilson , Navid Asadizanjani , Domenic Forte , Damon L. Woodard

Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…

Numerical Analysis · Mathematics 2019-10-29 Cristian Guillermo Gebhardt , Dominik Schillinger , Marc Christian Steinbach , Raimund Rolfes

X-ray images ease the diagnosis and treatment process due to their rapid imaging speed and high resolution. However, due to the projection process of X-ray imaging, much spatial information has been lost. To accurately provide efficient…

Image and Video Processing · Electrical Eng. & Systems 2024-08-06 Lixing Tan , Shuang Song , Yaofeng He , Kangneng Zhou , Tong Lu , Ruoxiu Xiao

Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…

Low-dose emission tomography (ET) plays a crucial role in medical imaging, enabling the acquisition of functional information for various biological processes while minimizing the patient dose. However, the inherent randomness in the photon…

Three-dimensional reconstruction of atomic structure, known as atomic electron tomography (AET), has found increasing applications in materials science. The AET has been limited to very small nanoparticles due to the challenges of obtaining…

Materials Science · Physics 2024-01-24 Liangze Mao , Jizhe Cui , Rong Yu

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy