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Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In…

Numerical Analysis · Mathematics 2023-06-21 Leopold Veselka , Peter Elbau , Leonidas Mindrinos , Lisa Krainz , Wolfgang Drexler

We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or…

We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz…

Analysis of PDEs · Mathematics 2015-08-05 Habib Ammari , Simon Boulier , Pierre Millien

Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…

Signal Processing · Electrical Eng. & Systems 2024-09-23 Sampath Kumar Dondapati , Omkar Nitsure , Satish Mulleti

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce…

Numerical Analysis · Mathematics 2015-06-15 Yann Grisel , Jean-Pierre Raymond , Pierre-Alain Mazet , Vincent Mouysset

A prime goal of quantum tomography is to provide quantitatively rigorous characterisation of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in…

Quantum Physics · Physics 2015-06-12 Nathan K. Langford

We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and…

Quantum Physics · Physics 2013-11-07 Yu. I. Bogdanov , S. P. Kulik

The reconstruction of three-dimensional sparse volume functions from few tomographic projections constitutes a challenging problem in image reconstruction and turns out to be a particular instance problem of compressive sensing. The…

Numerical Analysis · Mathematics 2012-08-31 Stefania Petra , Christoph Schnörr

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this Note, we derive a hybrid reconstruction…

Analysis of PDEs · Mathematics 2015-06-11 Kun Wang , Mark A. Anastasio

In this paper, compressed sensing with noisy measurements is addressed. The theoretically optimal reconstruction error is studied by evaluating Tanaka's equation. The main contribution is to show that in several regions, which have…

Information Theory · Computer Science 2013-02-19 Junan Zhu , Dror Baron

An accelerated model-based information theoretic approach is presented to perform the task of Magnetic Resonance (MR) thermal image reconstruction from a limited number of observed samples on k-space. The key idea of the proposed approach…

Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative…

Analysis of PDEs · Mathematics 2017-02-16 Markus Haltmeier , Lukas Neumann , Linh V. Nguyen , Simon Rabanser

We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the…

Analysis of PDEs · Mathematics 2021-09-22 Faouzi Triki , Qi Xue

The goal in acousto-electric tomography (AET) is to reconstruct an image of the unknown electric conductivity in an object from exterior electrostatic currents and voltages that are measured on the boundary of the object while the object is…

Numerical Analysis · Mathematics 2022-03-29 Bjørn Christian Skov Jensen , Kim Knudsen

The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A…

Numerical Analysis · Mathematics 2009-11-13 Mark Agranovsky , Peter Kuchment

Tunable Diode Laser Absorption Spectroscopy (TDLAS) tomography has been widely used for in situ combustion diagnostics, yielding images of both species concentration and temperature. The temperature image is generally obtained from the…

Image and Video Processing · Electrical Eng. & Systems 2020-07-14 Yong Bao , Rui Zhang , Godwin Enemali , Zhang Cao , Bin Zhou , Hugh McCann , Chang Liu

We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…

We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…

Machine Learning · Computer Science 2013-11-05 Franz J. Király , Louis Theran

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the…

Mathematical Physics · Physics 2015-05-14 Guillaume Bal , Alexandre Jollivet , Vincent Jugnon

The accurate and reliable description of measurement devices is a central problem in both observing uniquely non-classical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum…

Quantum Physics · Physics 2020-01-30 Aonan Zhang , Jie Xie , Huichao Xu , Kaimin Zheng , Han Zhang , Yiu-Tung Poon , Vlatko Vedral , Lijian Zhang