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Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics

Petra, Stefania and Schnörr, Christoph and Schröder, Andreas (2013) Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics. Fundamenta Informaticae, Vol. 125 (3-4), pp. 285-312. IOS Press. DOI: 10.3233/FI-2013-850 ISSN 0169-2968

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Official URL: http://fi.mimuw.edu.pl/index.php/FI/pages/view/issues/

Abstract

We analyze representative ill-posed scenarios of tomographic PIV (particle image velocimetry) 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 projection equations are probabilistically analyzed in order to determine: (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.

Item URL in elib:https://elib.dlr.de/82074/
Document Type:Article
Additional Information:ISSN: 1875-8681 (Online), Subject: Computer Science, Mathematical Analysis and Theory of Computation
Title:Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Petra, StefaniaUniversity of Heidelberg, GermanyUNSPECIFIED
Schnörr, ChristophUniversity of Heidelberg, GermanyUNSPECIFIED
Schröder, AndreasUNSPECIFIEDUNSPECIFIED
Date:2013
Journal or Publication Title:Fundamenta Informaticae
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:Vol. 125
DOI :10.3233/FI-2013-850
Page Range:pp. 285-312
Publisher:IOS Press
ISSN:0169-2968
Status:Published
Keywords:compressed sensing, underdetermined nonnegative linear systems, sparsity, large deviation, tail bound, limited angle tomography, TomoPIV
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation & Validation (old)
Location: Göttingen
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > Experimental Methods
Deposited By: Micknaus, Ilka
Deposited On:30 May 2013 15:29
Last Modified:30 May 2013 15:29

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