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TomoPIV meets Compressed Sensing

Petra, Stefania and Schnörr, Christoph

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Abstract

We study the discrete tomography problem in Experimental Fluid Dynamics - Tomographic Particle Image Velocimetry (TomoPIV) - from the viewpoint of compressed sensing (CS). The CS theory of recoverability and stability of sparse solutions to underdetermined linear inverse problems has rapidly evolved during the last years. We show that all currently available CS concepts predict an extremely poor worst case performance, and a low expected performance of the TomoPIV measurement system, indicating why low particle densities only are currently used by engineers in practice. Simulations demonstrate however that slight random perturbations of the TomoPIV measurement matrix considerably boost both worst-case and expected reconstruction performance. This finding is interesting for CS theory and for the design of TomoPIV measurement systems in practice.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 17 Aug 2009 07:34
Date: 2009
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Uncontrolled Keywords: compressed sensing , underdetermined systems of linear equations , positivity constraints in ill-posed problems , sparsest solution , TomoPIV
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