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

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 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.Comment: 22 pages, submitted to Fundamenta Informaticae. arXiv admin note: text overlap with arXiv:1208.589

TomoPIV meets Compressed Sensing

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

Redox Mediation at 11-Mercaptoundecanoic Acid Self-Assembled Monolayers on Gold

Cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and digital simulation techniques were used to investigate quantitatively the mechanism of electron transfer (ET) through densely packed and well-ordered self-assembled monolayers (SAMs) of 11-mercaptoundecanoic acid on gold, either pristine or modified by physically adsorbed glucose oxidase (GOx). In the presence of ferrocenylmethanol (FcMeOH) as a redox mediator, ET kinetics involving either solution-phase hydrophilic redox probes such as [Fe(CN)6]3-/4- or surface-immobilized GOx is greatly accelerated: [Fe(CN)6]3-/4- undergoes diffusion-controlled ET, while the enzymatic electrochemical conversion of glucose to gluconolactone is efficiently sustained by FcMeOH. Analysis of the results, also including the digital simulation of CV and EIS data, showed the prevalence of an ET mechanism according to the so-called membrane model that comprises the permeation of the redox mediator within the SAM and the intermolecular ET to the redox probe located outside the monolayer. The analysis of the catalytic current generated at the GOx/SAM electrode in the presence of glucose and FcMeOH allowed the high surface protein coverage suggested by X-ray photoelectron spectroscopy (XPS) measurements to be confirmed.