Optimized analytic reconstruction for SPECT

International audienceWe develop optimized analytic reconstruction for the single-photon emission computed tomography (SPECT). This reconstruction is based on : (1) Novikov's exact and Chang's approximate inversion formulas for the attenuated ray transform, (2) filtering techniques, and (3) Morozov type discrepancy principle. Our numerical examples include comparisons with the standard least square and expectation maximization iterative SPECT reconstructions

On Wiener type filters in SPECT

International audienceFor 2D data with Poisson noise we give explicit formulas for the optimal space-invariant Wiener type filter with some a priori geometric restrictions on the window function. We show that, under some natural geometric condition, this restrictedly optimal Wiener type filter admits a very efficient approximation by an approximately optimal filter with unknown object power spectrum. Generalizations to the case of some more general noise model are also given. Proceeding from these results we (a) explain, in particular, an efficiency of some well-known "1D" approximately optimal space-invariant Wiener type filtering scheme with unknown object power spectrum in single-photon emission computed tomography (SPECT) and positron emission tomography (PET) imaging based on the classical FBP algorithm or its iterative use and (b) propose also an efficient 2D approximately optimal space-invariant Wiener type filter with unknown object power spectrum for SPECT imaging based on the generalized FBP algorithm (implementing the explicit formula for the nonuniform attenuation correction) and/or the classical FBP algorithm (used iteratively). An efficient space-variant version of the latter 2D filter is also announced. Numerical examples illustrating the aforementioned results in the framework of simulated SPECT imaging are given

Inversion of weighted Radon transforms via finite Fourier series weight approximations

International audienceWe consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a principal refinement as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT)

Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl. Phys. B [PM

Biomineralisation by earthworms: an investigation into the stability and distribution of amorphous calcium carbonate

Background Many biominerals form from amorphous calcium carbonate (ACC), but this phase is highly unstable when synthesised in its pure form inorganically. Several species of earthworm secrete calcium carbonate granules which contain highly stable ACC. We analysed the milky fluid from which granules form and solid granules for amino acid (by liquid chromatography) and functional group (by Fourier transform infrared (FTIR) spectroscopy) compositions. Granule elemental composition was determined using inductively coupled plasma-optical emission spectroscopy (ICP-OES) and electron microprobe analysis (EMPA). Mass of ACC present in solid granules was quantified using FTIR and compared to granule elemental and amino acid compositions. Bulk analysis of granules was of powdered bulk material. Spatially resolved analysis was of thin sections of granules using synchrotron-based μ-FTIR and EMPA electron microprobe analysis. Results The milky fluid from which granules form is amino acid-rich (≤ 136 ± 3 nmol mg−1 (n = 3; ± std dev) per individual amino acid); the CaCO3 phase present is ACC. Even four years after production, granules contain ACC. No correlation exists between mass of ACC present and granule elemental composition. Granule amino acid concentrations correlate well with ACC content (r ≥ 0.7, p ≤ 0.05) consistent with a role for amino acids (or the proteins they make up) in ACC stabilisation. Intra-granule variation in ACC (RSD = 16%) and amino acid concentration (RSD = 22–35%) was high for granules produced by the same earthworm. Maps of ACC distribution produced using synchrotron-based μ-FTIR mapping of granule thin sections and the relative intensity of the ν2: ν4 peak ratio, cluster analysis and component regression using ACC and calcite standards showed similar spatial distributions of likely ACC-rich and calcite-rich areas. We could not identify organic peaks in the μ-FTIR spectra and thus could not determine whether ACC-rich domains also had relatively high amino acid concentrations. No correlation exists between ACC distribution and elemental concentrations determined by EMPA. Conclusions ACC present in earthworm CaCO3 granules is highly stable. Our results suggest a role for amino acids (or proteins) in this stability. We see no evidence for stabilisation of ACC by incorporation of inorganic components

Pile – Soil Interaction during Vibratory Sheet Pile Driving : a Full Scale Field Study

Urban construction sites require strict control of their environmental impact, which, for vibratory sheet pile driving, can include damage to nearby structures due to ground vibrations. However, the lack of knowledge concerning the generation of soil vibrations makes the prediction of ground vibration levels difficult. This MSc. thesis in particular, focuses on a crucial link in the vibration transfer chain: the sheet pile – soil interface, which is also one of the least documented. The aim of this thesis is first, to carry out a full-scale field test consisting in the monitoring of sheet pile and ground vibrations during sheet pile vibratory driving. And second, to analyze a selected portion of the collected data with focus on the sheet pile – soil vibration transfer. Both aspects of the thesis work aim, more generally, to contribute to the understanding of ground vibration generation under vibratory sheet pile driving. The full-scale field study was performed in Solna in May 2013. It consisted in the vibratory driving of seven sheet piles, out of which three were fitted with accelerometers. During the driving, ground vibrations were measured by accelerometers, the closest ones placed only 0.5 m from the sheet pile line. The design and installation of the soil instrumentation was innovative in as much as accelerometers were not only set on the ground surface but also at three different depths (~ 3 m, 5 m and 6 m). The analysis presented in this thesis is primarily a comparison between sheet pile vibrations and ground vibrations measured 0.5 m from the sheet pile line. The principal aspects considered in the comparison are: the influence of penetration through different soil layers, the sheet pile – soil vibration transfer efficiency, the frequency content of sheet pile and soil vibrations, and differences between toe- and shaft-generated vibrations. The main conclusions from this study are: Most of the vibration loss occurs in the near field: 90-99% of the sheet pile vibration magnitude was dispersed within 0.5 m from the driven sheet pile. Moreover, the sheet pile – soil vibration transfer efficiency was reduced for higher sheet pile acceleration levels and higher frequencies. The soil characteristics strongly influence the sheet pile vibration levels. A clear distinction could be made between "smooth" and "hard" driving, the latter being associated with an impact situation at the sheet pile toe. The focus of ground vibration studies should not only be the vertical vibrations. Indeed, the ground vibrations’ horizontal component was found to be of the same or even higher magnitude than the vertical component