Inversion of the broken ray transform in the case of energy-dependent attenuation.

Broken Ray transform (BRT) arises when one considers a narrow x-ray beam propagating through medium under the assumption of single scattering. Previous algorithms for inverting the BRT assumed that the medium is characterized by a single attenuation coefficient µ. However x-rays lose their energy after Compton scattering and the energy loss depends on the scattering angle. Since the attenuation coefficient depends on energy, the µ's before and after scattering are different. When there are three or more detectors one should distinguish not only between µ's that are 'seen' by x-rays before and after scattering, but also between µ's that are 'seen' by x-rays traveling towards different detectors.The main thrust of this paper is inversion of the BRT with N ⩾ 3 detectors under the assumption that the attenuation coefficient can be accurately approximated by a linear function of energy within the window of relevant energies. When the number of detectors is four or greater, we derive a family of inversion formulas. If N > 4, we find the optimal formula, which provides the best stability with respect to noise in the data. If N = 4, the family collapses into a single formula and no optimization is possible. If µ is independent of energy, N = 3 is sufficient for inversion. We also develop iterative reconstruction algorithms that can use global and local data. The results of testing the algorithms are presented.

A study on HIV and hepatitis C virus among commercial sex workers in Tallinn.

INTRODUCTION: Estonia is confronted by a dramatic expansion of the initially injection drug use-driven HIV epidemic. Little is known about HIV occurrence in population groups at high risk other than injection drug users. OBJECTIVE: To obtain data on the prevalence of HIV and hepatitis C virus (HCV) among female sex workers (FSW) in Tallinn. DESIGN: An unlinked, anonymous, cross-sectional survey of FSW recruited in Tallinn from October 2005 to May 2006. METHODS: 227 FSW were recruited for the survey and biological sample collection (HIV, HCV antibodies detection) using a combination of time-location, community and respondent-driven sampling. RESULTS: Among 227 women the HIV and HCV prevalences were 7.6% (95% CI 4.6% to 12.5%) and 7.9% (95% CI 4.5% to 12.6%), respectively. HIV prevalence was higher among FSW working in the street (odds ratio (OR) 6.4; 95% CI 1.1 to 35.6) and at the brothels and apartments supervised by the organised sex industry (OR 5.0; 95% CI 1.3 to 18.4). The duration of sex work was negatively associated with HIV prevalence (OR 0.78; 95% CI 0.63 to 0.97). CONCLUSIONS: Prevention needs of FSW in this area include increasing rates of HIV testing and putting in place effective programmes that can help extend HIV prevention behaviours across a range of sexual and drug use risk behaviours.