Positron Emission Tomography and Random Coefficients Regression

We further explore the relation between random coefficients regression (RCR) and computerized tomography. Recently, Beran et al. (1996, Ann. Statist., 24, 2569–2592) explored this connection to derive an estimation method for the non-parametric RCR problem which is closely related to image reconstruction methods in X-ray computerized tomography. In this paper we emphasize the close connection of the RCR problem with positron emission tomography (PET). Specifically, we show that the RCR problem can be viewed as an idealized (continuous) version of a PET experiment, by demonstrating that the nonparametric likelihood of the RCR problem is equivalent to that of a specific PET experiment. Consequently, methods independently developed for either of the two problems can be adapted from one problem to the other. To demonstrate the close relation between the two problems we use the estimation method of Beran, Feuerverger and Hall for image reconstruction in PET.     

Experimental and theoretical study of radon levels and entry mechanisms in a mediterranean climate house

An experimental study has been carried out in an inhabited single-family house. Radon concentration in the different rooms of the house and in its garden soil has been measured with Nuclear Track Detectors. No high differences of radon concentration have been observed between the different rooms of the house, so that the proximity of the room level to the soil seems not to affect the radon concentration. The annual radon concentration obtained indoors and in the soil has been respectively 35 Bq m⁻³ and 24 kBq m⁻³. Since radon generation in the source, entry into indoor air and accumulation indoors depend on several parameters, the effect of a specific parameter on indoor radon concentration is difficult to explain from the radon measurements only. The RAGENA (RAdon Generation, ENtry and Accumulation indoors) model has been adapted to the room in the basement of the house. The mean radon concentration values obtained with the model are compared to experimental results derived from measurements using Nuclear Track Detectors. The use of the model, together with the experimental study, has allowed characterising radon sources, levels and entry mechanisms in the house. The concrete walls have been found to be the most relevant radon source, while the contribution of the soil is negligible in this case. The indoor radon level is given by the balance of the permanent exhalation from concrete and the removal due to ventilation. The indoor radon levels are close to the average value for the Barcelona area which, in turn, is close to the world averaged value.     

Influences on indoor radon concentrations in Riyadh,Saudi Arabia

The influences on indoor radon concentrations in Riyadh, Saudi Arabia survey was carried out for 786 dwellings. The measurements were obtained by using a passive integrating ionization system with an E-Perm^® Electret ion chamber. Radon levels ranged from 1 to 195 Bq m⁻³, with a mean value of 24.68 Bq m⁻³, the geometric mean and the geometric standard deviation are 21 and 2 respectively. 98.5% of the results were below the action level recommended by WHO of 100 Bq.m⁻³. The results were found to vary substantially due to types of houses and rooms, ventilation, seasons and building materials. Radon concentrations were higher in houses with no ventilation systems, and central air conditioners, and were relatively lower in well ventilated houses with red bricks and water air conditioners.     

Relation between radon concentrations and morphotectonics of the Dead Sea transform in Wadi Araba, Jordan

Radon concentrations were measured along six profiles crossing three morphotectonic features of the Dead Sea transform fault in Wadi Araba. Two profiles of detectors were placed across a fault scarp, a sag pond and a pressure ridge formed along the active Wadi Araba strike-slip fault. The maximum radon peak was measured in the pressure ridges . This high concentration may be due to the up squeezing and heterogeneous fracturing of the Cretaceous and the Pleistocene Lisan beds beneath the pressure ridges. The minimum radon readings were measured in the sag pond floor , the fractures are concentrated at the pond borders and not in the pond floor. The sag ponds are filled with fine sediments, which decreases the porosity and hence the upward radon migration. The fault scarp has intermediate radon radiation, with concentration values ranging between 1.1 and .     

A new approach for the estimation of the axial velocity using ultrasound

The most used estimation method for calculating the blood velocity in commercial scanners is the autocorrelation approach. The calculation of the mean velocity used in this method depends on the center frequency of the interacting ultrasound pulse which downshifts as a function of depth, introducing a bias. A new velocity estimator for the mean axial velocity is presented. The estimation principle is based on the 2D Fourier transform and the Radon transform. The input data are a sequence of RF data forming a 2D data input, one column for each pulse emission. A 2D segment is selected for a specific depth. This data segment is first transformed by a 2D Fourier transform, and the result is then transformed by a Radon transform. The center of gravity for the angles of the lines intersecting the origin of the R-theta coordinate system in the Radon domain gives the mean axial velocity for the data segment. The benefit of this method is an estimate of the mean axial velocity which is independent of the center frequency of the propagating ultrasound pulse. The estimate will only depend on f(s) and f(pr f). Results of the estimation method is presented based on both simple generated RF harmonic data for different signal/noise ratios and simulated acoustic RF responses from a 3D measurement situation with an array transducer and a tube with plug flow. The new method shows improvement with a factor of 1.5-4 on the standard deviation on the estimated mean velocity for the simulated case.     

Bounds for singular fractional integrals and related Fourier integral operators

We prove sharp L^p−L^q endpoint bounds for singular fractional integral operators and related Fourier integral operators, under the nonvanishing rotational curvature hypothesis.     

On the shape–from–moments problem and recovering edges from noisy Radon data

We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from–moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near–optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data.Mathematics Subject Classification (2000):62C20, 62G20, 94A12     

Soil radon response around an active volcano

Soil radon behavior related to the volcanic eruptive period 1997–1999 of Popocatepetl volcano has been studied as a function of the volcanic activity. Since the volcano is located 60 km from Mexico City, the risk associated with an explosive eruptive phase is high and an intense surveillance program has been implemented. Previous studies in this particular volcano showed soil radon pulses preceding the initial phase of the eruption. The radon survey was performed with LR-115 track detectors at a shallow depth and the effect of the soil moisture during the rainy season has been observed on the detectors response. In the present state of the volcanic activity the soil radon behavior has shown more stability than in previous eruptive stages.