M\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation

In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real matrices of determinant one via M\"{o}bius transformations. Our approach is based on a deconvolution technique which relies on the Helgason--Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random M\"{o}bius transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincar\'{e} plane exactly describes the physical system that is of statistical interest.Comment: Published in at http://dx.doi.org/10.1214/09-AOS783 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Improved beamforming performance using pulsed plane wave decomposition

A tool for calculating the beamformer setup associated with a specified pulsed acoustic field is presented. The method is named Pulsed Plane Wave Decomposition (PPWD) and is based on the decomposition of a pulsed acoustic field into a set of PPWs at a given depth. Each PPW can be propagated to the location of the elements of an array transducer by a time delay. The contribution of each propagated PPW is summed to form one time function for each array element (the BMF matrix). This approach gives the beamformer setup needed to obtain a close approximation to the desired bounded pulsed acoustic field without involving any optimization scheme. The approximation arises due to the limited size of the acoustic aperture and the spatial sampling property of the array transducer. Thus, the acoustical field can be designed according to the imaging needs. The method is demonstrated by examples in the 2D space by analytical equations, simulation, and experimental results

Performance of a vector velocity estimator

It is a well-known limitation of all commercially available scanners that only the velocity component along the propagation direction of the emitted pulse is measured, when evaluating blood velocities with ultrasound. Proposals for solving this limitation using several transducers or speckle tracking can be found in the literature, but no method with a satisfactory performance has been found that can be used in a commercial implementation. A method for estimation of the velocity vector is presented. Here an oscillation transverse to the ultrasound beam is generated, so that a transverse motion yields a change in the received signals. The method uses two ultrasound beams for sampling the in-phase and quadrature component of the lateral field, and a set of samples (in-phase and quadrature in both time and space) are taken for each pulse-echo line. These four samples are then used in an autocorrelation approach that yields both the axial and the lateral velocity, and thus the velocity ve..

Horizontal Stratification in Access to Danish University Programmes

In this paper, we use register data to examine horizontal stratification within university institutions and university fields of study in Denmark, a country that has experienced a reduction of the social class gap in access to higher education. First, we argue that it is important to use a relatively detailed classification of parents’ occupations to determine how students are endowed with different forms of capital, even when their parents would typically be characterised as belonging to the same social group. Second, we distinguish among disciplines and among university institutions to explain the dynamics of horizontal stratification in the Danish university system. Using unique and exhaustive register data, including all higher education institutions and the entire 1984 cohort as of the age of 24, we uncover distinct differences in the magnitude and type of horizontal stratification in different fields of study and university institutions. Most importantly, we find distinct patterns of horizontal stratification by field of study and parental occupation that would have remained hidden had we used more aggregated classifications for field of study and social origin.</jats:p