Theory of carrier phase ambiguity resolution

Carrier phase ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. A proper handling of carrier phase ambiguity resolution requires a proper understanding of the underlying theory of integer inference. In this contribution a brief review is given of the probabilistic theory of integer ambiguity estimation. We describe the concept of ambiguity pull-in regions, introduce the class of admissible integer estimators, determine their probability mass functions and show how their variability affect the uncertainty in the so-called ‘fixed’ baseline solution. The theory is worked out in more detail for integer least-squares and integer bootstrapping. It is shown that the integer least-squares principle maximizes the probability of correct integer estimation. Sharp and easy-to-compute bounds are given for both the ambiguity success rate and the baseline’s probability of concentration. Finally the probability density function of the ambiguity residuals is determined. This allows one for the first time to formulate rigorous tests for the integerness of the parameters

Geometric Sensitivity of ClearPET (TM) Neuro

ClearPET (TM) Neuro is a small-animal positron emission tomography (PET) scanner dedicated to brain studies on rats and primates. The design of ClearPET (TM) Neuro leads to a specific geometric sensitivity, characterized by inhomogeneous and, depending on the measurement setup, even incomplete data. With respect to reconstruction techniques, homogeneous and complete data sets are a 'must' for analytical reconstruction methods, whereas iterative methods take the geometrical sensitivity into account during the reconstruction process. Nevertheless, here a homogeneous geometric sensitivity over the field of view is highly desirable. Therefore, this contribution aims at studying the impact of different scanner geometries and measurement setups on the geometric sensitivity. A data set of coincident events is computed for certain settings that contains each possible crystal combination once. The lines of response are rebinned into normalizing sinograms and backprojected into sensitivity images. Both, normalizing sinograms and sensitivity images mirror the geometric sensitivity and therefore, provide information which setting enables most complete and homogeneous data sets. An optimal measurement setup and scanner geometry in terms of homogeneous geometric sensitivity is found by analyzing the sensitivity images. (c) 2006 Elsevier B.V. All rights reserved

Compensation strategies for PET scanners with unconventional scanner geometry

The small animal PET scanner ClearPET®Neuro, developed at the Forschungszentrum Julich GmbH in cooperation with the Crystal Clear Collaboration (CERN), represents scanners with an unconventional geometry: due to axial and transaxial detector gaps ClearPet®Neuro delivers inhomogeneous sinograms with missing data. When filtered backprojection (FBP) or Fourier rebinning (FORE) are applied, strong geometrical artifacts appear in the images. In this contribution we present a method that takes the geometrical sensitivity into account and converts the measured sinograms into homogeneous and complete data. By this means artifactfree images are achieved using FBP or FORE. Besides an advantageous measurement setup that reduces inhomogeneities and data gaps in the sinograms, a modification of the measured sinograms is necessary. This modification includes two steps: a geometrical normalization and corrections for missing data. To normalize the measured sinograms, computed sinograms are used that describe the geometrical sensitivity for a given measurement setup. Corrections for the data gaps are achieved by a provisional reconstruction followed by a forward projection of the image. The modified sinograms are homogeneous and complete. Modification of the sinograms and reconstruction with FBP or FORE lead to images without geometrical artifacts and still cost less computation time than using iterative reconstruction algorithms