22 research outputs found
Kodierung von Gaußmaßen
Es sei ein Gaußmaß auf der Borelschen -Algebra des separablen Banachraums . Für gelte . Wir untersuchen den mittleren Fehler, der bei Kodierung von respektive mit Punkten entsteht, und bestimmen untere und obere Abschätzungen für die Asymptotik () dieses Fehlers. Hierbei betrachten wir zu Gütekriterien wie folgt: Deterministische Kodierung Zufällige Kodierung Die seien hierbei i.i.d., unabhängig von , und nach verteilt. Das Infimum wird über alle Wahrscheinlichkeitsmaße gebildet. Für das Gütekriterium wird ausgehend von der Definition von nicht optimal, sondern gewählt. Das Gütekriterium ergibt sich aus der Quellkodierungstheorie nach Shannon. Es gilt Wir stellen folgenden Zusammenhang zwischen der Asymptotik von und den logarithmischen kleinen Abweichungen von her: Es gebe und mit psi(varepsilon) := -log P{X1.Let be a Gaussian measure on the Borel -algebra of the separable Banach space . Let with . We investigate the average error in coding resp. with points and obtain lower and upper bounds for the error asymptotics (). We consider, given , fidelity criterions as follows: Deterministic Coding Random Coding The above are i.i.d., independent of , and distributed according to . The infimum is taken with respect to all probability measures . For the fidelity criterion , starting from the definition of , is not chosen optimal, but as . The fidelity criterion is given according to the source coding theory of Shannon. The fidelity criterions are connected through We obtain the following connection between the asymptotics of and the den logarithmic small deviations of : Let and with psi(varepsilon) := -log P{X1
Statistical iterative reconstruction algorithm for X-ray phase-contrast CT.
Grating-based phase-contrast computed tomography (PCCT) is a promising imaging tool on the horizon for pre-clinical and clinical applications. Until now PCCT has been plagued by strong artifacts when dense materials like bones are present. In this paper, we present a new statistical iterative reconstruction algorithm which overcomes this limitation. It makes use of the fact that an X-ray interferometer provides a conventional absorption as well as a dark-field signal in addition to the phase-contrast signal. The method is based on a statistical iterative reconstruction algorithm utilizing maximum-a-posteriori principles and integrating the statistical properties of the raw data as well as information of dense objects gained from the absorption signal. Reconstruction of a pre-clinical mouse scan illustrates that artifacts caused by bones are significantly reduced and image quality is improved when employing our approach. Especially small structures, which are usually lost because of streaks, are recovered in our results. In comparison with the current state-of-the-art algorithms our approach provides significantly improved image quality with respect to quantitative and qualitative results. In summary, we expect that our new statistical iterative reconstruction method to increase the general usability of PCCT imaging for medical diagnosis apart from applications focused solely on soft tissue visualization
Media 2: Constrained X-ray tensor tomography reconstruction
Originally published in Optics Express on 15 June 2015 (oe-23-12-15134
Media 1: Constrained X-ray tensor tomography reconstruction
Originally published in Optics Express on 15 June 2015 (oe-23-12-15134
Media 3: Constrained X-ray tensor tomography reconstruction
Originally published in Optics Express on 15 June 2015 (oe-23-12-15134
X-ray nanotomography using near-field ptychography
International audiencePropagation-based imaging or inline holography in combination with computed tomography (holotomography) is a versatile tool to access a sample's three-dimensional (3D) micro or nano structure. However, the phase retrieval step needed prior to tomographic reconstruction can be challenging especially for strongly absorbing and refracting samples. Near-field ptychography is a recently developed phase imaging method that has been proven to overcome this hurdle in projection data. In this work we extend near-field ptychography to three dimensions and we show that, in combination with tomography, it can access the nano structure of a solid oxide fuel cell (SOFC). The quality of the resulting tomographic data and the structural properties of the anode extracted from this volume were compared to previous results obtained with holotomography. This work highlights the potential of 3D near-field ptychography for reliable and detailed investigations of samples at the nanometer scale, with important applications in materials and life sciences among others. (C) 2015 Optical Society of Americ