scholarly journals Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature

2021 ◽  
Author(s):  
Rohit Kumar Mishra ◽  
François Monard
Keyword(s):  
Singular Value Decomposition ◽  
Constant Curvature ◽  
Singular Value ◽  
X Ray ◽  
Ray Transform ◽  
Value Decomposition

scholarly journals Singular value decomposition as a tool for background corrections in time-resolved XFEL scattering data

2014 ◽  
Vol 369 (1647) ◽  
pp. 20130336 ◽  
Author(s):  
Kristoffer Haldrup
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Scattering Data ◽  
High Time Resolution ◽  
Light Sources ◽  
Time Resolved ◽  
X Ray ◽  
Very Large Datasets ◽  
Chaotic Nature ◽  
Value Decomposition

The development of new X-ray light sources, XFELs, with unprecedented time and brilliance characteristics has led to the availability of very large datasets with high time resolution and superior signal strength. The chaotic nature of the emission processes in such sources as well as entirely novel detector demands has also led to significant challenges in terms of data analysis. This paper describes a heuristic approach to datasets where spurious background contributions of a magnitude similar to (or larger) than the signal of interest prevents conventional analysis approaches. The method relies on singular-value decomposition of no-signal subsets of acquired datasets in combination with model inputs and appears generally applicable to time-resolved X-ray diffuse scattering experiments.

scholarly journals Application of Singular Value Decomposition to the Analysis of Time-Resolved Macromolecular X-Ray Data

2003 ◽  
Vol 84 (3) ◽  
pp. 2112-2129 ◽  
Author(s):  
Marius Schmidt ◽  
Sudarshan Rajagopal ◽  
Zhong Ren ◽  
Keith Moffat
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Time Resolved ◽  
X Ray ◽  
Value Decomposition

Singular value decomposition analysis of time-resolved small-angle X-ray scattering during morphological transition in a block copolymer

2003 ◽  
Vol 36 (4) ◽  
pp. 982-985 ◽  
Author(s):  
Shigeru Okamoto ◽  
Shinichi Sakurai
Keyword(s):  
Block Copolymer ◽  
Singular Value Decomposition ◽  
Temperature Jump ◽  
Singular Value ◽  
Morphological Transition ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
Value Decomposition ◽  
Ray Scattering

Time-resolved small-angle X-ray scattering (TR-SAXS) studies of the structural changes in a block copolymer after a temperature jump are reported. The sample used was a polystyrene-block-poly(ethylene-alt-butylene)-block-polystyrene (SEBS) triblock copolymer, which has a number-average molecular weight of 54000 g mol−1and a volume fraction of polystyrene of 0.227. The film specimen was prepared by the solution-cast method using a selective solvent. The as-cast specimen with lamellar microdomains underwent the temperature jump from 363 to 403 K and the morphological transition from lamellae to cylinders was observed as a function of time by the TR-SAXS technique. The singular value decomposition (SVD) analysis was performed on the scattering profiles. This analysis strongly suggested the existence of a third basis component of the X-ray scattering profiles, thus supporting that there is an intermediate state during the transition from lamellae to cylinders.

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