scholarly journals Momentum ray transforms, II: range characterization in the Schwartz space

2020 ◽  
Vol 36 (4) ◽  
pp. 045009 ◽  
Author(s):  
Venkateswaran P Krishnan ◽  
Ramesh Manna ◽  
Suman Kumar Sahoo ◽  
Vladimir A Sharafutdinov
Keyword(s):  
Schwartz Space ◽  
Range Characterization ◽  
Ray Transforms

scholarly journals A geometric based preprocessing for weighted ray transforms with applications in SPECT

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fedor Goncharov
Keyword(s):  
Single Photon ◽  
Photon Emission ◽  
Reconstruction Algorithm ◽  
Emission Computed Tomography ◽  
Radon Transforms ◽  
Single Photon Emission Computed ◽  
Ray Transforms ◽  
Straight Lines ◽  
The Impact ◽  
Photon Emission Computed Tomography

AbstractIn this work we investigate numerically the reconstruction approach proposed in [F. O. Goncharov and R. G. Novikov, An analog of Chang inversion formula for weighted Radon transforms in multidimensions, Eurasian J. Math. Comput. Appl. 4 2016, 2, 23–32] for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a geometric reduction of the data modeled by weighted ray transforms to new data modeled by weighted Radon transforms along two-dimensional planes in 3D. Such reduction could be seen as a preprocessing procedure which could be further completed by any preferred reconstruction algorithm. In a series of numerical tests on modelized and real SPECT (single photon emission computed tomography) data we demonstrate that such procedure can significantly reduce the impact of noise on reconstructions.

THE NON-COMMUTATIVE SCHWARTZ SPACE IS WEAKLY AMENABLE

2016 ◽  
Vol 59 (2) ◽  
pp. 437-443 ◽  
Author(s):  
KRZYSZTOF PISZCZEK
Keyword(s):  
Open Problem ◽  
Schwartz Space

AbstractWe show in a straightforward way that the non-commutative Schwartz space is weakly amenable. At the end, we leave an open problem.

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