Local Representations for Small-angle X-ray Scattering Tensor Tomography
Publicerad
Författare
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
In small-angle X-ray scattering tensor tomography, a reconstruction of the reciprocal
space map of a sample is performed using small-angle X-ray scattering
measurements, providing information about the local reciprocal space in the
volume of the sample. Previous methods of reconstruction have posed it as an
inverse problem in linear and non-linear formulations using spherical harmonic
representations of the reciprocal space map, solving it using quasi-Newton
methods. Local representations have advantages, such as making the problem
separable and allowing for positivity constraints on the reconstructed spherical
functions. In this work, two local representations, one based on spherical pixels
and one based on radial basis functions (including spherical splines), were implemented.
The studied radial basis functions were based on Gaussian, Matérn
and Wendland functions. In addition, regularization using the L1-norm, the
L1-norm and the total variation were implemented. After selecting hyperparameters
for the various reconstruction methods using the L-curve method and
minimization of the residual, comparisons of the local representation methods
and an existing method using a real spherical harmonic representation were
carried out on simulated data as well as a trabecular bone sample. Studying
the correlation between the reconstructed reciprocal space map and the true
coefficients, the radial basis function representations were shown to perform
comparably to the real spherical harmonics representation. Increases in correlation
were seen under the application of regularization terms. The correlation
between neighboring voxels of the orientation of features increased under regularization,
where total variation regularization was shown to perform similarly
to L1-regularization.
Beskrivning
Ämne/nyckelord
small-angle X-ray scattering, small-angle X-ray scattering tensor tomography, tensor tomography, spherical spline, radial basis function, total variation, spherical pixel, HEALPix