Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 5 of 5 for “"X-ray transform"”.
-
The broken non-abelian X-ray transform and inverse problems for connections at high fixed frequency
… problem we study is the broken non-abelian X-ray transform. Given a connection A, its broken non-abelian X-ray transform is given by its parallel transports over a set of broken geodesics that start and end on the boundary. Here, a broken geodesic is a piecewise smooth curve formed by the …
-
The Calderón problem for connections
… identity to reduce the problem to a suitable $X$-ray transform on $M_0$. The construction is based on our proof of existence of Gaussian Beams on $M_0$, which are a family of smooth approximate solutions to $d_A^*d_Au = 0$ depending on a parameter $\tau \in \mathbb{R}$, bounded in $L^2$ norm and …
-
SEARCHLIGHT CT: A NEW REGULARIZED RECONSTRUCTION METHOD FOR HIGHLY COLLIMATED X-RAY TOMOGRAPHY
… The algorithm uses an iteration of the X-ray Transform and its regularized inverse. The performance of the algorithm is illustrated on simulated phantoms as well as experimental data. It is tested initially on 2D data and studied in detail for the 3D case including the adaptation to spiral …
-
Complex-Analytic Methods in Reconstructive Integral Geometry
… formulae for the attenuated and non-attenuated X-ray transform over a wide class of curves in a simply-connected region of 2-dimensional Euclidean space. The method used to derive these formulae is based on the complexication of the vector felds defing the particle transport,thereby making the …
-
Stability, Range and Statistical Aspects of non-Abelian X-ray tomography
The non-Abelian X-ray transform on a Riemannian manifold with boundary (M,g) is a nonlinear map A → CA that associates to a matrix-valued and possibly direction-dependent function A, referred to as attenuation, its scattering data CA. The scattering data records initial-to-end-value maps for the …