6 papers
Range Characterization of the Weighted Divergent Beam and Cone Integral Transforms
Fatma Terzioglu, Lili Yan
We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^…
An analytic inversion formula for the n-dimensional cylindrical Radon transform
Jenna Jones, Fatma Terzioglu
We study the overdetermined problem of inverting the n-dimensional cylindrical Radon transform, which maps a function to its integrals over cylindrical surfaces. In practice, the c…
Stability of the -Plane Transform on Measures and Hölder-Type Comparisons of Wasserstein Metrics
Fatma Terzioglu, Ryan Murray
We establish stability estimates for the -plane transform on finite positive Radon measures, with emphasis on Fourier and Wasserstein metrics. We first introduce a metric on …
THE ROLE OF FOURIER ANALYSIS IN TWO DIMENSIONAL TOMOGRAPHY
Andre Mas, Fatma Terzioglu, Ilse C. F. Ipsen
We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by derivin…
Mapping estimates for the -plane transform in Sobolev, Besov, and Triebel--Lizorkin Spaces
Fatma Terzioglu
We study mapping properties of the -plane transform in Sobolev, Besov, and Triebel--Lizorkin spaces. For , the -plane transform integrates a function over -…
Non-unique water and contrast agent solutions in dual-energy CT
JP Phillips, Emil Y. Sidky, Fatma Terzioglu +3
The goal of this work is to study occurrences of non-unique solutions in dual-energy CT (DECT) for objects containing water and a contrast agent. Previous studies of the Jacobian o…