Publications (7)
On non-parametric density estimation on linear and non-linear manifolds using generalized Radon transforms
James Webber, Erika Hussey, Eric Miller +1
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a…
Microlocal analysis of a spindle transform
James Webber, Sean Holman
An analysis of the stability of the spindle transform, introduced in ("Three dimensional Compton scattering tomography" arXiv:1704.03378 [math.FA]), is presented. We do this via a…
X-ray Compton scattering tomography
James Webber
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a…
Compton scattering tomography in translational geometries
James Webber, Eric Miller
Here we present new injectivity results for 2-D and 3-D Compton scattering tomography (CST) problems in translational geometries. The results are proven through the explicit…
Three dimensional Compton scattering tomography
James Webber, William Lionheart
We propose a new acquisition geometry for electron density reconstruction in three dimensional X-ray Compton imaging using a monochromatic source. This leads us to a new three dime…
A joint reconstruction and lambda tomography regularization technique for energy-resolved X-ray imaging
James Webber, Eric Todd Quinto, Eric L. Miller
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the at…