31 research outputs found
Differential Phase-contrast Interior Tomography
Differential phase contrast interior tomography allows for reconstruction of
a refractive index distribution over a region of interest (ROI) for
visualization and analysis of internal structures inside a large biological
specimen. In this imaging mode, x-ray beams target the ROI with a narrow beam
aperture, offering more imaging flexibility at less ionizing radiation.
Inspired by recently developed compressive sensing theory, in numerical
analysis framework, we prove that exact interior reconstruction can be achieved
on an ROI via the total variation minimization from truncated differential
projection data through the ROI, assuming a piecewise constant distribution of
the refractive index in the ROI. Then, we develop an iterative algorithm for
the interior reconstruction and perform numerical simulation experiments to
demonstrate the feasibility of our proposed approach
Solving the interior problem of computed tomography using a priori knowledge
A case of incomplete tomographic data for a compactly supported attenuation function is studied. When the attenuation function is a priori known in a subregion, we show that a reduced set of measurements are enough to uniquely determine the attenuation function over all the space. Furthermore, we found stability estimates showing that reconstruction can be stable near the region where the attenuation is known. These estimates also suggest that reconstruction stability collapses quickly when approaching the set of points that is viewed under less than 180°. This paper may be seen as a continuation of the work \u27Truncated Hilbert transform and image reconstruction from limited tomographic data\u27 (Defrise et al 2006 Inverse Problems 22 1037). This continuation tackles new cases of incomplete data that could be of interest in applications of computed tomography
Direct inversion of the Longitudinal Ray Transform for 2D residual elastic strain fields
We examine the problem of Bragg-edge elastic strain tomography from energy
resolved neutron transmission imaging. A new approach is developed for
two-dimensional plane-stress and plane-strain systems whereby elastic strain
can be reconstructed from its Longitudinal Ray Transform (LRT) as two parts of
a Helmholtz decomposition based on the concept of an Airy stress potential. The
solenoidal component of this decomposition is reconstructed using an inversion
formula based on a tensor filtered back projection algorithm whereas the
potential part can be recovered using either Hooke's law or a finite element
model of the elastic system. The technique is demonstrated for two-dimensional
plane-stress systems in both simulation, and on real experimental data. We also
demonstrate that application of the standard scalar filtered back projection
algorithm to the LRT in these systems recovers the trace of the solenoidal
component of strain and we provide physical meaning for this quantity in the
case of 2D plane-stress and plane-strain systems.Comment: 30 pages, 9 figure
Towards Omni-Tomography—Grand Fusion of Multiple Modalities for Simultaneous Interior Tomography
We recently elevated interior tomography from its origin in computed tomography (CT) to a general tomographic principle, and proved its validity for other tomographic modalities including SPECT, MRI, and others. Here we propose “omni-tomography”, a novel concept for the grand fusion of multiple tomographic modalities for simultaneous data acquisition in a region of interest (ROI). Omni-tomography can be instrumental when physiological processes under investigation are multi-dimensional, multi-scale, multi-temporal and multi-parametric. Both preclinical and clinical studies now depend on in vivo tomography, often requiring separate evaluations by different imaging modalities. Over the past decade, two approaches have been used for multimodality fusion: Software based image registration and hybrid scanners such as PET-CT, PET-MRI, and SPECT-CT among others. While there are intrinsic limitations with both approaches, the main obstacle to the seamless fusion of multiple imaging modalities has been the bulkiness of each individual imager and the conflict of their physical (especially spatial) requirements. To address this challenge, omni-tomography is now unveiled as an emerging direction for biomedical imaging and systems biomedicine