Data-Driven Affine Deformation Estimation and Correction in Cone Beam Computed Tomography

Abstract

In computed tomography (CT), motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images. To remedy these artefacts, we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections. The proposed technique is data driven and thus removes the need for markers and/or a tracking system. A relationship between affine transformations and the cone beam transform is proved and used to correct the projections. The deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane-based inconsistency criterion. The criterion compares each projection of the main scan with all projections of a fast reference scan, which is acquired prior or posterior to the main scan. Experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam CT images.

Ab initio nonrigid X-ray nanotomography

“…If the nonrigid deformation processes are sufficiently slow, periodic or even externally controlled, then it is possible to collect a reference tomogram 9,18 , partial tomograms during which the sample is assumed to stay static 2,3,10 , or exploit the periodicity of the deformation process to improve the reconstruction 3,4,19 . However, these assumptions can often be too limiting if the deformation process is fast with respect to the tomogram acquisition time or if the process is unrepeatable.…”

“…Assuming that the dynamic process can be described by a diffeomorphic deformation, the coarsest deformation model is an affine transformation 1,18,20–22 . The affine transformation provides many advantages, such as exact reconstruction methods 20,23 and direct estimation of the deformation field from the measured projections 18 . However, affine transformations and other methods based on straight-ray projections 22,23 are not general, and in some cases can be an inadequate approximation to describe a realistic deformation processes.…”

“…Since our method is able to account for dynamic sample deformation during each angular sub-tomogram, it could relax the stringent requirements on the acquisition speed for in-vivo imaging and thus allow to use laboratory-based X-ray phase tomography methods 45,46 . In addition, the nonrigid tomographic geometry is able to better describe complex deformation fields that can originate from internal sample changes 11,18,47,48 and that may not be well described by affine transformations or linear deformation evolution.…”

3d virtual histology of neuronal tissue by propagation-based x-ray phase-contrast tomography

“…For a known motion this can be corrected, e.g., by shifting the projections accordingly (in the case of rigid motion in vertical or horizontal direction) or performing a filtered backprojection along dynamically curved paths [146]. In the case of a global affine motion in cone-beam tomography, a method for the detection and correction was presented in [177]. In most cases, however, the motion cannot be accounted for and artifacts can only be circumvented by changing the recording scheme, e.g., by decreasing the total scan time.…”

Cone-beam x-ray phase-contrast tomography for the observation of single cells in whole organs

“…A better treatment of motion and its correction in tomographic measurements is currently a hot topic in tomographic research. Recently an approach to detect and correct a global affine motion was presented in [121].…”