Data consistency conditions for truncated fanbeam and parallel projections

Abstract

New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

An iterative projection‐based motion estimation and compensation scheme for head x‐ray CT

“…The method could be further improved by modeling the motion as a parameterized function of time (or view number). 13,16 This would reduce the number of unknowns and impose a physically meaningful smoothness to the estimated motion.…”

“…7 Artificial or anatomical landmarks can be also tracked in the image or projection domains. 8,9 Indirect estimation methods have been proposed where motion is estimated through the minimization of errors in consistency conditions [10][11][12][13] or iteratively updating the motion together with the reconstruction process. [14][15][16][17] Another approach has used similarity measures to quantify changes between successive projections to measure subject motion.…”

“…Among these methods, some addressed the problem in 2D parallel-beam or fan-beam geometries. [10][11][12][13] Other retrospective motion estimation and compensation methods addressed the problem for 3D circular cone beam CT (CBCT). 8,9,14,15 The methods in Refs.…”

On locality of Radon to Riesz transform

“…A common approximation of the noise on such data in the context of medical imaging is a centered Gaussian additive noise proportional to the value R θ !f ðsÞ [6,3]. In the following we add to R θ !f ðsÞ the noise value…”

Motion compensation for cone-beam CT using Fourier consistency conditions

“…Several extensions of the HLCC exist for the fan-beam geometry and have been used for motion estimation or detection by (Yu and Wang; 2007; Leng et al; 2007; Clackdoyle and Desbat; 2015). Recently, an extension to three-dimensional cone-beam geometries has been proposed by Clackdoyle and Desbat (2013). It requires that all X-ray source positions are on a plane which does not intersect the object.…”