Examining the Opposite Ray Algorithm 
	   As a Means of Detecting Motion in 
	CT Images From Fan-Beam Projection Systems


	A.J. Godbout, N.C. Linney


Abstract

A current problem in medical tomography systems is motion artifacts. 
These are errors introduced into an image as a result of motion in 
the object during imaging.  Various methods have been implemented to
try and remove or reduce such artifacts.  This research focuses on
improving a previously developed method [3], whereby only data 
already present in the image is used to identify and remove motion 
errors.  The original “opposite ray algorithm” [3] used a first 
order Taylor series expansion around a particular projection ray to 
estimate its exact opposite.  Then the opposite ray was used in 
conjunction with the original ray to isolate and identify motion 
error.  Using that method with a first order Taylor series 
expansion produced good results for removing translation motion 
artifacts. However less success was found in removing rotational 
or deformational motions.  This research explores the use of a 
second order Taylor series expansion about a particular projection 
ray to determine the opposite ray and the effect this has on 
identifying translation, rotation and deformation motions.
	
	By comparing results found in cases involving translation 
motion to those involving deformation or rotation motion we were 
able to gauge how well the algorithm is at identifying such motions.
Although, we show that the second order Taylor series expansion 
introduces additional unwanted spatial error into the image making 
it hard to isolate motion error we also show that the opposite ray 
algorithm detects a strong motion signal for all three types of 
motion.  Results presented here show that the “opposite ray” 
algorithm can be used effectively to identify motion error from 
deformation or rotation motion on par with that of translation 
motion.  

Index Terms – Biomedical signal processing, CT, motion artifacts, 
tomography