Null space and resolution in dynamic computerized tomography. (11th January 2016)

• Record Type: Journal Article
• Authors: Hahn, Bernadette N
• Is Part Of: Inverse problems. Volume 32:Number 2(2016:Feb.)
• Publication Date: 2016-01-11
• Subjects: singular value decomposition -- null space -- resolution -- dynamic computerized tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/2/025006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: One major challenge in computerized tomography is to image objects which change during the data acquisition and hence lead to inconsistent data sets. Motion artefacts in the reconstructions can be reduced by applying specially adapted algorithms which take the dynamic behaviour into account. Within this article, we analyse the achievable resolution in the dynamic setting in case of two-dimensional affine deformations. To this end, we characterize the null space of the operator describing the dynamic case, using its singular value decomposition and a necessary dynamic consistency condition. This shows that independent of any reconstruction method, the specimen's dynamics results in a loss of resolution compared to the stationary setting. Our theoretical results are illustrated at a numerical example.