Grayscale Uncertainty of Projection Geometries and Projections Sets

• Published in: Combinatorial Image Analysis Vol. 12148; pp. 123 - 138
• Main Authors: Varga, László G., Lékó, Gábor, Balázs, Péter
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Algebraic reconstruction; Computed tomography; Uncertainty
• ISBN: 9783030510015; 3030510018
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-51002-2_9

In some cases of tomography, the projection acquisition process has limits, and thus one cannot gain enough projections for an exact reconstruction. In this case, the low number of projections leads to a lack of information, and uncertainty in the reconstructions. In practice this means that the pixel values of the reconstruction are not uniquely determined by the measured data and thus can have variable values. In this paper, we provide a theoretically proven uncertainty measure that can be used for measuring the variability of pixel values in grayscale reconstructions. The uncertainty values are based on linear algebra and measure the slopes of the hyperplane of solutions in the algebraic formulation of tomography. The methods can also be applied for any linear equation system, that satisfy a given set of conditions. Using the uncertainty measure, we also derive upper and lower limits on the possible pixel values in tomographic reconstructions.