On the conditioning of basis materials and its impact on multimaterial decomposition-based spectral imaging in...

Material-specific imaging and virtual monochromatic imaging/analysis are the two forms of spectral imaging in CT implemented via either energy-integration or photon-counting data acquisition. Aimed at further understanding the fundamentals and providing guidelines on its design and implementation, we quantitatively investigate the conditioning (sufficiency in dimensionality, well-posedness in basis functions, and matching of K-edge materials) of basis materials and its impact on the performance of spectral imaging in photon-counting CT.

Initially, singular value decomposition (SVD) is employed to investigate the dimensionality of material space for multimaterial decomposition-based spectral imaging in photon-counting CT over the energy range [18 150] keV. Then, the SVD is extended to study the well-posedness of basis functions, its relationship with the dimensionality of materials to be imaged, and its impact on imaging performance. A number of phantoms are designed to mimic the soft and bony tissues in the head and contrast enhancement materials (iodine and gadolinium). Simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, are carried out to evaluate and verify the proposed approach of conditioning analysis and the relationship between the conditioning of basis materials and the performance of spectral imaging in photon-counting CT.

The preliminary data show that the dimensionality of biological tissues, including both soft and bony tissues, is effectively equal to two. The dimensionality increments with inclusion of K-edge materials into the materials to be imaged. The well-posedness of basis functions depends on the correlation between the functions and impacts the noise in material decomposition substantially, but affects the noise in virtual monochromatic imaging/analysis moderately. If a K-edge material is in the materials to be imaged, the same K-edge material has to be one of the basis materials, but its concentration does not affect the accuracy of material decomposition significantly. Moreover, inclusion of K-edge material into the basis material makes the tuning of correlation among the basis functions feasible and thus improves the performance of spectral imaging in photon-counting CT.

The extension of SVD for systematic analysis of multimaterial decomposition-based spectral imaging in photon-counting CT is of innovation and significance. In addition to providing more information on the fundamentals, the approach used in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in either photon-counting or energy-integration CT, as well as other x-ray-related imaging modalities such as radiography and tomosynthesis.