On the Conditioning of Spectral Channelization (Energy Binning) and Its Impact on Multi-Material Decomposition Based Spectral Imaging in Photon-Counting CT

Objective: The conditioning (well-posedness) of basis materials (functions) and spectral channelization play important roles in determining the performance of spectral imaging (material specific imaging and virtual monochromatic imaging/analysis) in photon-counting CT. Aimed at further understanding the fundamentals of photon-counting spectral CT and providing guidelines on its design and implementation, we propose a singular value decomposition (SVD) and analysis based approach in this work to assess the conditioning of spectral channelization and its impact on the performance of spectral imaging under both ideal and realistic detector spectral response. Methods: Via simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, the condition number acquired via SVD and analysis is employed to assess the conditioning of spectral channelization in photon-counting CT and its impact on the performance of spectral imaging. The simulation study runs over two- and three-material decom-position based spectral imaging (material specific imaging and virtual monochromatic imaging/analysis over the energy range [18] [150] keV). Under both ideal and realistic detector spectral response, a specially designed phantom that mimics the soft and bony tissues in the head is utilized to quantitatively reveal the relationship between the conditioning (condition number) of spectral channelization and the performance (mainly noise and contrast-to-noise ratio) of spectral imaging in photon-counting CT. The simulation study is also extended over the cases wherein up to 50% spectral overlapping occurs. Results: The results show that, under ideal detector spectral response, the condition number of spectral channelization reaches the minimum while no overlapping occurs in spectral channels. The condition number of spectral channelization increments with increasing spectral overlapping in the channels. The distortion in detector's spectral response induced by scattering, charge-sharing and fluorescent escaping results in spectral overlapping in spectral channels and thus degrades the conditioning (larger condition number) of spectral channelization. Respectively, the noise increases and contrast-to-noise ratio decreases in material- specific imaging and virtual monochromatic imaging/analysis, while the condition number of spectral channelization increments with increasing spectral overlapping. Conclusion: The SVD and analysis based approach can be utilized to systematically analyze the conditioning of spectral channelization and its impact on the performance of spectral imaging in photon-counting CT. Significance: The approach proposed by us brings innovation and has significance. In addition to providing information for insightful understanding of the fundamentals, the approach proposed in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in photon-counting CT and energy-integration CT as well, along with its applicability to other x-ray related imaging modalities such as radiography and tomosynthesis.