Assessing the Condition of Spectral Channelization (Energy Binning) in Photon-counting CT: A Singular Value Decomposition Based Approach

To further understand the fundamentals of photon-counting spectral CT and provide guidelines on its design and implementation, we propose a singular value decomposition (SVD) based approach to assess the conditioning of spectral channelization and its impact on the performance of spectral imaging under both ideal and realistic detector spectral response. The study runs over two- and three-material decomposition based spectral imaging (material specific imaging). A specially designed phantom that mimics the soft and bony tissues in the head is used to reveal the relationship between the conditioning of spectral channelization and the imaging performance (noise and contrast-to-noise ratio). The study also runs over the cases with up to 50% spectral overlapping and gapping. Under ideal detector spectral response, the condition number of spectral channelization reaches the minimum while no overlapping occurs in spectral channels, and increments with increasing spectral overlapping, and so does in the situation while gapping occurs. The distortion in detector's spectral response due to charge-sharing and fluorescent escaping inevitably leads to spectral overlapping and thus degrades the conditioning of spectral channelization. With increasing condition number, the noise increases and contrast-to-noise ratio decreases, respectively. The proposed approach, especially its coverage on the situation wherein gapping occurs in spectral channelization, is novel and may provide information for insightful understanding of the fundamentals and guidelines on implementation of spectral imaging in photon-counting and energy-integration CT, and other x-ray imaging modalities such as radiography and tomosynthesis.