Optimal “image‐based” weighting for energy‐resolved CT

This paper investigates a method of reconstructing images from energy-resolved CT data with negligible beam-hardening artifacts and improved contrast-to-nosie ratio (CNR) compared to conventional energy-weighting methods. Conceptually, the investigated method first reconstructs separate images from each energy bin. The final image is a linear combination of the energy-bin images, with the weights chosen to maximize the CNR in the final image. The optimal weight of a particular energy-bin image is derived to be proportional to the contrast-to-noise-variance ratio in that image. The investigated weighting method is referred to as "image-based" weighting, although, as will be described, the weights can be calculated and the energy-bin data combined prior to reconstruction. The performance of optimal image-based energy weighting with respect to CNR and beam-hardening artifacts was investigated through simulations and compared to that of energy integrating, photon counting, and previously studied optimal "projection-based" energy weighting. Two acquisitions were simulated: dedicated breast CT and a conventional thorax scan. The energy-resolving detector was simulated with five energy bins. Four methods of estimating the optimal weights were investigated, including task-specific and task-independent methods and methods that require a single reconstruction versus multiple reconstructions. Results demonstrated that optimal image-based weighting improved the CNR compared to energy-integrating weighting by factors of 1.15-1.6 depending on the task. Compared to photon-counting weighting, the CNR improvement ranged from 1.0 to 1.3. The CNR improvement factors were comparable to those of projection-based optimal energy weighting. The beam-hardening cupping artifact increased from 5.2% for energy-integrating weighting to 12.8% for optimal projection-based weighting, while optimal image-based weighting reduced the cupping to 0.6%. Overall, optimal image-based energy weighting provides images with negligible beam-hardening artifacts and improved CNR compared to energy-integrating and photon-counting methods.