title: CT energy weighting in the presence of scatter and limited energy resolution.
abstract: OBJECTIVE
  Energy-resolved CT has the potential to improve the contrast-to-noise ratio (CNR) through optimal weighting of photons detected in energy bins. In general, optimal weighting gives higher weight to the lower energy photons that contain the most contrast information. However, low-energy photons are generally most corrupted by scatter and spectrum tailing, an effect caused by the limited energy resolution of the detector. This article first quantifies the effects of spectrum tailing on energy-resolved data, which may also be beneficial for material decomposition applications. Subsequently, the combined effects of energy weighting, spectrum tailing, and scatter are investigated through simulations.
  
  
  METHODS
  The study first investigated the effects of spectrum tailing on the estimated attenuation coefficients of homogeneous slab objects. Next, the study compared the CNR and artifact performance of images simulated with varying levels of scatter and spectrum tailing effects, and reconstructed with energy integrating, photon-counting, and two optimal linear weighting methods: Projection-based and image-based weighting. Realistic detector energy-response functions were simulated based on a previously proposed model. The energy-response functions represent the probability that a photon incident on the detector at a particular energy will be detected at a different energy. Realistic scatter was simulated with Monte Carlo methods.
  
  
  RESULTS
  Spectrum tailing resulted in a negative shift in the estimated attenuation coefficient of slab objects compared to an ideal detector. The magnitude of the shift varied with material composition, increased with material thickness, and decreased with photon energy. Spectrum tailing caused cupping artifacts and CT number inaccuracies in images reconstructed with optimal energy weighting, and did not impact images reconstructed with photon counting weighting. Spectrum tailing did not significantly impact the CNR in reconstructed images. Scatter reduced the CNR for all energy-weighting methods; however, the effect was greater for optimal energy weighting. For example, optimal energy weighting improved the CNR of iodine and water compared to energy-integrating weighting by a factor of approximately 1.45 in the absence of scatter and by a factor of approximately 1.1 in the presence of scatter (8.9 degrees cone angle, SPR 0.5). Without scatter correction, the difference in CNR resulting from photon-counting and optimal energy weighting was negligible (< 15%) for cone angles greater than 4.4 degrees (SPR > 0.3). Optimal weights combined with deterministic scatter correction provided a 1.3 and 1.1 improvement in CNR compared to energy-integrating and photon-counting weighting, respectively, for the 8.9 degrees cone angle simulation. In the absence of spectrum tailing, image-based weighting demonstrated reduced cupping artifact compared to projection-based weighting; however, both weighting methods exhibited similar cupping artifacts when spectrum tailing was simulated. There were no statistically significant differences in the CNR resulting from projection an image-based weighting for any of the simulated conditions.
  
  
  CONCLUSIONS
  Optimal linear energy weighting introduces artifacts and CT number inaccuracies due to spectrum tailing. While optimal energy weighting has the potential to improve CNR compared to conventional weighting methods, the benefits are reduced as scatter increases. Efficient methods for reducing scatter and correcting spectrum tailing effects are required to obtain the highest benefit from optimal energy weighting.
authors.affiliation: Department of Biomedical Engineering, Marquette University, Milwaukee, Wisconsin 53201, USA. taly.gilat-schmidt@marquette.edu
authors.forename: Taly Gilat
authors.initials: TG
authors.lastname: Schmidt
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D008962:Models, Theoretical; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012542:Scattering, Radiation; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*; D014965:X-Rays