[Incident Photon Number and Reconstructed Linear Attenuation Coefficients in Iterative CT Image Reconstruction]

[Purpose] The iterative CT image reconstruction (IR) method has been successfully incorporated into commercial CT scanners as a means to promote low-dose CT with high image quality. However, the algorithm of the IR method has not been made publicly available by scanner manufacturers. Kudo reviewed the fundamentals of IR methods on the basis of the articles published by the joint research group of each manufacture that were released before and during product development (Med Imag Tech 32: 239-248, 2014). According to this review, the object function of the IR method consists of the data fidelity term (likelihood) and the regularization term. The regularization term plays a significant role in the IR method; however, it has not been clarified whether or not the variance of projection data should be included into the likelihood to act the regularization term effectively. Our purpose in this study was to investigate the relationship of the incident photon number and the reconstructed linear attenuation coefficients of the IR method by numerical experiments.[Methods] We assumed the X-ray beam was a pencil beam, and the system matrix was given by the line integral of linear attenuation coefficients because we focused on the accuracy of the reconstructed linear attenuation coefficients in the ideal photon detection system equations given by Kudo. Total variation (TV) and the relative difference function were used for regularization of the IR method. Three kinds of numerical phantoms with 256×256 pixels were used as test images. Poisson noise was added to the projection data with 256 linear sampling and 256 views over 180°. The accuracy of reconstructed linear attenuation coefficients was evaluated by the mean reconstructed value within a region of interest (ROI) and the relative root mean square errors (%RMSEs) to the object image.[Results] The linear attenuation coefficients were reconstructed accurately by the IR method including the variance of projection data into the likelihood in comparison with the IR method without including the variance. When the incident photon number ranged from 100 to 2000 for the object having a mean linear attenuation coefficient of 0.067 to 0.087 cm^-1, the reconstructed linear attenuation coefficients in ROI were close to the true values. However, when the incident photon number was 50, both the accuracy and the uniformity of reconstructed images decreased.[Discussion] From the viewpoint of the visual observation, the image quality of the IR method was superior to that of the filtered back-projection (FBP) image processed with the Gaussian filter of FWHM equal to 3 pixels. For the object with a high absorber, the FBP gives linear attenuation coefficients that were lower than the true values. This phenomenon was also observed in the IR method. The projection data of CT were given by the logarithm operation of the ratio between the incident photon and the transmitted photon numbers. If the transmitted photon number happened to be equal to 0 owing to the influence of noise, it was held to a value of 1 to avoid the logarithm of zero. This process caused an error of the linear attenuation coefficients.[Conclusion] The variance of projection data should be included into the likelihood to act the regularization term effectively in the IR method.