[Implementation of Statistically-Based Image Reconstruction Algorithms for CT and Numerical Evaluation of Image Quality].

[Purpose] Statistically-based image reconstruction (SIR) methods that have been incorporated into commercial CT scanners have succeeded in promoting low-dose CT with high image quality in comparison with scanners using the filtered back-projection (FBP) method. Not only researchers but also medical doctors and technologists engaged in CT studies have an interest in the algorithms of the SIR methods, however, the algorithms have not been made available to users by the CT manufacturers. Kudo reviewed the fundamentals of SIR methods on the basis of the articles published by the joint research group of each manufacturer released before product development (Med Imag Tech 32: 239-248, 2014). He classified the SIR methods into true iterative reconstruction (true IR), hybrid IR, and image space denoising (ISD) methods. His review article has made a significant contribution to the CT community of users. However, the reconstructed images obtained by those methods have not been presented. Our purpose in this study is to implement the mathematical equations of three IR methods, one each of the true IR, hybrid IR and ISD methods, and evaluate their image quality.[Methods] The system matrix of IR methods used in commercial CT scanners uses a physical photon detection process based on the finite size of an X-ray focal spot, the beam width, and the X-ray detector. However, we assumed the X-ray beam was a pencil beam and the system matrix was then given by the line integral of linear attenuation coefficients because we focus on the image quality in the ideal photon detection system equations given by Kudo. Total variation (TV) was used for regularization of the true IR, hybrid IR and ISD methods. Four kinds of numerical phantoms with 256×256 pixels were used as test images. Gaussian noise of 15, 20, 25, and 30 dB was added to the projection data with 256 linear samplings and 256 views over 180°.[Results] Root mean square errors (RMSEs) of the true IR, hybrid IR, and ISD methods were 4.28-5.70, 15.87-16.47, and 16.94-17.17, respectively. RMSE of the FBP method ranged from 27.64-33.02 and that of the FBP method processed with a Gaussian filter of FWHM (full width at half maximum) of 3 pixels ranged from 8.14-17.28. The image quality of the true IR method was superior to that of the hybrid IR and ISD methods and the FBP method.[Discussion] The noise was slightly suppressed by including the variance of projection data; however, the regularization was inevitable even if the noise levels were in the range of 25-30 dB. The noise was not suppressed sufficiently by the hybrid IR and ISD methods because the noise due to the FBP image used as the initial image for these IR methods has a dominating effect in successive reconstruction or denoise processing. Mathematical equations of each IR method were easily realized by observing the intermediate images such as the regularization term of the iteration process. In addition to these equations, the reconstructed images by the SIR methods and their RMSEs presented in this study are useful in CT research.[Conclusions] The fundamental point of SIR methods is the regularization term used in minimizing the object function.