Unbiased statistical image reconstruction in low-dose CT

When x-ray exposure level is lowered in the attempt to reduce radiation dose in x-ray computed tomography (CT), noise level is elevated. While this is well known in the community, less attention has been paid to another critically important fact in low dose CT: the accuracy of CT number is also compromised. Namely, CT numbers for some organs are increased while the CT number may be decreased in some other organs. The application of denoising methods can reduce noise level, but the denoising method, generally speaking, does not reduce the CT number biases. This has been shown in systematic experimental studies using clinically available reconstruction methods such as the conventional filtered backprojection or the statistical model based image reconstruction method. Although it has been known that the bias can be eliminated in statistical reconstruction if the Poisson log-likelihood function is not approximated by its quadratic form, the computation cost is quite expensive and thus these types of methods are not used in currently available commercial CT products. In this paper, we present an innovative way to design the statistical weighting function to enable unbiased statistical reconstruction with a quadratic data fidelity term and a regularizer.