Regularization Analysis and Design for Prior-Image-Based X-Ray CT Reconstruction

Prior-image-based reconstruction (PIBR) methods have demonstrated great potential for radiation dose reduction in computed tomography applications. PIBR methods take advantage of shared anatomical information between sequential scans by incorporating a patient-specific prior image into the reconstruction objective function, often as a form of regularization. However, one major challenge with PIBR methods is how to optimally determine the prior image regularization strength which balances anatomical information from the prior image with data fitting to the current measurements. Too little prior information yields limited improvements over traditional model-based iterative reconstruction, while too much prior information can force anatomical features from the prior image not supported by the measurement data, concealing true anatomical changes. In this paper, we develop quantitative measures of the bias associated with PIBR. This bias exhibits as a fractional reconstructed contrast of the difference between the prior image and current anatomy, which is quite different from traditional reconstruction biases that are typically quantified in terms of spatial resolution or artifacts. We have derived an analytical relationship between the PIBR bias and prior image regularization strength and illustrated how this relationship can be used as a predictive tool to prospectively determine prior image regularization strength to admit specific kinds of anatomical change in the reconstruction. Because bias is dependent on local statistics, we further generalized shift-variant prior image penalties that permit uniform (shift invariant) admission of anatomical changes across the imaging field of view. We validated the mathematical framework in phantom studies and compared bias predictions with estimates based on brute force exhaustive evaluation using numerous iterative reconstructions across regularization values. The experimental results demonstrate that the proposed analytical approach can predict the bias-regularization relationship accurately, allowing for prospective determination of the prior image regularization strength in PIBR. Thus, the proposed approach provides an important tool for controlling image quality of PIBR methods in a reliable, robust, and efficient fashion.