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 (CT) applications. PIBR methods take ad-vantage of shared anatomical information between sequential scans by incorporating a patient-specific prior image into the re-construction objective function, often as a form of regularization. However, one major challenge with PIBR methods is how to opti-mally 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 itera-tive reconstruction (MBIR), 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 work, 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 which are typically quantified in terms of spatial resolution or ar-tifacts. 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 prospec-tively determine prior image regularization strength to admit spe-cific kinds of anatomical change in the reconstruction. Because bias is dependent on local statistics, we further generalized shift-variant prior image penalties which permit uniform (shift-invari-ant) admission of anatomical changes across the imaging field-of-view (FOV). We validated the mathematical framework in phan-tom studies and compared bias predictions with estimates based on brute force exhaustive evaluation using numerous iterative re-constructions across regularization values. The experimental re-sults demonstrate that the proposed analytical approach can pre-dict the bias-regularization relationship accurately, allowing for prospective determination of the prior image regularization strength in PIBR. Thus, the proposed approach provides an im-portant tool for controlling image quality of PIBR methods in a reliable, robust, and efficient fashion.