A signal detection model for quantifying overregularization in nonlinear image reconstruction.

Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for nonlinear image reconstruction. The vast majority of metrics employed for evaluating nonlinear image reconstruction are based on some form of global image fidelity, such as image root mean square error (RMSE). Use of such metrics can lead to overregularization in the sense that they can favor removal of subtle details in the image. To address this shortcoming, we develop an image quality metric based on signal detection that serves as a surrogate to the qualitative loss of fine image details. The metric is demonstrated in the context of a breast CT simulation, where different equal-dose configurations are considered. The configurations differ in the number of projections acquired. Image reconstruction is performed with a nonlinear algorithm based on total variation constrained least-squares (TV-LSQ). The resulting images are studied as a function of three parameters: number of views acquired, total variation constraint value, and number of iterations. The images are evaluated visually, with image RMSE, and with the proposed signal-detection-based metric. The latter uses a small signal, and computes detectability in the sinogram and in the reconstructed image. Loss of signal detectability through the image reconstruction process is taken as a quantitative measure of loss of fine details in the image. Loss of signal detectability is seen to correlate well with the blocky or patchy appearance due to overregularization with TV-LSQ, and this trend runs counter to the image RMSE metric, which tends to favor the over-regularized images. The proposed signal detection-based metric provides an image quality assessment that is complimentary to that of image RMSE. Using the two metrics in concert may yield a useful prescription for determining CT algorithm and configuration parameters when nonlinear image reconstruction is used.