  Purpose: Many useful image quality metrics for evaluating linear image
reconstruction techniques do not apply to or are difficult to interpret for
non-linear image reconstruction. The vast majority of metrics employed for
evaluating non-linear 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 over-regularization 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. Methods: 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 non-linear
algorithm based on total variation constrained least-squares (TV-LSQ). 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. Results: Loss of
signal detectability is seen to correlate well with the blocky or patchy
appearance due to over-regularization with TV-LSQ, and this trend runs counter
to the image RMSE metric, which tends to favor the over-regularized images.
Conclusions: 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 non-linear image reconstruction is used.
