The Contrast Order: An Order-Based Image Quality Criterion for Nonlinear Beamformers

Many modern ultrasound beamformers report improved image quality when evaluated using classical criteria like the contrast ratio and contrast-to-noise ratio, which are based on summary statistics of regions of interest (ROIs). However, nonlinear beamformers and post-processing methods can substantially alter these statistics, raising concerns that the reported improvements may reflect changes in dynamic range or remapping rather than a reflection of true information gain, such as clutter suppression. New criteria like the generalized contrast-to-noise ratio (gCNR) address these concerns, but rely on noisy estimates of the underlying distribution. To address this, we introduce a new image quality criterion, called the contrast order (CO), defined as the expected value of the sign of the difference in brightness between two ROIs. The CO is invariant under all strictly monotonic transformations of the image values, as it depends only on their relative ordering, and is interpretable as the probability that one ROI is brighter than the other minus the probability that it is darker. Unlike the gCNR, the CO has a simple unbiased estimator whose variance decreases with the number of samples in each ROI. We further propose the effective contrast ratio (ECR), which calibrates the contrast order to the familiar contrast ratio such that the two coincide under ideal Rayleigh-speckle statistics. Together, the CO and ECR provide order- and sign-preserving, dynamic-range-invariant criteria for evaluating lesion contrast, offering a principled alternative to classical and newer image quality criteria when assessing modern beamformers.