Methods for Enhancing the Robustness of the Generalized Contrast-to-Noise Ratio

The generalized contrast-to-noise ratio (gCNR) is a new but increasingly popular metric for measuring lesion detectability due to its use of probability distribution functions that increase robustness against transformations and dynamic range alterations. The value of these kinds of metrics has become increasingly important as it becomes clear that traditional metrics can be arbitrarily boosted with advanced beamforming or the right kinds of postprocessing. The gCNR works well for most cases; however, we will demonstrate that for some specific cases the implementation of gCNR using histograms requires careful consideration, as histograms can be poor estimates of probability density functions (PDFs) when designed improperly. This is demonstrated with simulated lesions by altering the amount of data and the number of bins used in the calculation, as well as by introducing some extreme transformations that are represented poorly by uniformly spaced histograms. In this work, the viability of a parametric gCNR implementation is tested, more robust methods for implementing histograms are considered, and a new method for estimating gCNR using empirical cumulative distribution functions (eCDFs) is shown. The most consistent methods found were to use histograms on rank-ordered data or histograms with variable bin widths, or to use eCDFs to estimate the gCNR.