The problem of relating objective measurements of signals and noise encountered in diagnostic imaging procedures to empirical measures of observer performance, such as Receiver Operating Characteristic (ROC) curves (Ref. 1) is both important and difficult.
David J. Goodenough,
"Objective Measures Related To ROC Curves", Proc. SPIE 0047, Application of Optical Instrumentation in Medicine III, (1 February 1975); doi: 10.1117/12.954042; https://doi.org/10.1117/12.954042