In an earlier studies we reported on the application of Renyi entropy, If (r), r < 2, for the detection of precancerous lesions, by detection subtle changes in backscattered waveforms f(t) that occured as targeted nanoparticles slowly accumulated near the lesion. In contrast, the signal energy, defined as the sum of squares of the over the same moving window, was unable to detect this change (as was conventional B-mode imaging). Although the computational effort to obtain the result precluded its clinical application with currently available equipment, the study raised the possibility of further sensitivity improvements by using values of r closer to the limiting value of 2, where If (r) approaches infinity. The current study demonstrates that by extracting the asymptotic form of If (r) as r → 2 there is no loss of sensitivity. However, the resulting algorithm is must faster than previous approaches and has an operation count that is suitable for implementation in a real-time imaging system.