Real-time calculation of a limiting form of the Renyi entropy applied to detection of subtle changes in scattering architecture

Abstract

Previously a new method for ultrasound signal characterization using entropy Hf was reported, and it was demonstrated that in certain settings, further improvements in signal characterization could be obtained by generalizing to Renyi entropy-based signal characterization If(r) with values of r near 2 (specifically r=1.99) [M. S. Hughes et al., J. Acoust. Soc. Am. 125, 3141–3145 (2009)]. It was speculated that further improvements in sensitivity might be realized at the limit r→2. At that time, such investigation was not feasible due to excessive computational time required to calculate If(r) near this limit. In this paper, an asymptotic expression for the limiting behavior of If(r) as r→2 is derived and used to present results analogous to those obtained with If(1.99). Moreover, the limiting form If,∞ is computable directly from the experimentally measured waveform f(t) by an algorithm that is suitable for real-time calculation and implementation.