Application of a real-time, calculable limiting form of the Renyi entropy for molecular imaging of tumors

Abstract

Previously, we reported new methods for ultrasound signal characterization using entropy, Hf; a generalized entropy, the Renyi entropy, If(r); and a limiting form of Renyi entropy suitable for real-time calculation, If,∞. All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the Renyi entropy, If,∞, is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to detect reliably the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model.

Joint entropy of continuously differentiable ultrasonic waveforms

“…9 All of these investigations required acquisition of thousands of radio frequency (RF) signals, f ðtÞ. For each of these captured waveforms, viewed as a sampled version of a differentiable function, the probability density function of values was computed using the digitized values of f ðtÞ.…”

Acoustic firearm discharge detection and classification in an enclosed environment

“…To address the need to identify weapon types from their acoustic signatures, we have investigated various entropies as previous studies have demonstrated their utility for analysis of ultrasonic signals in both materials characterization and medical ultrasonics. [1][2][3][4][5][6][7][8][9][10][11][12][13] The current study demonstrates the utility of entropies for analysis of acoustic signals in the audio range as well. When used in conjunction with energy analysis it appears that acoustic discrimination of weapon type is also possible.…”

Use of smoothing splines for analysis of backscattered ultrasonic waveforms: Application to monitoring of steroid treatment of dystrophic mice

“…This relationship between energy and entropy images has been observed in previous studies. [8, 9, 12] Second, in the I f ,∞ image obtained using optimal smoothing splines, we note the perfectly white region between the transducer, which is above the mouse, as well as the white region at deeper and thus more highly attenuated regions of the image. These correspond to regions where the smoothing spline algorithm has returned a masked value indicating that a valid value of I f ,∞ can not be obtained.…”

“…The most notable feature of later studies is that I f ,∞ is computable using an algorithm having a lower operation count than that required to produce B-Mode grayscale images and may thus be computed in real-time. [9, 12]…”