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. 2009 May;125(5):3141-5.
doi: 10.1121/1.3097489.

Application of Renyi entropy for ultrasonic molecular imaging

M S Hughes  1 , J N Marsh, J M Arbeit, R G Neumann, R W Fuhrhop, K D Wallace, L Thomas, J Smith, K Agyem, G M Lanza, S A Wickline, J E McCarthy
Affiliations

Application of Renyi entropy for ultrasonic molecular imaging

M S Hughes et al. J Acoust Soc Am. 2009 May.

Abstract

Previous work has demonstrated that a signal receiver based on a limiting form of the Shannon entropy is, in certain settings, more sensitive to subtle changes in scattering architecture than conventional energy-based signal receivers [M. S. Hughes et al., J. Acoust. Soc. Am. 121, 3542-3557 (2007)]. In this paper new results are presented demonstrating further improvements in sensitivity using a signal receiver based on the Renyi entropy.

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Figures

Figure 1
Figure 1
A time-domain waveform, f(t), with three critical points (left), and its associated density function wf(y) which has three corresponding (integrable) singularities.
Figure 2
Figure 2
Left panel: A plot of If(r) (left) showing that If(1)=−Hf and that If(r) grows without bound as r→2. Right panel: Even though two similar waveforms f(t) and f(t)+ξ(t) may have nearly equal entropies, Hf, it is possible that as r→2 their Renyi entropies may diverge.
Figure 3
Figure 3
A cross-sectional diagram of the nanoparticles used in our study.
Figure 4
Figure 4
A diagram of the apparatus used to acquire rf data backscattered from HPV mouse ears in vivo together with a histologically stained section of the ear indicating portions where αvβ3-targeted nanoparticles could adhere and a fluorescent image demonstrating presence of targeted nanoparticles.
Figure 5
Figure 5
A plot of average enhancement, i.e., change relative to value at time 0, obtained by analysis of If(1.99) (top) and Hf (bottom) images from four HPV mice injected with αvβ3-targeted nanoparticles.
Figure 6
Figure 6
A plot of average enhancement, i.e., change relative to value at time 0, obtained by analysis of If(1.99) (top) and Hf (bottom) images from four HPV mice injected with nontargeted nanoparticles. Neither plot exhibits a statistically significant change.
See this image and copyright information in PMC

References

    1. Hughes M. S., McCarthy J. E., Marsh J. N., Arbeit J. M., Neumann R. G., Fuhrhop R. W., Wallace K. D., Znidersic D. R., Maurizi B. N., Baldwin S. L., Lanza G. M., and Wickline S. A., “Properties of an entropy-based signal receiver with an application to ultrasonic molecular imaging,” J. Acoust. Soc. Am. 10.1121/1.2722050 121, 3542–3557 (2007). - DOI - PubMed
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    1. Bracewell R. N., The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

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