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Entropy 2015, 17(6), 3518-3551; doi:10.3390/e17063518

Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation

1
Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99354, USA
2
Department of Mathematics,Washington University in St. Louis, 1 Brookings Dr., St Louis, MO 63130, USA
3
School of Medicine, Washington University in St. Louis, 660 S. Euclid Ave, St Louis, MO 63110, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 20 January 2015 / Accepted: 20 May 2015 / Published: 25 May 2015
View Full-Text   |   Download PDF [1026 KB, uploaded 25 May 2015]   |  

Abstract

Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information”, as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., noise). Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an “optimal” reference for the joint entropy emerges, which also has been validated in several studies. View Full-Text
Keywords: information wave; optimal detection; entropy image; joint entropy information wave; optimal detection; entropy image; joint entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Hughes, M.S.; McCarthy, J.E.; Bruillard, P.J.; Marsh, J.N.; Wickline, S.A. Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation. Entropy 2015, 17, 3518-3551.

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