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

Entropy

Michael S. Hughes¹  John E. McCarthy³  Paul J. Bruillard¹  Jon N. Marsh²  Samuel A. Wickline² 

[1] Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99354, USA; E-Mail:;School of Medicine, Washington University in St. Louis, 660 S. Euclid Ave, St Louis, MO 63110, USA; E-Mails:;Department of Mathematics, Washington University in St. Louis, 1 Brookings Dr., St Louis, MO 63130, USA; E-Mail:

关键词: information wave;    optimal detection;    entropy image;    joint entropy;   

DOI  :  10.3390/e17063518

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland