# ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION

## Abstract

Virtually all modern imaging devices function by collecting either electromagnetic or acoustic backscattered waves and using the energy carried by these waves to determine pixel values that build up what is basically an ”energy” picture. However, waves also carry ”informa- tion” that also may be used to compute the pixel values in an image. We have employed several measures of information, all of which are based on different forms of entropy. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods for materials characterization and medical imaging. Similar results also have been obtained with microwaves. The most sensitive information measure appears to be the joint entropy of the backscattered wave and a reference signal. A typical study is comprised of repeated acquisition of backscattered waves from a specimen that is changing slowing with acquisition time or location. The sensitivity of repeated experimental observations of such a slowly changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., observed noise). We compute the sensitivity for joint entropy and signal energy measurements assuming that noise is Gaussian and using Wiener integration to compute the required mean values and variances. Thesemore »

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1214883

- Report Number(s):
- PNNL-SA-104976

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Entropy, 17(6):3518-3551

- Additional Journal Information:
- Journal Name: Entropy, 17(6):3518-3551

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Information Theory; Signal Processing; Signal Detection; Entropy; Joint Entropy

### Citation Formats

```
Hughes, Michael S., McCarthy, John, Bruillard, Paul J., Marsh, Jon N., and Wicklines, Samuel A.
```*ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION*. United States: N. p., 2015.
Web. doi:10.3390/e17063518.

```
Hughes, Michael S., McCarthy, John, Bruillard, Paul J., Marsh, Jon N., & Wicklines, Samuel A.
```*ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION*. United States. doi:10.3390/e17063518.

```
Hughes, Michael S., McCarthy, John, Bruillard, Paul J., Marsh, Jon N., and Wicklines, Samuel A. Mon .
"ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION". United States. doi:10.3390/e17063518.
```

```
@article{osti_1214883,
```

title = {ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION},

author = {Hughes, Michael S. and McCarthy, John and Bruillard, Paul J. and Marsh, Jon N. and Wicklines, Samuel A.},

abstractNote = {Virtually all modern imaging devices function by collecting either electromagnetic or acoustic backscattered waves and using the energy carried by these waves to determine pixel values that build up what is basically an ”energy” picture. However, waves also carry ”informa- tion” that also may be used to compute the pixel values in an image. We have employed several measures of information, all of which are based on different forms of entropy. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods for materials characterization and medical imaging. Similar results also have been obtained with microwaves. The most sensitive information measure appears to be the joint entropy of the backscattered wave and a reference signal. A typical study is comprised of repeated acquisition of backscattered waves from a specimen that is changing slowing with acquisition time or location. The sensitivity of repeated experimental observations of such a slowly changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., observed noise). We compute the sensitivity for joint entropy and signal energy measurements assuming that noise is Gaussian and using Wiener integration to compute the required mean values and variances. These can be written as solutions to the Heat equation, which permits estimation of their 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.},

doi = {10.3390/e17063518},

journal = {Entropy, 17(6):3518-3551},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}