## Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data

Applied Optics, Vol. 44, Issue 18, pp. 3846-3855 (2005)

http://dx.doi.org/10.1364/AO.44.003846

Acrobat PDF (325 KB)

### Abstract

The basic measurement equation r = B + alpha d + n is solved for alpha (the weight or abundance of the spectral target vector d) by two methods: (a) by subtracting the stochastic spectral background vector B from the spectral measurement/s vector r (subtraction solution) and (b) by orthogonal subspace projection (OSP) of the measurements to a subspace orthogonal to B (the OSP solution). The different geometry of the two solutions and in particular the geometry of the noise vector n is explored. The angular distribution of the noise angle between B and n is the key factor for determining and predicting which solution is better. When the noise-angle distribution is uniform, the subtraction solution is always superior regardless of the orientation of the spectral target vector d. When the noise is more concentrated in the direction parallel to B, the OSP solution becomes better (as expected). Simulations and one-dimensional hyperspectral measurements of vapor concentration in the presence of background radiation and noise are given to illustrate these two solutions.

© 2005 Optical Society of America

**OCIS Codes**

(000.5490) General : Probability theory, stochastic processes, and statistics

(070.4790) Fourier optics and signal processing : Spectrum analysis

(100.0100) Image processing : Image processing

(280.0280) Remote sensing and sensors : Remote sensing and sensors

(280.1120) Remote sensing and sensors : Air pollution monitoring

(300.6340) Spectroscopy : Spectroscopy, infrared

**Citation**

Avishai Ben-David and Hsuan Ren, "Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data," Appl. Opt. **44**, 3846-3855 (2005)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-18-3846

Sort: Year | Journal | Reset

### References

- A. Ben-David and H. Ren, "Detection, identification, and estimation of biological aerosols and vapors with a Fourier-transform infrared spectrometer," Appl. Opt. 42, 4887-4900 (2003).
- M. L. Polak, J. L. Hall, and K. C. Herr, "Passive Fourier-transform infrared spectroscopy of chemical plumes: an algorithm for quantitative interpretation and real-time background removal," Appl. Opt. 34, 5406-5412 (1995).
- D. R. Morgan, "Spectral absorption pattern detection and estimation," Appl. Spectrosc. 31, 404-424 (1977).
- G. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996), Chap. 2.
- T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation (Prentice-Hall, Upper Saddle River, N.J., 2000), Chap. 2.
- S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, N.J., 1993), Chap. 8.
- A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2802-2809 (1996).
- J. Harsanyi and C.-I. Chang, "Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach," IEEE Trans. Geosci. Remote Sensing 32, 779-785 (1994).
- C.-I. Chang and H. Ren, "An experiment-based quantitative and comparative analysis of target detection and image classification algorithms for hyperspectral imagery," IEEE Trans. Geosci. Remote Sensing 38, 1044-1063 (2000).
- J. J. Settle, "On the relationship between spectral unmixing and subspace projection," IEEE Trans. Geosci. Remote Sensing 42, 1045-1046 (1996).
- C.-I. Chang, "Further results on relationship between spectral unmixing and subspace projection," IEEE Trans. Geosci. Remote Sensing 36, 1030-1032 (1998).
- L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (Addison-Wesley, Reading, Pa., 1991).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

OSA is a member of CrossRef.