Probability Density and CFAR Threshold Estimation for Hyperspectral Imaging
The work reported here shows the proof of principle (using a small data set) for a suite of algorithms designed to estimate the probability density function of hyperspectral background data and compute the appropriate Constant False Alarm Rate (CFAR) matched filter decision threshold for a chemical plume detector. Future work will provide a thorough demonstration of the algorithms and their performance with a large data set. The LASI (Large Aperture Search Initiative) Project involves instrumentation and image processing for hyperspectral images of chemical plumes in the atmosphere. The work reported here involves research and development on algorithms for reducing the false alarm rate in chemical plume detection and identification algorithms operating on hyperspectral image cubes. The chemical plume detection algorithms to date have used matched filters designed using generalized maximum likelihood ratio hypothesis testing algorithms [1, 2, 5, 6, 7, 12, 10, 11, 13]. One of the key challenges in hyperspectral imaging research is the high false alarm rate that often results from the plume detector [1, 2]. The overall goal of this work is to extend the classical matched filter detector to apply Constant False Alarm Rate (CFAR) methods to reduce the false alarm rate, or Probability of False Alarm P{sub FA} of the matched filter [4, 8, 9, 12]. A detector designer is interested in minimizing the probability of false alarm while simultaneously maximizing the probability of detection P{sub D}. This is summarized by the Receiver Operating Characteristic Curve (ROC) [10, 11], which is actually a family of curves depicting P{sub D} vs. P{sub FA}parameterized by varying levels of signal to noise (or clutter) ratio (SNR or SCR). Often, it is advantageous to be able to specify a desired P{sub FA} and develop a ROC curve (P{sub D} vs. decision threshold r{sub 0}) for that case. That is the purpose of this work. Specifically, this work develops a set of algorithms and MATLAB implementations to compute the decision threshold r{sub 0}*that will provide the appropriate desired Probability of False Alarm P{sub FA} for the matched filter. The goal is to use prior knowledge of the background data to generate an estimate of the probability density function (pdf) [13] of the matched filter threshold r for the case in which the data measurement contains only background data (we call this case the null hypothesis, or H{sub 0}) [10, 11]. We call the pdf estimate {cflx f}(r|H{sub 0}). In this report, we use histograms and Parzen pdf estimators [14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Once the estimate is obtained, it can be integrated to compute an estimate of the P{sub FA}as a function of the matched filter detection threshold r. We can then interpolate r vs. P{sub FA} to obtain a curve that gives the threshold r{sub 0}* that will provide the appropriate desired Probability of False Alarm P{sub FA}for the matched filter. Processing results have been computed using both simulated and real LASI data sets. The algorithms and codes have been validated, and the results using LASI data are presented here. Future work includes applying the pdf estimation and CFAR threshold calculation algorithms to the LASI matched filter based upon global background statistics, and developing a new adaptive matched filter algorithm based upon local background statistics. Another goal is to implement the 4-Gamma pdf modeling method proposed by Stocker et. al. [4] and comparing results using histograms and the Parzen pdf estimators.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15011636
- Report Number(s):
- UCRL-TR-209277; TRN: US200507%%599
- Resource Relation:
- Other Information: PBD: 21 Sep 2004
- Country of Publication:
- United States
- Language:
- English
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