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Using Multiple Robust Parameter Design Techniques to Improve Hyperspectral Anomaly Detection Algorithm Performance Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-9-2009 Using Multiple Robust Parameter Design Techniques to Improve Hyperspectral Anomaly Detection Algorithm Performance Matthew T. Davis Follow this and additional works at: https://scholar.afit.edu/etd Part of the Other Operations Research, Systems Engineering and Industrial Engineering Commons, and the Remote Sensing Commons Recommended Citation Davis, Matthew T., "Using Multiple Robust Parameter Design Techniques to Improve Hyperspectral Anomaly Detection Algorithm Performance" (2009). Theses and Dissertations. 2506. https://scholar.afit.edu/etd/2506 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. USING MULTIPLE ROBUST PARAMETER DESIGN TECHNIQUES TO IMPROVE HYPERSPECTRAL ANOMALY DETECTION ALGORITHM PERFORMANCE THESIS Matthew Davis, Captain, USAF AFIT/GOR/ENS/09-05 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense or the United States Government. AFIT/GOR/ENS/09-05 USING MULTIPLE ROBUST PARAMETER DESIGN TECHNIQUES TO IMPROVE HYPERSPECTRAL ANOMALY DETECTION ALGORITHM PERFORMANCE THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Operations Research Matthew Davis, B.S. Captain, USAF March 2009 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/GOR/ENS/09-05 USING MULTIPLE ROBUST PARAMETER DESIGN TECHNIQUES TO IMPROVE HYPERSPECTRAL ANOMALY DETECTION ALGORITHM PERFORMANCE Matthew Davis, B.S. Captain, USAF Approved: Kenneth W. Bauer, Jr., Ph.D. Date Chairman J.O. Miller, Ph.D. Date Member AFIT/GOR/ENS/09-05 Abstract Detecting and identifying objects of interest is the goal of all remote sensing. New advances, specifically in hyperspectral imaging technology have provided the analyst with immense amounts of data requiring evaluation. Several filtering tech- niques or anomaly detection algorithms have been proposed. However, most new algorithms are insufficiently verified to be robust to the broad range of hyperspec- tral data being made available. One such algorithm, AutoGAD, is tested here via two separate robust parameter design techniques to determine optimal parameters for consistent performance on a range of data with large attribute variances. Ad- ditionally, the results of the two techniques are compared for overall effectiveness. The results of the test as well as optimal parameters for AutoGAD are presented and future research efforts proposed. iv Acknowledgements I must first thank my wife and daughters for their unwavering support through- out this journey. Their constant encouragement has been central to achieving this goal. They have sacrificed much, and I'm very grateful. I must also express my gratitude to my advisor, Dr. Kenneth Bauer. His support and guidance during this research effort was invaluable to me. I would also like to thank Dr. J.O. Miller for his direction and assistance in producing a better final product. Special thanks go to my peers, Maj Michael Miller, Maj Glen Shilland, Capt Christopher Arendt, Capt Andrew Chaney, and Capt Emily Knight. Their collabora- tion thoughout the many disparate efforts that constitute research was indispensable. Matthew Davis v Table of Contents Page Abstract . iv Acknowledgements . .v List of Figures . viii List of Tables . .x 1. Introduction . 1-1 1.1 Background . 1-1 1.2 Methodology . 1-2 1.3 Research Objectives . 1-4 2. Literature Review . 2-1 2.1 HSI Basics . 2-1 2.2 Approaches to HSI Analysis . 2-3 2.3 Overview of AutoGAD . 2-7 2.4 Robust Parameter Design . 2-9 2.4.1 Crossed Array Designs | The Taguchi Approach 2-11 2.4.2 Combined Array Designs { Response Surface Meth- ods........................ 2-16 3. Methodology . 3-1 3.1 Inputs . 3-1 3.2 Outputs . 3-2 3.3 Crossed Array Method . 3-3 3.4 Combined Array Method . 3-8 vi Page 3.4.1 Mean Model . 3-13 3.4.2 Variance Model . 3-15 3.5 Reducing Multiple Responses to a Single Dimension . 3-17 4. Analysis of Results . 4-1 4.1 Analysis of the Crossed Array . 4-1 4.2 Combined Array . 4-17 4.3 Verifcation Experiment . 4-27 5. Conclusions . 5-1 5.1 Review . 5-1 5.2 Research Contributions . 5-2 5.3 Future Research . 5-3 Bibliography . BIB-1 Appendix A. Additional Data Tables and Analysis from the Crossed Array Design . A-1 Appendix B. Additional Figures and Analysis from the Combined Ar- ray Design . B-1 Appendix C. Code for AutoGAD and Iterative Master Function . C-1 Appendix D. Blue Dart . D-1 Vita...................................... VITA-1 vii List of Figures Figure Page 2.1. Electromagnetic Spectrum [6] . 2-2 2.2. Dimensions of Hyperspectral Data Cube [11] . 2-3 2.3. Spectral Layers of Hyperspectral Data Cube [7] . 2-4 2.4. Transforming a HSI data cube into a data matrix [7] . 2-5 2.5. Process Flow for Target Detection [5] . 2-7 2.6. Control-by-Noise Interaction Plot [2] . 2-11 2.7. 22 × 22 crossed array [10] . 2-12 3.1. Sample Mean and SNR Plots . 3-7 4.1. Dimension Adjust vs. Marginal Means of Mean Response and SNR................................ 4-5 4.2. Max Score vs. Marginal Means of Mean Response and SNR . 4-6 4.3. Bin Width SNR vs. Marginal Means of Mean Response and SNR 4-7 4.4. PT SNR Threshold vs. Marginal Means of Mean Response and SNR................................ 4-8 4.5. Bin Width Ident vs. Marginal Means of Mean Response and SNR................................ 4-9 4.6. Smooth Iter High vs. Marginal Means of Mean Response and SNR................................ 4-10 4.7. Smooth Iter Low vs. Marginal Means of Mean Response and SNR................................ 4-11 4.8. Low SNR vs. Marginal Means of Mean Response and SNR . 4-12 4.9. Window Size vs. Marginal Means of Mean Response and SNR 4-13 4.10. Threshold Both Sides vs. Marginal Means of Mean Response and SNR . 4-14 4.11. Clean Signal vs. Marginal Means of Mean Response and SNR 4-15 viii Figure Page 4.12. Elements of γ and ∆ within the Variance Model . 4-24 4.13. Products of Squared terms, p, and q within first summation term in Eq. 3.7 . 4-24 4.14. Covariance terms summed within the second term of Eq. 3.7 . 4-25 B.1. Table lays out steps for developing the Mean Model from the General Model . B-5 B.2. Reduced Mean Model . B-5 ix List of Tables Table Page 3.1. Control and Noise Factors and their ranges . 3-2 3.2. Measures of Performance and their ranges . 3-3 3.3. Sample IA point means and their subsequent Marginal Means 3-7 3.4. Control and Noise Factor Designators . 3-9 3.5. ANOVA for Time Response . 3-11 3.6. Observed Probability of Occurrence for Noise Categories . 3-14 3.7. Transformations and Resultant Adjusted R2's . 3-17 4.1. One Dimensional Standardized Mean Responses and SNR's . 4-3 4.2. Marginal Mean Responses for all Conrol Variable Levels . 4-4 4.3. Significant Controls Variables, Their Levels, and Expected Stan- dardized Mean Responses . 4-16 4.4. Significant Controls Variables, Their Levels, and Expected SNR 4-17 4.5. Combined Array Standardized Response Data . 4-19 4.6. Combined Array One Dimensional Standardized Response Data 4-20 4.7. ANOVA for One Dimensional Standardized Response . 4-21 4.8. Variance Model Control Factors and their ranges . 4-25 4.9. Control Factor Levels producing Minimized Variance . 4-26 4.10. Estimated Mean Model Control Factors and their ranges . 4-26 4.11. Control Factor Levels producing Minimized Variance and Opti- mized Response . 4-27 4.12. Mean and Variances from Crossed Array Verification Experiment 4-29 4.13. Mean and Variances from Combined Array Verification Exper- iment . 4-30 4.14. Control Factor Level Differences between Crossed and Com- bined Array Techniques . 4-31 4.15. Johnson's Suggested Control Factor Levels . 4-32 4.16. Mean and Variances from Johnson Verification Experiment . 4-33 A.1. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 1) in the Crossed Array Design A-4 A.2. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 2) in the Crossed Array Design A-8 x Table Page A.3. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 3) in the Crossed Array Design A-12 A.4. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 4) in the Crossed Array Design A-16 A.5. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 5) in the Crossed Array Design A-20 A.6. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 6) in the Crossed Array Design A-24 A.7. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 7) in the Crossed Array Design A-28 A.8. Inner Array Design Points and Resultant Responses for the first Outer Array Design Point (Block 8) in the Crossed Array Design A-32 A.9.
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