PREFACE ..................................................... xxiii
1 OVERVIEW AND INTRODUCTION .................................. 1
1.1 Overview ................................................... 2
1.2 Issues of Multispectral and Hyperspectral Imageries ........ 3
1.3 Divergence of Hyperspectral Imagery from Multispectral
Imagery .................................................... 4
1.3.1 Misconception: Hyperspectral Imaging is a Natural
Extension of Multispectral Imaging .................. 4
1.3.2 Pigeon-Hole Principle: Natural Interpretation of
Hyperspectral Imaging ............................... 5
1.4 Scope of This Book ......................................... 7
1.5 Book's Organization ....................................... 10
1.5.1 Part I: Preliminaries .............................. 10
1.5.2 Part II: Endmember Extraction ...................... 12
1.5.3 Part III: Supervised Linear Hyperspectral Mixture
Analysis ........................................... 13
1.5.4 Part IV: Unsupervised Hyperspectral Analysis ....... 13
1.5.5 Part V: Hyperspectral Information Compression ...... 15
1.5.6 Part VI: Hyperspectral Signal Coding ............... 16
1.5.7 Part VII: Hyperspectral Signal Feature
Characterization ................................... 17
1.5.8 Applications ....................................... 17
1.5.8.1 Chapter 30: Applications of Target Detection ... 17
1.5.8.2 Chapter 31: Nonlinear Dimensionality
Expansion to Multispectral Imagery .................... 18
1.5.8.3 Chapter 32: Multispectral Magnetic Resonance
Imaging ............................................... 19
1.6 Laboratory Data to be Used in This Book ................... 19
1.6.1 Laboratory Data .................................... 19
1.6.2 Cuprite Data ....................................... 19
1.6.3 NIST/EPA Gas-Phase Infrared Database ............... 19
1.7 Real Hyperspectral Images to be Used in this Book ......... 20
1.7.1 AVIRISData ......................................... 20
1.7.1.1 Cuprite Data ................................... 21
1.7.1.2 Purdue's Indiana Indian Pine Test Site ......... 25
1.7.2 HYDICE Data ........................................ 26
1.8 Notations and Terminologies to be Used in this Book ....... 29
I: PRELIMINARIES .......................................... 31
2 FUNDAMENTALS OF SUBSAMPLE AND MIXED SAMPLE ANALYSES ....... 33
2.1 Introduction .............................................. 33
2.2 Subsample Analysis ........................................ 35
2.2.1 Pure-Sample Target Detection ....................... 35
2.2.2 Subsample Target Detection ......................... 38
2.2.2.1 Adaptive Matched Detector (AMD) ................ 39
2.2.2.2 Adaptive Subspace Detector (ASD) ............... 41
2.2.3 Subsample Target Detection: Constrained Energy
Minimization (СЕМ) ...................................... 43
2.3 Mixed Sample Analysis ..................................... 45
2.3.1 Classification with Hard Decisions ................. 45
2.3.1.1 Fisher's Linear Discriminant Analysis (FLDA) ... 46
2.3.1.2 Support Vector Machines (SVM) .................. 48
2.3.2 Classification with Soft Decisions ................. 54
2.3.2.1 Orthogonal Subspace Projection (OSP) ........... 54
2.3.2.2 Target-Constrained Interference-Minimized
Filter (TCIMF) ........................................ 56
2.4 Kernel-Based Classification ............................... 57
2.4.1 Kernel Trick Used in Kernel-Based Methods .......... 57
2.4.2 Kernel-Based Fisher's Linear Discriminant
Analysis (KFLDA) ................................... 58
2.4.3 Kernel Support Vector Machine (K-SVM) .............. 59
2.5 Conclusions ............................................... 60
3 THREE-DIMENSIONAL RECEIVER OPERATING CHARACTERISTICS (3D
ROC) ANALYSIS ............................................. 63
3.1 Introduction .............................................. 63
3.2 Neyman-Pearson Detection Problem Formulation .............. 65
3.3 ROC Analysis .............................................. 67
3.4 3D ROC Analysis ........................................... 69
3.5 Real Data-Based ROC Analysis .............................. 72
3.5.1 How to Generate ROC Curves from Real Data .......... 72
3.5.2 How to Generate Gaussian-Fitted ROC Curves ......... 73
3.5.3 How to Generate 3D ROC Curves ...................... 75
3.5.4 How to Generate 3D ROC Curves for Multiple Signal
Detection and Classification ....................... 77
3.6 Examples .................................................. 78
3.6.1 Hyperspectral Imaging .............................. 79
3.6.1.1 Hyperspectral Target Detection ................. 79
3.6.1.2 Linear Hyperspectral Mixture Analysis .......... 80
3.6.2 Magnetic Resonance (MR) Breast Imaging ............. 83
3.6.2.1 Breast Tumor Detection ......................... 84
3.6.2.2 Brain Tissue Classification .................... 87
3.6.3 Chemical/Biological Agent Detection ................ 91
3.6.4 Biometrie Recognition .............................. 95
3.7 Conclusions ............................................... 99
4 DESIGN OF SYNTHETIC IMAGE EXPERIMENTS .................... 101
4.1 Introduction ............................................. 102
4.2 Simulation of Targets of Interest ........................ 103
4.2.1 Simulation of Synthetic Subsample Targets ......... 103
4.2.2 Simulation of Synthetic Mixed-Sample Targets ...... 104
4.3 Six Scenarios of Synthetic Images ........................ 104
4.3.1 Panel Simulations ................................. 104
4.3.2 Three Scenarios for Target Implantation (TI) ...... 106
4.3.2.1 Scenario TI1 (Clean Panels Implanted into
Clean Background) .................................... 106
4.3.2.2 Scenario TI2 (Clean Panels Implanted into
Noisy Background) .................................... 107
4.3.2.3 Scenario TI3 (Gaussian Noise Added to Clean
Panels Implanted into Clean Background) .............. 108
4.3.3 Three Scenarios for Target Embeddedness (ТЕ) ...... 108
4.3.3.1 Scenario TE1 (Clean Panels Embedded in Clean
Background) .......................................... 109
4.3.3.2 Scenario TE2 (Clean Panels Embedded in Noisy
Background) .......................................... 109
4.3.3.3 Scenario ТЕ3 (Gaussian Noise Added to Clean
Panels Embedded in Background) ....................... 110
4.4 Applications ............................................. 112
4.4.1 Endmember Extraction .............................. 112
4.4.2 Linear Spectral Mixture Analysis (LSMA) ........... 113
4.4.2.1 Mixed Pixel Classification .................... 114
4.4.2.2 Mixed Pixel Quantification .................... 114
4.4.3 Target Detection .................................. 114
4.4.3.1 Subpixel Target Detection ..................... 114
4.4.3.2 Anomaly Detection ............................. 122
4.5 Conclusions .............................................. 123
5 VIRTUAL DIMENSIONALITY OF HYPERSPECTRAL DATA ............. 124
5.1 Introduction ............................................. 124
5.2 Reinterpretation of VD ................................... 126
5.3 VD Determined by Data Characterization-Driven Criteria ... 126
5.3.1 Eigenvalue Distribution-Based Criteria ............ 127
5.3.1.1 Thresholding Energy Percentage ................ 127
5.3.1.2 Thresholding Difference between Normalized
Correlation Eigenvalues and Normalized Co variance
Eigenvalues .......................................... 128
5.3.1.3 Finding First Sudden Drop in the Normalized
Eigenvalue Distribution .............................. 128
5.3.2 Eigen-Based Component Analysis Criteria ........... 128
5.3.2.1 Singular Value Decomposition (SVD) ............ 128
5.3.2.2 Principal Components Analysis (PCA) ........... 129
5.3.3 Factor Analysis: Malinowski's Error Theory ........ 129
5.3.4 Information Theoretic Criteria (ITC) .............. 130
5.3.4.1 AIC ........................................... 131
5.3.4.2 MDL ........................................... 131
5.3.5 Gershgorin Radius-Based Methods ................... 131
5.3.5.1 Thresholding Gershgorin Radii ................. 134
5.3.5.2 Thresholding Difference Gershgorin Radii
between RL×L and KL×L ............................. 134
5.3.6 HFC Method ........................................ 135
5.3.7 Discussions on Data Characterization-Driven
Criteria .......................................... 138
5.4 VD Determined by Data Representation-Driven Criteria ..... 140
5.4.1 Orthogonal Subspace Projection (OSP) .............. 140
5.4.2 Signal Subspace Estimation (SSE) .................. 142
5.4.3 Discussions on OSP and SSE/НуSime ................. 143
5.5 Synthetic Image Experiments .............................. 144
5.5.1 Data Characterization-Driven Criteria ............. 144
5.5.1.1 Target Implantation (TI) Scenarios ............ 145
5.5.1.2 Target Embeddedness (ТЕ) Scenarios ............ 146
5.5.2 Data Representation-Driven Criteria ............... 149
5.6 VD Estimated for Real Hyperspectral Images ............... 155
5.7 Conclusions .............................................. 163
6 DATA DIMENSIONALITY REDUCTION ............................ 168
6.1 Introduction ............................................. 168
6.2 Dimensionality Reduction by Second-Order Statistics-
Based Component Analysis Transforms ...................... 170
6.2.1 Eigen Component Analysis Transforms ............... 170
6.2.1.1 Principal Components Analysis ................. 170
6.2.1.2 Standardized Principal Components Analysis .... 172
6.2.1.3 Singular Value Decomposition .................. 174
6.2.2 Signal-to-Noise Ratio-Based Components Analysis
Transforms ............................................. 176
6.2.2.1 Maximum Noise Fraction Transform .............. 176
6.2.2.2 Noise-Adjusted Principal Component Transform .. 177
6.3 Dimensionality Reduction by High-Order Statistics-Based
Components Analysis Transforms ........................... 179
6.3.1 Sphering .......................................... 179
6.3.2 Third-Order Statistics-Based Skewness ............. 181
6.3.3 Fourth-Order Statistics-Based Kurtosis ............ 182
6.3.4 High-Order Statistics ............................. 182
6.3.5 Algorithm for Finding Projection Vectors .......... 183
6.4 Dimensionality Reduction by Infinite-Order Statistics-
Based Components Analysis Transforms ..................... 184
6.4.1 Statistics-Prioritized 1СA-DR (SPICA-DR) .......... 187
6.4.2 Random ICA-DR ..................................... 188
6.4.3 Initialization Driven ICA-DR ...................... 189
6.5 Dimensionality Reduction by Projection Pursuit-Based
Components Analysis Transforms ........................... 190
6.5.1 Projection Index-Based Projection Pursuit ......... 191
6.5.2 Random Projection Index-Based Projection Pursuit .. 192
6.5.3 Projection Index-Based Prioritized Projection
Pursuit ........................................... 193
6.5.4 Initialization Driven Projection Pursuit .......... 194
6.6 Dimensionality Reduction by Feature Extraction-Based
Transforms ............................................... 195
6.6.1 Fisher's Linear Discriminant Analysis ............. 195
6.6.2 Orthogonal Subspace Projection .................... 196
6.7 Dimensionality Reduction by Band Selection ............... 196
6.8 Constrained Band Selection ............................... 197
6.9 Conclusions .............................................. 198
II: ENDMEMBER EXTRACTION ...................................... 201
7 SIMULTANEOUS ENDMEMBER EXTRACTION ALGORITHMS (SM-EEAs) ... 207
7.1 Introduction ............................................. 208
7.2 Convex Geometry-Based Endmember Extraction ............... 209
7.2.1 Convex Geometry-Based Criterion: Orthogonal
Projection ............................................. 209
7.2.2 Convex Geometry-Based Criterion: Minimal Simplex
Volume ................................................. 214
7.2.2.1 Minimal-Volume Transform (MVT) ................ 214
7.2.2.2 Convex Cone Analysis (CCA) .................... 214
7.2.3 Convex Geometry-Based Criterion: Maximal Simplex
Volume ................................................. 215
7.2.3.1 Simultaneous N-FINDR (SM N-FINDR) ............. 216
7.2.3.2 Iterative N-FINDR (IN-FINDR) .................. 216
7.2.3.3 Various Versions of Implementing IN-FINDR ..... 218
7.2.3.4 Discussions on Various Implementation
Versions of IN-FINDR .......................... 222
7.2.3.5 Comparative Study Among Various Versions of
IN-FINDR ...................................... 222
7.2.3.6 Alternative SM N-FINDR ........................ 223
7.2.4 Convex Geometry-Based Criterion: Linear Spectral
Mixture Analysis ....................................... 225
7.3 Second-Order Statistics-Based Endmember Extraction ....... 228
7.4 Automated Morphological Endmember Extraction (AMEE) ...... 230
7.5 Experiments .............................................. 231
7.5.1 Synthetic Image Experiments ....................... 231
7.5.1.1 Scenario TI1 (Endmembers Implanted in
a Clean Background) .................................. 232
7.5.1.2 Scenario TI2 (Endmembers Implanted in
a Noisy Background) .................................. 233
7.5.1.3 Scenario TI3 (Noisy Endmembers Implanted in
a Noisy Background) .................................. 234
7.5.1.4 Scenario TE1 (Endmembers Embedded into
a Clean Background) .................................. 235
7.5.1.5 Scenario TE2 (Endmembers Embedded into
a Noisy Background) .................................. 235
7.5.1.6 Scenario ТЕЗ (Noisy Endmembers Embedded into
a Noisy Background) .................................. 236
7.5.2 Cuprite Data ...................................... 237
7.5.3 HYDICE Data ....................................... 237
7.6 Conclusions .............................................. 239
8 SEQUENTIAL ENDMEMBER EXTRACTION ALGORITHMS (SQ-EEAs) ..... 241
8.1 Introduction ............................................. 241
8.2 Successive N-FINDR (SC N-FINDR) .......................... 244
8.3 Simplex Growing Algorithm (SGA) .......................... 244
8.4 Vertex Component Analysis (VCA) .......................... 247
8.5 Linear Spectral Mixture Analysis-Based SQ-EEAs ........... 248
8.5.1 Automatic Target Generation Process-EEA
(ATGP-EEA) ........................................ 248
8.5.2 Unsupervised Nonnegativity Constrained Least-
Squares-EEA (UNCLS-EEA) ........................... 249
8.5.3 Unsupervised Fully Constrained Least-Squares-EEA
(UFCLS-EEA) ....................................... 250
8.5.4 Iterative Error Analysis-EEA (IEA-EEA) ............ 251
8.6 High-Order Statistics-Based SQ-EEAS ...................... 252
8.6.1 Third-Order Statistics-Based SQ-EEA ............... 252
8.6.2 Fourth-Order Statistics-Based SQ-EEA .............. 252
8.6.3 Criterion for kth Moment-Based SQ-EEA ............. 253
8.6.4 Algorithm for Finding Projection Vectors .......... 253
8.6.5 ICA-Based SQ-EEA .................................. 254
8.7 Experiments .............................................. 254
8.7.1 Synthetic Image Experiments ....................... 255
8.7.2 Real Hyperspectral Image Experiments .............. 258
8.7.2.1 Cuprite Data .................................. 258
8.7.2.2 HYDICE Data ................................... 260
8.8 Conclusions .............................................. 262
9 INITIALIZATION-DRIVEN ENDMEMBER EXTRACTION ALGORITHMS
(ID-EEAs) ................................................ 265
9.1 Introduction ............................................. 265
9.2 Initialization Issues .................................... 266
9.2.1 Initial Conditions to Terminate an EEA ............ 267
9.2.2 Selection of an Initial Set of Endmembers for
an EEA ............................................ 267
9.2.3 Issues of Random Initial Conditions Demonstrated
by Experiments ......................................... 268
9.2.3.1 HYDICE Experiments ............................ 268
9.2.3.2 AVIRIS Experiments ............................ 270
9.3 Initialization-Driven EEAs ............................... 271
9.3.1 Initial Endmember-Driven EEAs ..................... 272
9.3.1.1 Finding Maximum Length of Data Sample
Vectors .............................................. 272
9.3.1.2 Finding Sample Mean of Data Sample Vectors .... 273
9.3.2 Endmember Initialization Algorithm for SM-EEAs .... 274
9.3.2.1 SQ-EEAs ....................................... 274
9.3.2.2 Maxmin-Distance Algorithm ..................... 275
9.3.2.3 ISODATA ....................................... 275
9.3.3 EIA-Driven EEAs ................................... 275
9.4 Experiments .............................................. 278
9.4.1 Synthetic Image Experiments ....................... 278
9.4.2 Real Image Experiments ............................ 281
9.5 Conclusions .............................................. 283
10 RANDOM ENDMEMBER EXTRACTION ALGORITHMS (REEAs) ........... 287
10.1 Introduction ............................................. 287
10.2 Random PPI (RPPI) ........................................ 288
10.3 Random VC A (RVC A) ...................................... 290
10.4 Random N-FINDR (RN-FINDR) ................................ 290
10.5 Random SGA (RSGA) ........................................ 292
10.6 Random ICA-Based EEA (RICA-EEA) .......................... 292
10.7 Synthetic Image Experiments .............................. 293
10.7.1 RPPI .............................................. 293
10.7.2 Various Random Versions of IN-FINDR ............... 296
10.7.2.1 Scenario TI2 .................................. 297
10.7.2.2 Scenario TI3 .................................. 299
10.7.2.3 TE2 ........................................... 301
10.7.2.4 ТЕЗ Scenario .................................. 303
10.8 Real Image Experiments ................................... 305
10.8.1 HYDICE Image Experiments .......................... 305
10.8.1.1 RPPI .......................................... 306
10.8.1.2 RN-FINDR ...................................... 306
10.8.2 AVIRIS Image Experiments .......................... 309
10.8.2.1 RPPI .......................................... 309
10.8.2.2 RN-FINDR ...................................... 310
10.9 Conclusions .............................................. 313
11 EXPLORATION ON RELATIONSHIPS AMONG ENDMEMBER EXTRACTION
ALGORITHMS ............................................... 316
11.1 Introduction ............................................. 316
11.2 Orthogonal Projection-Based EEAs ......................... 318
11.2.1 Relationship among PPI, VCA, and ATGP ............. 319
11.2.1.1 Relationship Between PPI and ATGP ............. 319
11.2.1.2 Relationship Between PPI and VCA .............. 320
11.2.1.3 Relationship Between ATGP and VCA ............. 321
11.2.1.4 Discussions ................................... 322
11.2.2 Experiments-Based Comparative Study and Analysis .. 323
11.2.2.1 Synthetic Image Experiment: TI2 ............... 323
11.2.2.2 Real Image Experiments ........................ 325
11.3 Comparative Study and Analysis Between SGA and VCA ....... 330
11.4 Does an Endmember Set Really Yield Maximum Simplex
Volume? .................................................. 339
11.5 Impact of Dimensionality Reduction on EEAs ............... 344
11.6 Conclusions .............................................. 348
III: SUPERVISED LINEAR HYPERSPECTRAL MIXTURE ANALYSIS ......... 351
12 ORTHOGONAL SUBSPACE PROJECTION REVISITED ................. 355
12.1 Introduction ............................................. 355
12.2 Three Perspectives to Derive OSP ......................... 358
12.2.1 Signal Detection Perspective Derived from
(d,U)-Model and OSP-Model ......................... 359
12.2.2 Fisher" s Linear Discriminant Analysis
Perspective from OSP-Model ........................ 360
12.2.3 Parameter Estimation Perspective from OSP-Model ... 362
12.2.4 Relationship Between δ1.SαP(r) and Least-Squares
Linear Spectral Mixture Analysis .................. 362
12.3 Gaussian Noise in OSP .................................... 364
12.3.1 Signal Detector in Gaussian Noise Using
OSP-Model ......................................... 365
12.3.2 Gaussian Maximum Likelihood Classifier Using
OSP-Model ......................................... 366
12.3.3 Gaussian Maximum Likelihood Estimator ............. 367
12.3.4 Examples .......................................... 367
12.4 OSP Implemented with Partial Knowledge ................... 372
12.4.1 СЕМ ............................................... 373
12.4.1.1 d Is Orthogonal to U (i.e., P 1/U = d) and
R = I (i.e., Spectral Correlation is Whitened) ....... 374
12.4.1.2 An Alternative Approach to Implementing СЕМ ... 374
12.4.1.3 СЕМ Implemented in Conjunction with P 1/U ..... 375
12.4.1.4 СЕМ Implemented in Conjunction with P 1/U in
White Noise .......................................... 376
12.4.2 TCIMF ............................................. 377
12.4.2.1 D = mp = d with nD = 1 and U = [m1, m2 ...
mp-1] with nU = p - 1 ................................ 378
12.4.2.2 D = mp = d with nD = 1 and U = [m1, m2 ...
mp-1] with nU = p - 1 and
R = I ................................................ 378
12.4.2.3 D = d and U = Ø (i.e., Only the Desired
Signature d is Available) ............................ 378
12.4.3 Examples .......................................... 379
12.5 OSP Implemented Without Knowledge ........................ 383
12.6 Conclusions .............................................. 390
13 FISHER'S LINEAR SPECTRAL MIXTURE ANALYSIS ................ 391
13.1 Introduction ............................................. 391
13.2 Feature Vector-Constrained FLSMA (FVC-FLSMA) ............. 392
13.3 Relationship Between FVC-FLSMA and LCMV, TCIMF, and СЕМ .. 395
13.4 Relationship Between FVC-FLSMA and OSP ................... 396
13.5 Relationship Between FVC-FLSMA and LCDA .................. 396
13.6 Abundance-Constrained Least Squares FLDA (ACLS-FLDA) ..... 397
13.7 Synthetic Image Experiments .............................. 398
13.8 Real Image Experiments ................................... 402
13.8.1 Image Background Characterized by Supervised
Knowledge .............................................. 402
13.8.2 Image Background Characterized by Unsupervised
Knowledge .............................................. 405
13.9 Conclusions ............................................. 409
14 WEIGHTED ABUNDANCE-CONSTRAINED LINEAR SPECTRAL MIXTURE
ANALYSIS ................................................. 411
14.1 Introduction ............................................. 411
14.2 Abundance-Constrained LSMA (AC-LSMA) ..................... 413
14.3 Weighted Least-Squares Abundance-Constrained LSMA ........ 413
14.3.1 Weighting Matrix Derived from a Parameter
Estimation Perspective ................................. 414
14.3.1.1 MD-Weighted AC-LSMA ........................... 415
14.3.1.2 LCMV-Weighted AC-LSMA ......................... 415
14.3.2 Weighting Matrix Derived from Fisher's Linear
Discriminant Analysis Perspective ...................... 416
14.3.3 Weighting Matrix Derived from an Orthogonal
Subspace Projection Perspective ........................ 417
14.3.3.1 OSP-Weighted AC-LSMA .......................... 417
14.3.3.2 SSP-Weighted AC-LSMA .......................... 418
14.4 Synthetic Image-Based Computer Simulations ............... 419
14.5 Real Image Experiments ................................... 426
14.6 Conclusions .............................................. 432
15 KERNEL-BASED LINEAR SPECTRAL MIXTURE ANALYSIS ............ 434
15.1 Introduction ............................................. 434
15.2 Kernel-Based LSMA (KLSMA) ................................ 436
15.2.1 Kernel Least Squares Orthogonal Subspace
Projection (KLSOSP) .................................... 436
15.2.2 Kernel-Based Non-Negative Constraint Least
Square (KNCLS) ......................................... 438
15.2.3 Kernel-Based Fully Constraint Least Square
(KFCLS) ................................................ 439
15.2.4 A Note on Kernelization ........................... 440
15.3 Synthetic Image Experiments .............................. 441
15.4 AVIRIS Data Experiments .................................. 444
15.4.1 Radial Basis Function Kernels ..................... 449
15.4.2 Polynomial Kernels ................................ 452
15.4.3 Sigmoid Kernels ................................... 454
15.5 HYDICE Data Experiments .................................. 460
15.6 Conclusions .............................................. 462
IV: UNSUPERVISED HYPERSPECTRAL IMAGE ANALYSIS ................. 465
16 HYPERSPECTRAL MEASURES ................................... 469
16.1 Introduction ............................................. 469
16.2 Signature Vector-Based Hyperspectral Measures for
Target Discrimination and Identification ................. 470
16.2.1 Euclidean Distance ................................ 471
16.2.2 Spectral Angle Mapper ............................. 471
16.2.3 Orthogonal Projection Divergence .................. 471
16.2.4 Spectral Information Divergence ................... 471
16.3 Correlation-Weighted Hyperspectral Measures for Target
Discrimanition and Identification ........................ 472
16.3.1 Hyperspectral Measures Weighted by A Priori
Correlation ............................................ 473
16.3.1.1 OSP-Based Hyperspectral Measures for
Discrimination ....................................... 473
16.3.1.2 OSP-Based Hyperspectral Measures for
Identification ....................................... 473
16.3.2 Hyperspectral Measures Weighted by A Posteriori
Correlation ............................................ 474
16.3.2.1 Covariance Matrix-Weighted Hyperspectral
Measures ............................................. 474
16.3.2.2 Correlation Matrix-Weighted Hyperspectral
Measures ............................................. 475
16.3.2.3 Covariance Matrix-Weighted Matched Filter
Distance ............................................. 475
16.3.2.4 Correlation Matrix-Weighted Matched Filter
Distance ............................................. 476
16.4 Experiments .............................................. 477
16.4.1 HYDICE Image Experiments .......................... 477
16.4.2 AVIRIS Image Experiments .......................... 478
16.5 Conclusions .............................................. 482
17 UNSUPERVISED LINEAR HYPERSPECTRAL MIXTURE ANALYSIS ....... 483
17.1 Introduction ............................................. 483
17.2 Least Squares-Based ULSMA ................................ 486
17.3 Component Analysis-Based ULSMA ........................... 488
17.4 Synthetic Image Experiments .............................. 490
17.4.1 LS-ULSMA .......................................... 491
17.4.2 CA-ULSMA .......................................... 499
17.5 Real-Image Experiments ................................... 503
17.5.1 LS-ULSMA .......................................... 503
17.5.2 CA-ULSMA .......................................... 505
17.5.3 Qualitative and Quantitative Analyses between
ULSMA and SLSMA ........................................ 511
17.6 ULSMA Versus Endmember Extraction ........................ 517
17.7 Conclusions .............................................. 524
18 PIXEL EXTRACTION AND INFORMATION ......................... 526
18.1 Introduction ............................................. 526
18.2 Four Types of Pixels ..................................... 527
18.3 Algorithms Selected to Extract Pixel Information ......... 528
18.4 Pixel Information Analysis via Synthetic Images .......... 528
18.5 Real Image Experiments ................................... 534
18.5.1 AVIRIS Image Data ................................. 534
18.5.2 DAIS 7915 Image Data .............................. 537
18.6 Conclusions .............................................. 539
V: HYPERSPECTRAL INFORMATION COMPRESSION ...................... 541
19 EXPLOITATION-BASED HYPERSPECTRAL DATA COMPRESSION ........ 545
19.1 Introduction ............................................. 545
19.2 Hyperspectral Information Compression Systems ............ 547
19.3 Spectral/Spatial Compression ............................. 549
19.3.1 Dimensionality Reduction by Transform-Based
Spectral Compression ................................... 550
19.3.1.1 Determination of Number of PCs/ICs to be
Retained ............................................. 551
19.3.1.2 PCA (ICA)/2D Compression ...................... 551
19.3.1.3 PCA (ICA)/3D Compression ...................... 552
19.3.1.4 Inverse PCA (Inverse ICA)/2D Compression ...... 553
19.3.1.5 Inverse PCA (Inverse PCA)/3D Compression ...... 553
19.3.1.6 Mixed Component Transforms for Hyperspectral
Compression .......................................... 554
19.3.2 Dimensionality Reduction by Band Selection-Based
Spectral Compression ................................... 556
19.4 Progressive Spectral/Spatial Compression ................. 557
19.5 3D Compression ........................................... 557
19.5.1 3D-Multicomponent JPEG ............................ 557
19.5.2 3D-SPIHT Compression .............................. 558
19.6 Exploration-Based Applications ........................... 559
19.6.1 Linear Spectral Mixture Analysis .................. 559
19.6.2 Subpixel Target Detection ......................... 559
19.6.3 Anomaly Detection ................................. 560
19.6.4 Endmember Extraction .............................. 561
19.7 Experiments .............................................. 561
19.7.1 Synthetic Image Experiments ....................... 562
19.7.2 Real Image Experiments ............................ 567
19.8 Conclusions .............................................. 580
20 PROGRESSIVE SPECTRAL DIMENSIONALITY PROCESS .............. 581
20.1 Introduction ............................................. 582
20.2 Dimensionality Prioritization ............................ 584
20.3 Representation of Transformed Components for DP .......... 585
20.3.1 Projection Index-Based PP ......................... 585
20.3.2 Mixed Projection Index-Based Prioritized PP
(M-PIPP) ............................................... 587
20.3.3 Projection Index-Based Prioritized PP (PI-PRPP) ... 587
20.3.4 Initialization-Driven PIPP (ID-PIPP) .............. 588
20.4 Progressive Spectral Dimensionality Process .............. 589
20.4.1 Progressive Principal Components Analysis ......... 591
20.4.1.1 Simultaneous PC A ............................. 591
20.4.1.2 Progressive PC A .............................. 592
20.4.1.3 Sequential PCA ................................ 593
20.4.1.4 Initialization-Driven PCA ..................... 595
20.4.2 Progressive High-Order Statistics Component
Analysis ............................................... 596
20.4.3 Progressive Independent Component Analysis ........ 596
20.5 Hyperspectral Compression by PSDP ........................ 597
20.5.1 Progressive Spectral Dimensionality Reduction ..... 597
20.5.2 Progressive Spectral Dimensionality Expansion ..... 597
20.6 Experiments for PSDP ..................................... 598
20.6.1 Endmember Extraction .............................. 598
20.6.2 Land Cover/Use Classification ..................... 599
20.6.3 Linear Spectral Mixture Analysis .................. 603
20.7 Conclusions .............................................. 608
21 PROGRESSIVE BAND DIMENSIONALITY PROCESS .................. 613
21.1 Introduction ............................................. 614
21.2 Band Prioritization ...................................... 615
21.3 Criteria for Band Prioritization ......................... 617
21.3.1 Second-Order Statistics-Based BPC ................. 617
21.3.1.1 Variance-Based BPC ............................ 617
21.3.1.2 Signal-to-Noise-Ratio-Based BPC ............... 618
21.3.2 High-Order Statistics-Based BPC ................... 618
21.3.2.1 Skewness ...................................... 618
21.3.2.2 Kurtosis ...................................... 618
21.3.3 Infinite-Order Statistics-Based BPC ............... 618
21.3.3.1 Entropy ....................................... 619
21.3.3.2 Information Divergence ........................ 619
21.3.4 Classification-Based BPC .......................... 619
21.3.4.1 Fisher's Linear Discriminant Analysis
(FLDA)-Based BPC ..................................... 619
21.3.4.2 OSP-BasedBPC .................................. 620
21.3.5 Constrained Band Correlation/Dependence
Minimization ........................................... 620
21.3.5.1 Band Correlation/Dependence Minimization ...... 621
21.3.5.2 Band Correlation Constraint ................... 622
21.4 Experiments for BP ....................................... 624
21.4.1 Applications Using Highest-Prioritized Bands ...... 625
21.4.1.1 Unsupervised Linear Spectral Mixture
Analysis ............................................. 626
21.4.1.2 Endmember Extraction .......................... 632
21.4.2 Applications Using Least-Prioritized Bands ........ 635
21.4.2.1 Unsupervised Linear Spectral Mixture
Analysis ............................................. 636
21.4.2.2 Endmember Extraction .......................... 637
21.4.3 Applications Using Mixing Highest-Prioritized
and Least-Prioritized Bands ............................ 646
21.4.3.1 Unsupervised Linear Spectral Mixture
Analysis ............................................. 646
21.4.3.2 Endmember Extraction .......................... 646
21.5 Progressive Band Dimensionality Process .................. 651
21.6 Hyperspectral Compresssion by PBDP ....................... 653
21.6.1 Progressive Band Dimensionality Reduction Via BP .. 654
21.6.2 Progressive Band Dimensionality Expansion Via BP .. 655
21.7 Experiments for PB DP .................................... 656
21.7.1 Endmember Extraction .............................. 656
21.7.2 Land Cover/Use Classification ..................... 658
21.7.3 Linear Spectral Mixture Analysis .................. 660
21.8 Conclusions .............................................. 662
22 DYNAMIC DIMENSIONALITY ALLOCATION ........................ 664
22.1 Introduction ............................................. 664
22.2 Dynamic Dimensionality Allocaction ....................... 665
22.3 Signature Discriminatory Probabilties .................... 667
22.4 Coding Techniques for Determining DDA .................... 667
22.4.1 Shannon Coding-Based DDA .......................... 667
22.4.2 Huffman Coding-Based DDA .......................... 668
22.4.3 Hamming Coding-Based DDA .......................... 669
22.4.4 Notes on DDA ...................................... 669
22.5 Experiments for Dynamic Dimensionality Allocation ........ 669
22.5.1 Reflectance Cuprite Data .......................... 670
22.5.2 Purdue's Data ..................................... 672
22.5.3 HYDICE Data ....................................... 674
22.6 Conclusions .............................................. 682
23 PROGRESSIVE BAND SELECTION ............................... 683
23.1 Introduction ............................................. 683
23.2 Band De-correlation ...................................... 684
23.2.1 Spectral Measure-Based BD ......................... 684
23.2.2 Orthogonalization-Based BD ........................ 685
23.3 Progressive Band Selection ............................... 686
23.3.1 PBS: BP Followed by BD ............................ 687
23.3.2 PBS: BD Followed by BP ............................ 687
23.4 Experiments for Progressive Band Selection ............... 688
23.5 Endmember Extraction ..................................... 688
23.6 Land Cover/Use Classification ............................ 690
23.7 Linear Spectral Mixture Analysis ......................... 694
23.8 Conclusions .............................................. 715
VI: HYPERSPECTRAL SIGNAL CODING ............................... 717
24 BINARY CODING FOR SPECTRAL SIGNATURES .................... 719
24.1 Introduction ............................................. 719
24.2 Binary Coding ............................................ 720
24.2.1 SPAM Binary Coding ................................ 720
24.2.2 Median Partition Binary Coding .................... 721
24.2.3 Halfway Partition Binary Coding ................... 722
24.2.4 Equal Probability Partition Binary Coding ......... 722
24.3 Spectral Feature-Based Coding ............................ 723
24.4 Experiments .............................................. 725
24.4.1 Computer Simulations .............................. 725
24.4.2 Real Hyperspectral Image Data ..................... 730
24.5 Conclusions .............................................. 740
25 VECTOR CODING FOR HYPERSPECTRAL SIGNATURES ............... 741
25.1 Introduction ............................................. 741
25.2 Spectral Derivative Feature Coding ....................... 743
25.2.1 Re-interpretation of SPAM and SFBC ................ 743
25.2.2 Spectral Derivative Feature Coding ................ 744
25.2.3 AVIRIS Data Experiments ........................... 746
25.2.3.1 Signature Discrimination ..................... 747
25.2.3.2 Mixed Signature Classification ............... 748
25.2.4 NIST Gas Data Experiments ......................... 749
25.2.4.1 Signature Discrimination ..................... 750
25.2.4.2 Mixed Signature Classification ............... 751
25.3 Spectral Feature Probabilistic Coding .................... 755
25.3.1 Arithmetic Coding ................................. 755
25.3.2 Spectral Feature Probabilistic Coding ............. 756
25.3.3 AVIRIS Data Experiments ........................... 758
25.3.4 NIST Gas Data Experiments ......................... 760
25.4 Real Image Experiments ................................... 764
25.4.1 SDFC .............................................. 764
25.4.2 SFPC .............................................. 766
25.5 Conclusions .............................................. 771
26 PROGRESSIVE CODING FOR SPECTRAL SIGNATURES ...............772
26.1 Introduction ............................................. 772
26.2 Multistage Pulse Code Modulation ......................... 774
26.3 MPCM-Based Progressive Spectral Signature Coding ......... 783
26.3.1 Spectral Discrimination ........................... 784
26.3.2 Spectral Identification ........................... 785
26.4 NIST-GAS Data Experiments ................................ 786
26.5 Real Image Hyperspectral Experiments ..................... 790
26.6 Conclusions .............................................. 796
VII: HYPERSPECTRAL SIGNAL CHARACTERIZATION .................... 797
27 VARIABLE-NUMBER VARIABLE-BAND SELECTION FOR
HYPERSPECTRAL SIGNALS .................................... 799
27.1 Introduction ............................................. 799
27.2 Orthogonal Subspace Projection-Based Band
Prioritization Criterion ................................. 801
27.3 Variable-Number Variable-Band Selection .................. 803
27.4 Experiments .............................................. 806
27.4.1 Hyperspectral Data ................................ 806
27.4.1.1 Signature Discrimination ...................... 806
27.4.1.2 Signature Classification Identification ....... 809
27.4.1.3 Noise Effect on VNVBS ......................... 811
27.4.2 NIST-GasData ...................................... 813
27.4.2.1 Signature Discrimination ...................... 813
27.4.2.2 Signature Classification/Identification ....... 814
27.4.2.3 Signature Discrimination between Two
Signatures with Different Numbers of Bands ........... 816
27.5 Selection of Reference Signatures ........................ 819
27.6 Conclusions .............................................. 819
28 KALMAN FILTER-BASED ESTIMATION FOR HYPERSPECTRAL
SIGNALS .................................................. 820
28.1 Introduction ............................................. 820
28.2 Kaiman Filter-Based Linear Unmixing ...................... 822
28.3 Kaiman Filter-Based Spectral Characterization Signal-
Processing Techniques .................................... 824
28.3.1 Kaiman Filter-based Spectral Signature Estimator .. 825
28.3.2 Kaiman Filter-Based Spectral Signature
Identifier ............................................. 826
28.3.3 Kaiman Filter-Based Spectral Signature
Quantifier ............................................. 828
28.4 Computer Simulations Using AVIRIS Data ................... 831
28.4.1 KFSSE ............................................. 831
28.4.2 KFSSI ............................................. 832
28.4.2.1 Subpixel Target Identification by KFSSI ....... 832
28.4.2.2 Mixed Target Identification by KFSSI .......... 838
28.4.3 KFSSQ ............................................. 839
28.4.3.1 Subpixel Target Quantification by KFSSQ ....... 839
28.4.3.2 Mixed Target Quantification by KFSSQ .......... 840
28.5 Computer Simulations Using NIST-Gas Data ................. 843
28.5.1 KFSSE ............................................. 843
28.5.2 KFSSI ............................................. 843
28.5.2.1 Subpixel Target Identification by KFSSI ....... 843
28.5.2.2 Mixed Target Identification by KFSSI .......... 848
28.5.3 KFSSQ ............................................. 849
28.5.3.1 " Subpixel Target Identification by KFSSQ ..... 849
28.5.3.2 Mixed Target Quantification by KFSSQ .......... 849
28.6 Real Data Experiments .................................... 852
28.6.1 KFSSE ............................................. 852
28.6.2 KFSSI ............................................. 852
28.6.3 KFSSQ ............................................. 856
28.7 Conclusions .............................................. 857
29 WAVELET REPRESENTATION FOR HYPERSPECTRAL SIGNALS ......... 859
29.1 Introduction ............................................. 859
29.2 Wavelet Analysis ......................................... 860
29.2.1 Multiscale Approximation .......................... 860
29.2.2 Scaling Function .................................. 861
29.2.3 Wavelet Function .................................. 862
29.3 Wavelet-Based Signature Characterization Algorithm ....... 863
29.3.1 Wavelet-Based Signature Characterization
Algorithm for Signature Self-Tuning .................... 863
29.3.2 Wavelet-Based Signature Characterization
Algorithm for Signature Self-Correction ................ 866
29.3.3 Signature Self-Discrimination, Classification,
and Identification ..................................... 867
29.4 Synthetic Image-Based Computer Simulations ............... 868
29.4.1 Signature Self-Tuning and Self-Denoising .......... 869
29.4.2 Signature Self-Discrimination, Self-
Classification, and Self-Identification ................ 870
29.5 Real Image Experiments ................................... 871
29.6 Conclusions .............................................. 875
VIII: APPLICATIONS ............................................ 877
30 APPLICATIONS OF TARGET DETECTION ......................... 879
30.1 Introduction ............................................. 879
30.2 Size Estimation of Subpixel Targets ...................... 880
30.3 Experiments .............................................. 881
30.3.1 Synthetic Image Experiments ....................... 881
30.3.2 HYDICE Image Experiments .......................... 886
30.4 Concealed Target Detection ............................... 891
30.5 Computer-Aided Detection and Classification Algorithm
for Concealed Targets .................................... 892
30.6 Experiments for Concealed Target Detection ............... 893
30.7 Conclusions .............................................. 895
31 NONLINEAR DIMENSIONALITY EXPANSION TO MULTISPECTRAL
IMAGERY .................................................. 897
31.1 Introduction ............................................. 897
31.2 Band Dimensionality Expansion ............................ 899
31.2.1 Rationale for Developing BDE ...................... 899
31.2.2 Band Expansion Process ............................ 901
31.3 Hyperspectral Imaging Techniques Expanded by BDE ......... 902
31.3.1 BEP-Based Orthogonal Subspace Projection .......... 903
31.3.2 BEP-Based Constrained Energy Minimization ......... 903
31.3.3 BEP-Based RX-Detector ............................. 903
31.4 Feature Dimensionality Expansion by Nonlinear Kernels .... 904
31.4.1 FDE by Transformation ............................. 905
31.4.2 FDE by Classification ............................. 907
31.4.2.1 FDE by Classification using Sample Spectral
Correlation .......................................... 907
31.4.2.2 FDE by Classification using Intrapixel
Spectral Correlation ................................. 908
31.5 BDE in Conjunction with FDE .............................. 909
31.6 Multispectral Image Experiments .......................... 909
31.7 Conclusion ............................................... 918
32 MULTISPECTRAL MAGNETIC RESONANCE IMAGING ................. 920
32.1 Introduction ............................................. 920
32.2 Linear Spectral Mixture Analysis for MRI ................. 923
32.2.1 Orthogonal Subspace Projection to MRI ............. 925
32.2.2 Band Expansion Process-Based OSP .................. 927
32.2.3 Unsupervised Orthogonal Subspace Projection ....... 928
32.3 Linear Spectral Random Mixture Analysis for MRI .......... 928
32.3.1 Source Separation-Based OC-ICA for MR Image
Analysis ............................................... 930
32.3.2 Band Expansion Process Over complete ICA for MR
Image Analysis ......................................... 931
32.3.2.1 Eigenvector-Prioritized ICA ................... 931
32.3.2.2 High-Order Statistics-Based PICA .............. 932
32.3.2.3 ATGP-Prioritized PCA .......................... 932
32.4 Kernel-Based Linear Spectral Mixture Analysis ............ 933
32.5 Synthetic MR Brain Image Experiments ..................... 933
32.6 Real MR Brain Image Experiments .......................... 951
32.7 Conclusions .............................................. 955
33 CONCLUSIONS .............................................. 956
33.1 Design Principles for Nonliteral Hyperspectral Imaging
Techniques ............................................... 956
33.1.1 Pigeon-Hole Principle ............................. 956
33.1.1.1 Multispectral Imagery Versus Hyperspectral
Imagery .............................................. 957
33.1.1.2 Virtual Dimensionality ........................ 957
33.1.2 Principle of Orthogonality ........................ 963
33.2 Endmember Extraction ..................................... 964
33.3 Linear Spectral Mixture Analysis ......................... 970
33.3.1 Supervised LSMA ................................... 970
33.3.2 Unsupervised LSMA ................................. 973
33.4 Anomaly Detection ........................................ 974
33.5 Support Vector Machines and Kernel-Based Approaches ...... 977
33.6 Hyperspectral Compression ................................ 981
33.7 Hyperspectral Signal Processing .......................... 984
33.7.1 Signal Coding ..................................... 986
33.7.2 Signal Estimation ................................. 986
33.8 Applications ............................................. 987
33.9 Further Topics ........................................... 987
33.9.1 Causal Processing ................................. 987
33.9.2 Real-Time Processing .............................. 988
33.9.3 FPGA Designs for Hardware Implementation .......... 989
33.9.4 Parallel Processing ............................... 990
33.9.5 Progressive Hyperspectral Processing .............. 990
GLOSSARY ...................................................... 993
APPENDIX: ALGORITHM COMPENDIUM ................................ 997
REFERENCES ................................................... 1052
INDEX ........................................................ 1071
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