21.5 Progressive Band Dimensionality Process
by Chein-I Chang
Hyperspectral Data Processing: Algorithm Design and Analysis
- Cover
- Title Page
- Copyright
- Dedication
- Preface
- Chapter 1: Overview and Introduction
- 1.1 Overview
- 1.2 Issues of Multispectral and Hyperspectral Imageries
- 1.3 Divergence of Hyperspectral Imagery from Multispectral Imagery
- 1.4 Scope of This Book
- 1.5 Book's Organization
- 1.6 Laboratory Data to be Used in This Book
- 1.7 Real Hyperspectral Images to be Used in this Book
- 1.8 Notations and Terminologies to be Used in this Book
- I: Preliminaries
- Chapter 2: Fundamentals of Subsample and Mixed Sample Analyses
- Chapter 3: Three-Dimensional Receiver Operating Characteristics (3D ROC) Analysis
- Chapter 4: Design of Synthetic Image Experiments
- Chapter 5: Virtual Dimensionality of Hyperspectral Data
- Chapter 6: Data Dimensionality Reduction
- 6.1 Introduction
- 6.2 Dimensionality Reduction by Second-Order Statistics-Based Component Analysis Transforms
- 6.3 Dimensionality Reduction by High-Order Statistics-Based Components Analysis Transforms
- 6.4 Dimensionality Reduction by Infinite-Order Statistics-Based Components Analysis Transforms
- 6.5 Dimensionality Reduction by Projection Pursuit-Based Components Analysis Transforms
- 6.6 Dimensionality Reduction by Feature Extraction-Based Transforms
- 6.7 Dimensionality Reduction by Band Selection
- 6.8 Constrained Band Selection
- 6.9 Conclusions
- II: Endmember Extraction
- Chapter 7: Simultaneous Endmember Extraction Algorithms (SM-EEAs)
- Chapter 8: Sequential Endmember Extraction Algorithms (SQ-EEAs)
- Chapter 9: Initialization-Driven Endmember Extraction Algorithms (ID-EEAs)
- Chapter 10: Random Endmember Extraction Algorithms (REEAs)
- Chapter 11: Exploration on Relationships among Endmember Extraction Algorithms
- III: Supervised Linear Hyperspectral Mixture Analysis
- Chapter 12: Orthogonal Subspace Projection Revisited
- Chapter 13: Fisher's Linear Spectral Mixture Analysis
- 13.1 Introduction
- 13.2 Feature Vector-Constrained FLSMA (FVC-FLSMA)
- 13.3 Relationship Between FVC-FLSMA and LCMV, TCIMF, and CEM
- 13.4 Relationship Between FVC-FLSMA and OSP
- 13.5 Relationship Between FVC-FLSMA and LCDA
- 13.6 Abundance-Constrained Least Squares FLDA (ACLS-FLDA)
- 13.7 Synthetic Image Experiments
- 13.8 Real Image Experiments
- 13.9 Conclusions
- Chapter 14: Weighted Abundance-Constrained Linear Spectral Mixture Analysis
- Chapter 15: Kernel-Based Linear Spectral Mixture Analysis
- IV: Unsupervised Hyperspectral Image Analysis
- V: Hyperspectral Information Compression
- VI: Hyperspectral Signal Coding
- VII: Hyperspectral Signal Characterization
- VIII: Applications
- Chapter 30: Applications of Target Detection
- Chapter 31: Nonlinear Dimensionality Expansion to Multispectral Imagery
- Chapter 32: Multispectral Magnetic Resonance Imaging
- Chapter 33: Conclusions
- 33.1 Design Principles for Nonliteral Hyperspectral Imaging Techniques
- 33.2 Endemember Extraction
- 33.3 Linear Spectral Mixture Analysis
- 33.4 Anomaly Detection
- 33.5 Support Vector Machines and Kernel-Based Approaches
- 33.6 Hyperspectral Compression
- 33.7 Hyperspectral Signal Processing
- 33.8 Applications
- 33.9 Further Topics
- Glossary
- Appendix: Algorithm Compendium
- References
- Index
21.5 Progressive Band Dimensionality Process
The introduction of BP is to set a stage for progressive band dimensionality process (PBDP) to perform PBDE and PBDR. Following the treatment given Section 20.4 similar definitions to (20.12)–(20.14) can be also derived as follows.
Assume that 
is a set of priority scores calculated by a BPC where 
is a priority score assigned to the jth band, Bj. Then for 
where 
determines how the L spectral bands, 
are selected by PBDP progressively. If 
is arranged in descending order according to their priorities, 
where
(21.41) 
and 
is a simply permutation of 
. Then the rank of all the L spectral bands, 
is arranged by 
. That is, 
and
where the smaller number the rank(Bl), the higher priority the Bl. It is worth noting that for a generic representation there is no particular BPC specified in 
in (21.40). However, for example, if BPC is specified by skewness, then 
.
By means of 
or 
PBDP can be performed by starting any band number and then progressively adding or removing spectral bands specified by their corresponding priority scores 
in accordance with their assigned ranks by 
specified by (21.42).
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