Know the EarthShow the Way Hyperspectral Imagery HSI

Know the Earth…Show the Way Hyperspectral Imagery (HSI) Dimensionality Reduction Ronald G. Resmini, Ph. D. 18 July 2005 Institute for Pure and Applied Mathematics (IPAM) v: 703 -735 -3899 • ronald. g. resminir@nga. mil Approved for Public Release 05 -269 NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Outline • Introduction to HSI • HSI Dimensionality Reduction (DR) Ø Do We Need DR? • HSI Algorithms • What Can You Do? How Should You Do It? Approved for Public Release 05 -269 Know the Earth…Show the Way 2

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Introduction to Hyperspectral Imagery (HSI) Remote Sensing HSI is, fundamentally: writ large. . . the phenomenology of spectra; remote material detection, identification, characterization and quantification Approved for Public Release 05 -269 Know the Earth…Show the Way 3

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI Remote Sensing: Frame of Reference. . . • Remote sensing of the earth Øairborne Øspaceborne Øground (portables) • But bear in mind other apps: Ømedical Øindustrial Ømany, many others Approved for Public Release 05 -269 Know the Earth…Show the Way 4

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Electromagnetic Energy Electromagnetic Spectrum V / NIR / SWIR / Electromagnetic Spectrum Shorter Wavelengths High Energy Longer Wavelengths Low Energy MWIR / LWIR Optical Region Cosmic Gamma Rays Wavelength (nm) 10 -5 10 -4 10 -3 10 -2 X Rays 10 -1 Microwaves (Radar) UV 10 101 400 14000 105 106 Reflected Energy B G R NIR Wavelength (nm) 400 ( m) 0. 4 Approved for Public Release 05 -269 SWIR 107 108 109 Radio & Television Waves 1010 1011 1012 Emitted Energy MWIR 700 1500 3000 0. 7 1. 5 3. 0 LWIR 5000 5. 0 LWIR 14000 14. 0 Know the Earth…Show the Way 5

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Reflected vs. Emitted Energy MWIR 1000 Earth Reflectance Earth Emission (100%) 100 (100%) 10 Assumes no atmosphere radiant exitance (W-m-2 -um-1) Irradiance (W-m-2 -um-1) 104 1 0. 1 . 4 . 7 1 3 5 7 10 Wavelength (µm) Approved for Public Release 05 -269 Know the Earth…Show the Way 6

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Sampling the Spectrum BGR 400 nm 700 NIR SWIR 1500 3000 LWIR MWIR 5000 14000 nm LOW Panchromatic: one very wide band MED Multispectral: several to tens of bands HIGH Hyperspectral: hundreds of narrow bands Approved for Public Release 05 -269 Know the Earth…Show the Way 7

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Interaction of energy and objects Emitted Energy MW-LWIR Reflected Energy Incident Energy V-MWIR Absorbed Energy Transmitted Energy Balance Equation: EI ( ) = ER( ) + EA( ) + ET( ) Approved for Public Release 05 -269 Know the Earth…Show the Way 8

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY NASA AVIRIS Cuprite, NV, HSI Data, (1995) Approved for Public Release 05 -269 Know the Earth…Show the Way 9

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY An AVIRIS (NASA) HSI Image Cube Approved for Public Release 05 -269 Know the Earth…Show the Way 10

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY The Spectrum is the Fundamental Datum of HSI RS Approved for Public Release 05 -269 Know the Earth…Show the Way 11

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Applications of HSI RS • Geology • Forestry • Agriculture • Mapping/land use, land cover analysis • Atmospheric analysis • Environmental monitoring • Littoral zone RS • Many, many others Approved for Public Release 05 -269 Know the Earth…Show the Way 12

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Levels of Spectral Information High Spectral Resolution Quantification: Determines the abundance of materials. Hyperspectral (100’s of bands) Multispectral (10’s of bands) Panchromatic Characterization: Determines variability of identified material (e. g. wet/dry sand, soil particle size effects). Identification: Determines the unique identity of the foregoing generic categories (i. e. material identification). Discrimination: Determines generic categories of the foregoing classes. Classification: Separates materials into spectrally similar groups. Detection: Determines the presence of materials, objects, activities, or events. Low Spectral Resolution Approved for Public Release 05 -269 Know the Earth…Show the Way 13

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Image from the NASA Langley Research Center, Atmospheric Sciences Division. http: //asd-www. larc. nasa. gov/erbe/ASDerbe. html Approved for Public Release 05 -269 Know the Earth…Show the Way 14

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Electromagnetic Energy Atmospheric Absorption Approved for Public Release 05 -269 Know the Earth…Show the Way 15

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Reflected Energy Reflectance: Is the ratio of reflected energy to incident energy. § Varies with wavelength § Function of the molecular properties of the material. Reflectance Signature: A plot of the reflectance of a material as a function of wavelength. Red brick Kaolinite Sandy loam Concrete Grass Approved for Public Release 05 -269 All solids and liquids have reflectance signatures that potentially can be used to identify them. Know the Earth…Show the Way 16

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Emissive Energy Basic Concepts • Blackbody – A theoretical material that absorbs and radiates 100% of the Spectral Radiant Emittance • • energy incident upon it. BB curve is a function of temperature and wavelength. Planck’s Law – gives shape of blackbody curve at a specific temperature. Wien’s Displacement Law – determines wavelength of peak emittance. Wavelength (µm) Peak Emittance 6000 K Sun 373 K Boiling Water 1500 K Hot Coals 3000 K Light Bulb 800 K 500 K 250 K 0. 2 Approved for Public Release 05 -269 0. 4 0. 7 1 2 3 300 K Ambient 5 8 10 30 Know the Earth…Show the Way 17

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY The Planck or Blackbody Radiation Equation: Units: Approved for Public Release 05 -269 Know the Earth…Show the Way 18

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Emissive Energy • Emissivity - is a measure of how efficiently an object radiates energy compared to a blackbody at the same temperature. § Varies with wavelength § Function of the molecular properties of the material. • Emissivity Signature - A plot of emissivity as a function of Emissivity wavelength. All materials have emissivity signatures that potentially can be used to identify them. 1. 0 Blackbody 0. 5 Graybody 0 Selective emitter Wavelength Approved for Public Release 05 -269 Red brick Kaolinite Grass Water Black paint Concrete (emissivity signature) Know the Earth…Show the Way 19

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Spectral Signature Libraries (. . . beyond scope for a discussion on DR; but. . . ) • Spectral signatures of thousands of materials (solid, liquid, gas) have been measured in the laboratory and gathered into “libraries”. • Library signatures are used as the basis for identification of materials in HSI data. Approved for Public Release 05 -269 Know the Earth…Show the Way 20

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Understanding Spectral Data: Signature Variability Factors Ø Brightness Ø BRDF Ø Target morphology • shape • orientation Ø Particle size Ø Moisture Ø Spectral mixing Approved for Public Release 05 -269 Ø Composition • original • change over time Ø Surface quality • roughness • weathering Ø Shade & Shadow Ø Temperature Know the Earth…Show the Way 21

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Reflected Energy • The manner in which a material reflects energy is primarily a function of the optical properties and surface roughness of the feature. • Most objects are diffuse reflectors Angle of Incidence = Angle of Reflectance Energy Scattered in All Directions Smooth Surface Specular Reflectance Approved for Public Release 05 -269 Diffuse Reflectance Rough Surface (Microscopic) Know the Earth…Show the Way 22

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Emissive Energy Identification of Gases Emission No Detection Absorption Detected Signature Wavelength Gases appear in either emission or absorption depending on the temperature contrast between the gas and the background. Plume Gas (Warm) Gas (Cool) Same Temperature Background (Cool) Approved for Public Release 05 -269 Background (Warm) Know the Earth…Show the Way 23

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Stefan-Boltzmann Law: Two surfaces radiating at each other: . . . from Welty, Wicks, and Wilson (1984) View Factor Algebra and Radiant Exchange. . . Approved for Public Release 05 -269 Know the Earth…Show the Way 24

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Spectral Mixture Analysis (SMA) ‘Mixture’ = 25%A + 35%B + 40%C • An area of ground of, say 1. 5 m by 1. 5 m may contain 3 materials: A, B, and C. • An HSI sensor with a GSD of 1. 5 m would measure the ‘Mixture’ spectrum • SMA is an inversion technique to determine the quantities of A, B, and C in the ‘Mixture’ spectrum • SMA is physically-based on the spectral interaction of photons of light and matter • SMA is in widespread use today in all sectors utilizing spectral remote sensing • Variations include different constraints on the inversion; linear SMA; nonlinear SMA Approved for Public Release 05 -269 Know the Earth…Show the Way 25

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Resolutions (. . . beyond scope for a discussion on DR; but. . . ) • Spatial Resolution • Radiometric Resolution • Temporal Resolution Approved for Public Release 05 -269 Know the Earth…Show the Way 26

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI Fundamentals Summary • Hyperspectral remote sensing involves measuring energy in the Visible – LWIR portions of the electromagnetic spectrum. • Some of the measured energy is reflected from objects while some energy is emitted from objects. • Every material has a unique spectral signature. • Spectral image data are collected such that signatures can be extracted for material detection, classification, identification, characterization, and quantification. • Spectral, spatial, radiometric, and temporal resolution determine the capabilities of the remote sensing sensor/system. Approved for Public Release 05 -269 Know the Earth…Show the Way 27

The General Data Analysis/Exploitation Flow Approved for Public Release 05 -269 DN Calibration Fixes/Corrections Data Ingest Look At/Inspect the Data!! Atmospheric Compensation Algorithms for Information Extraction Spectral Library Access Information Fusion Iteration Geometric/Geospatial Product/Report Generation Distribution Archive/Dissemination Planning for Additional Collections DR?

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI Remote Sensing: Frame of Reference. . . • A Scientist’s Approach to the Data: Ø look at the data(!) Ø observables have a physical, chemical, biological, etc. basis Ø must understand nature of observables Ø bumps and wiggles have real, physical (spectroscopic) significance Ø application of tools comes last! Approved for Public Release 05 -269 Know the Earth…Show the Way 29

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Defining HSI Dimensionality • Hundreds of bands of data in an HSI data cube • An HSI pixel (a spectrum) is an n-D vector Ø n = number of bands Ø a spectrum is a point in an n-D space • “Redundancy” of information • Embedding or spanning dimension • Intrinsic dimension/virtual dimension • A distinction Ø large volume of data Ø dimensionality Approved for Public Release 05 -269 Know the Earth…Show the Way 30

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY The n-D Space — Where Many Algorithms Operate Each HSI spectrum (or pixel) is an n-D vector that can be represented as a single point in n-D space is actually where many of our algorithms Reflectivity, r operate. Wavelength (mm) Approved for Public Release 05 -269 Know the Earth…Show the Way 31

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Four (A-D) Equivalent Notations/Representations A B Reflectance, r r, Band b . . . imagine an n-D hyperspace. . . Wavelength (micrometers) Spectrum s 1 r, Band a C (0. 11, 0. 23, 0. 30, 0. 25, 0. 16, 0. 27, 0. 31, 0. 37, . . . , ) D Approved for Public Release 05 -269 Know the Earth…Show the Way 32

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Some HSI Scatter Plots; Spectra as Points in ‘Hyperspace’ Approved for Public Release 05 -269 Know the Earth…Show the Way 33

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Defining HSI Dimensionality • “Curse of dimensionality” Ø for Gaussian distribution. . . Ø. . . for a given classification accuracy Ø # of training samples grows quadratically Ø based on exploitation methodology; e. g. : Mahalanobis Distance: Maximum Likelihood: Approved for Public Release 05 -269 Know the Earth…Show the Way 34

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI or MSI • 100’s of bands vs. 10’s of bands • Maybe all you need is 6 bands but. . . Ø you need six; and so on • Atmospheric compensation. . . • HSI is spectroscopy writ large Ø its about resolving spectral information Ø fine spectral features Ø broad spectral features • Today’s FPAs make HSI a breeze anyway. . . Approved for Public Release 05 -269 Know the Earth…Show the Way 35

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Multispectral - Hyperspectral Signature Comparison Multispectral Hyperspectral Resampled to Landsat TM 7 Bands Approved for Public Release 05 -269 Know the Earth…Show the Way 36

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Atmos. Comp. Minerals/Geology Iron oxides Fuels Aerosols O 2 Chlorophyll DOM/CDOM Paints Cirrus Fabrics Vegetation Plastics Bathymetry B Wavelength 400 (nm) ( m) 0. 40 G CO 2 R Soils SWIR NIR 700 1500 3000 0. 70 1. 50 3. 00 Similar figures may be constructed for M/LWIR regions. Approved for Public Release 05 -269 Know the Earth…Show the Way 37

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Estimating HSI Dimensionality • Eigenvalues of the covariance Ø principal components analysis (PCA)/aka KL Ø optimal, least squares sense • Eigenvalues of the correlation matrix • Visual—based on eigenvalues • Continuous significant linear dimensionality Ø CSD; eigenvalues (next slide. . . ) Umaña-Díaz, A. , and Vélez-Reyes, M. , (2003). Determining the dimensionality of hyperspectral imagery for unsupervised band selection. Proceedings of the SPIE, S. S Shen and P. E. Lewis, eds. , v. 5093, pp. 70 -81. (. . . and references cited therein. ) Approved for Public Release 05 -269 Know the Earth…Show the Way 38

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Covariance Matrix: Find the eigenvalues of the covariance (or correlation) matrix and then. . . or: where: li are the eigenvalues Approved for Public Release 05 -269 Know the Earth…Show the Way 39

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Virginia City Probe-1 HSI Data Eigenvalues from a PCA 116 bands out of 128 Approved for Public Release 05 -269 Band Number Know the Earth…Show the Way 40

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Urban Scene HYDICE HSI Data Eigenvalues from a PCA 162 bands out of 210 Approved for Public Release 05 -269 Band Number Know the Earth…Show the Way 41

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Mormon Mesa SEBASS HSI Data Eigenvalues from a PCA Band Number 128 bands out of 128 Approved for Public Release 05 -269 Know the Earth…Show the Way 42

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Estimating HSI Dimensionality • Wavelet basis • Nonlinear dimension estimation Ø Near neighbor method of Pettis Ø Fukunaga Ø Fractal and Olsen’s KL-related method dimension o Hausdorff dimension o Box-counting method o Correlation integral/dimension (next slide. . . ) Approved for Public Release 05 -269 Know the Earth…Show the Way 43

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Box Counting: Correlation Dimension: Correlation Function: where: r is box size (DB) or radius of a hypersphere (D) Approved for Public Release 05 -269 Know the Earth…Show the Way 44

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI Dimensionality Reduction • Techniques Ø Principal components analysis (PCA) Ø Minimum noise fraction (MNF) Ø Vector quantization (VQ) Ø Projection pursuit (PP) Ø The universe of data compression o lossless/lossy (when/why? ) o discrete cosine transformation (DCT) o wavelets-based compression Ø Best bands selection/band averaging Approved for Public Release 05 -269 Know the Earth…Show the Way 45

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Best-Bands Selection 2. 0 m to 2. 5 m – SWIR, Only Approved for Public Release 05 -269 Know the Earth…Show the Way 46

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Other Means of DR • Spectral mixture analysis (SMA) Ø basis vectors • Analysis of filter vectors (OSP algorithms. . . ) • Wavelet-based feature selection • On-board processing Ø transmit product Ø advanced computation Ø quantum computation? Approved for Public Release 05 -269 Know the Earth…Show the Way 47

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Other Means of DR • Transmit only bands of interest Ø best-bands selection/band averaging. . . Ø. . . perhaps after atmos. comp. • Spectral parameterizations • Derivative spectroscopy • Binary encoding Approved for Public Release 05 -269 Know the Earth…Show the Way 48

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Spectral Parameterization: Spectral Metrics (1 of 2) Soil Spectrum Approved for Public Release 05 -269 Know the Earth…Show the Way 49

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Spectral Parameterization: Spectral Metrics (2 of 2) Desert Soil (Malpais) 3. 5 - 4. 17 microns Band 1 Depth 0. 12 0. 10 0. 08 Disturbed Soil Pristine Soil Vehicle Treads 0. 06 0. 04 0. 02 0. 00 0. 10 0. 20 0. 30 0. 40 0. 50 3. 5 - 4. 17 microns Band 2 FWHM Approved for Public Release 05 -269 Know the Earth…Show the Way 50

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY The Need For DR • • • Is there a need for DR? Is there a “curse of dimensionality”? Well. . . it depends. . . Not with today’s (and tomorrow’s) computers Not with many capable HSI algorithms Structure of HSI in n-D space Ø linear mixing trends Ø mixed pixels; spectral endmembers Ø are these clusters? • Yes. . . if using traditional MSI classification techniques. . . Approved for Public Release 05 -269 Know the Earth…Show the Way 51

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Mahalanobis Distance Maximum Likelihood Approved for Public Release 05 -269 Know the Earth…Show the Way 52

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Jeffries-Matusita (JM) Distance Where B is the Bhattacharyya distance Approved for Public Release 05 -269 Know the Earth…Show the Way 53

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY HSI Algorithms Approved for Public Release 05 -269 Know the Earth…Show the Way 54

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Euclidean Distance: n-D Geometry Whole-Pixel Distance Metric in n-D Hyperspace Assume a two band spectral remote sensing system. Each two point ‘spectrum’ is a point in Band b vs. Band a space. A 2 D scatterplot with 2 spectra: Spectrum s 2 Band b Euclidean Distance Spectrum s 1 Band a Approved for Public Release 05 -269 Know the Earth…Show the Way 55

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY SAM: n-D Geometry Angular Distance Metric (Spectral Angle Mapper or SAM) Assume a two band spectral remote sensing system. Each two point ‘spectrum’ is a point in Band b vs. Band a space. A 2 D scatterplot with 2 spectra: The angle, , between the two Band b Spectrum s 2 Spectrum s 1 lines connecting each spectrum (point) to the origin is the angular separation of the two spectra. Smaller angular separations in- dicate more similar spectra. Band a Approved for Public Release 05 -269 Know the Earth…Show the Way 56

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY SAM: The Math • Chang (2003), ch. 2, pp. 20 -21; and. . . • Assume two 5 -band spectra as shown: Approved for Public Release 05 -269 Know the Earth…Show the Way 57

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Linear Spectral Unmixing The reflectance of an image pixel is a linear combination of reflectances from (typically) several “pure” substances (or endmembers) contained within the ground-spot sampled by the remote sensing system: where: Ri is the reflectance of a pixel in band i, fj is the fractional abundance of endmember j in the pixel, Mj, i is the reflectance of endmember substance j in band i, ri is the unmodeled reflectance for the pixel in band i, and n is the number of endmembers. Approved for Public Release 05 -269 Know the Earth…Show the Way 58

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY 7 x 1 7 x 5 5 x 1 A linear equation. . . x A b 5 endmembers in a 7 -band spectral data set Approved for Public Release 05 -269 Know the Earth…Show the Way 59

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY OSP/LPD/DSR: Scene-Derived Endmembers (Harsanyi et al. , 1994; see also ch. 3 of Chang, 2003) Approved for Public Release 05 -269 Know the Earth…Show the Way 60

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Approved for Public Release 05 -269 Know the Earth…Show the Way 61

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Approved for Public Release 05 -269 Know the Earth…Show the Way 62

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY The value of x. T which maximizes l is given by x. T = d. T This is equivalent to Unconstrained SMA Approved for Public Release 05 -269 Know the Earth…Show the Way 63

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Statistical Characterization of the Background (LPD/DSR) (Harsanyi et al. , 1994) Approved for Public Release 05 -269 Know the Earth…Show the Way 64

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Approved for Public Release 05 -269 Know the Earth…Show the Way 65

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Constrained Energy Minimization (CEM) • The description of CEM is similar to that of OSP/DSR (previous slides) • Like OSP and DSR, CEM is an Orthogonal Subspace Projection (OSP) family algorithm • CEM differs from OSP/DSR in the following, important ways: Ø CEM does not simply project away the first n eigenvectors Ø The CEM operator is built using a weighted combination of the eigenvectors (all or a subset) • Though an OSP algorithm, the structure of CEM is equally readily observed by a formal derivation using a Lagrange multiplier • CEM is a commonly used statistical spectral matched filter • CEM for spectral remote sensing has been published on for over 10 years • CEM has a much longer history in the multi-dimensional/array signal processing literature • Just about all HSI tools today contain CEM or a variant of CEM • If an algorithm is using M-1 d as the heart of its filter kernel (where M is the data covariance matrix and d is the spectrum of the target of interest), then that algorithm is simply a CEM variant Approved for Public Release 05 -269 Know the Earth…Show the Way 66

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Derivation taken from: Stocker, A. D. , Reed, I. S. , and Yu, X. , (1990). Multi-dimensional signal processing for electro. Optical target detection. In: Signal and Data Processing of Small Targets 1990, Proceedings of the SPIE, v. 1305, pp. 218 -231. Hº: pº(x)= J = # of Bands H 1: p 1(x)= Form the log-likelihood ratio test of Hº and H 1: Approved for Public Release 05 -269 Know the Earth…Show the Way 67

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Some algebra. . . Approved for Public Release 05 -269 Know the Earth…Show the Way 68

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY A trick. . . recast as a univariable problem: After lots of simple algebra applied to the r. h. s: Now, go back to matrix-vector notation: a scalar threshold Approved for Public Release 05 -269 Know the Earth…Show the Way 69

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Take the natural log: { >T for H 1; <T for H 0 Threshold, T Filter Kernel Approved for Public Release 05 -269 { { . . . a scalar for each pixel Pixel Know the Earth…Show the Way 70

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY “The vector: QTx is a projection of the original spectral data onto the eigenvectors of the covariance matrix, M, which corresponds to the principal axes of clutter distribution. ” Stocker et al. , 1990. Approved for Public Release 05 -269 Know the Earth…Show the Way 71

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY “Further SCR gain is obtained by forming the optimum weighted combination of principal components using the weight vector: ” From Stocker et al. , 1990. Approved for Public Release 05 -269 Know the Earth…Show the Way 72

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Its Important to Note That. . . Today’s HSI algorithms can also benefit from 1) spatial and spectral subsetting; 2) hierarchical application of techniques; 3) other. . . Approved for Public Release 05 -269 Know the Earth…Show the Way 73

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY What Should You Do? How Should You Do It? • Join the fray!. . . HSI is a big tent • Dump Lena/girl. . . Ø the spectrum is the fundamental datum • Conduct honest, rigorous comparisons with existing, current best-practices HSI techniques • Apply techniques to multiple, large, diverse data sets • Team with HSI expert(s) and subject-matter expert(s) • Seek peer-reviews from HSI experts Ø I’m happy to be a reviewer. . . • Learn about/care about the field; be relevant be more than buzz words Ø we’re more than an opportunity for statistical analyses Ø Approved for Public Release 05 -269 Know the Earth…Show the Way 74

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Contact Information Resmini The Boeing Company (Associate Technical Fellow); The National Geospatial-Intelligence Agency (NGA); and School of Computational Sciences, George Mason University v: 703 -735 -3899 e-mail(1): ronald. g. resmini@nga. mil e-mail(2): ronald. g. resmini@boeing. com Approved for Public Release 05 -269 Know the Earth…Show the Way 75

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Backup Slides Approved for Public Release 05 -269 Know the Earth…Show the Way 76

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Resources: Peer-Reviewed Journals • Remote Sensing of Environment • International Journal of Remote Sensing • IEEE Transactions on Geoscience and Remote Sensing • Journal of Geophysical Research • Solid Earth, Planets, Oceans and Atmospheres • Icarus • Remote Sensing Reviews • Photogrammetric Engineering and Remote Sensing • Applied Optics • Journal of the Optical Society of America • Many others, too! Approved for Public Release 05 -269 Know the Earth…Show the Way 77

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Resources: Non-Reviewed Journals • Published conference proceedings: • SPIE • your library may subscribe to SPIE • abstract services • AVIRIS (NASA) conference • IEEE/IGARSS • Proceedings of the ASPRS • Many others, too! Approved for Public Release 05 -269 Know the Earth…Show the Way 78

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY Linear Spectral Unmixing Theory Spectral unmixing theory states that the reflectance of an image pixel is a linear combination of reflectances from the (typically) several “pure” substances (or endmembers) contained within the ground-spot sampled by the remote sensing system. This is indicated below: where: Ri is the reflectance of a pixel in band i, fj is the fractional abundance of substance (or endmember) j in the pixel, and Mj, i is the reflectance of endmember substance j in band i. ri is the band-residual or unmodeled reflectance for the pixel in band i, and n is the number of endmembers. A spectral unmixing analysis results in n fraction-plane images showing the quantitative areal distribution of each of the endmember substances and one root mean squared (RMS) image showing an overall or global goodness of fit of the suite of endmembers for each pixel. The RMS image is formed, on a pixel-by-pixel basis, by: Objects may also be detected as anomalies in the RMS image. Approved for Public Release 05 -269 Know the Earth…Show the Way 79