高光谱光谱解混

4
Remote Sensing: Basics
E(λ) L(λ)
ρ(λ)
Surface
E ρ L λ
– Irradiance (W/m2) – Reflectance – Radiance (W/Sr/m2) – Wavelength (µm)
5
Remote Sensing: Atmosphere
m1 m2
∆x
m3 m4 m6
m5 m7
• Spectral Domain {m1, m2, L, mp} linearly independent
• Spatial
Domain
∆x
∆ x → ∆ x /4 ∆ y → ∆ y /4
13
Nonlinear Mixing Model (NLMM)
Intimate mixture (particulate media) Two-layers: canopies+ground
• • Infer the covariance matrix Determine maximizing the ratio eigenvectors of and are the
ordered by decreasing SNR
• Project data: Question: How to infer p ? Shortcoming: For colored noise, signal subspace does not span the
17
Spectral Linear Unmixing: SLU
Given N spectral vectors of dimension L
Subject to the LMM
Determine: • The mixing matrix A (endmember spectra) • The fractional abundance vectors s
• The shape of a given endmember is fairly consistent • The amplitude varies considerably
[Shaw &Burke, 2003]
LMM
Topographic modulation Variability Fractional abundances
• Complex models parameterized with scene parameters • Reliable unmixing is yet to be demonstrated [Keshsva, 03]
Linear mixing: • Accurate moddeling of checkerboard type scenes
• Hyperspectral
• more than 30 bands → [0.3-2.5] µm • spectral resolution → 10 nm
Advantages of Hyperspectral Scanners
• Better identification/classification of materials • Change spatial resolution with spectral resolution
[Lillesand & Keifer, 02]
(Energy blocked)
Photography Hyperspectral scanners Thermal scanners
Multispectral scanners UV
0.3µm
VI
N-IR
0.7µm
MID-IR
1µm 2.5µm
TERMAL-IR
23
Dimensionality Reduction: PCA and MNR results
24
Dimensionality Reduction (unknown p and i.id noise) HFC-Harsanyi-FarrandHFC-Harsanyi-Farrand-Chang [Harsanyi et al., 93]) NWHFC-[Chang & Du, 94] NWHFCBased on a hypothesis test on
1
Squematic view of spectral mixing/unmixing processes sensor
sunlight
radiance
unmixing
2
Multispectral/Hyperspectral Scanners
• Multispectral
• up to 20 bands → [0.3-10] µm • spectral resolution → 0.25 µm
15
Linear Mixing Model (LMM)
Fractional abundances Constraints: full additivity Calibration positivity
Mixing Matrix
Endmember reflectance
16
Spectral Variability
Spectral Unmixing
José M. Bioucas Dias Instituto Superior Técnico Instituto de Telecomunicações Lisbon, Portugal
First European School on Hyperspectral Imaging – Caceres, October 2007
Sample correlation matrix Eigendecomposition Eigenvectors ordered by decreasing magnitude of the correspondent eigenvalues
Rationale:
21
Dimensionality Reduction (unknown p and i.id. noise) PCAPCA-Principal Component Analysis •
Reasoning underlying DR 1. Lightens the computational complexity 2. Attenuates the noise power by a factor of
20
Dimensionality Reduction
Exact ML solution [Scharf, 91] (known p, i.i.d. Gaussian noise)
11
Linear Mixing Model (LMM)
Incident radiation only interacts with one component (checkerboard type scenes)
Band m
Band n

Hyperspectral Scanners
Change spatial resolution with spectral resolution Resolve m1
3
Outline
• Hyperspectral/Multispectral Scanning • Basic aspects of Remote Sensing • Spatial/Spectral Resolution • Observation model (Linear/Nonlinear) • Spectral Unmixing • Dimensionality Reduction • Endmember Determination • Inversion
Signal space dimension depends on the specified false alarm probability Shortcoming:
25
Dimensionality Reduction(unknown p and i.id noise)
HySimeHySime-hyperspectral signal identification by minimum error [Bioucas-Dias & Nascimento, 05]
10µm
MIC
1mm 6
Material Identification/Resolution
165 bands 10 µm Landsat 7 TM bands 12 3 4 5 6
7
Atmospheric Correction
Objective: Convert radiance into reflectance
8
Calibration example: offset determination by ATREM
9
Calibration Example: Gain determination by ATREM
10
Calibration using ATREM
Radiance (kaolonite) Reflectance (kaolonite)
3. Inversion
For each pixel, identify the vector of proportions
19
Dimensionality Reduction
Dim(A) = [L × p]
L
p
Problem: Identify the subspace generated by the columns of
Signal projection error power
Projected noise power
26
Dimensionality Reduction (Results on simulated data)
• Trades model accuracy for analytical tractability • Adequated for unsupervised-type appproaches to unmixing
Large research efforts have been devoted to the development of effective unmixing algorithms based on the linear mixing model
Radiative transfer theory
Material fractions
Media parameters
Single scattering
Double scattering
14
Linear versus Nonlinear Mixing Models
Nonlinear mixing: • Accurate moddeling of the light interactions with the scene
18
Algorithms for SLU
ThreeThree-step Approach 1. Dimensionality reduction
Identify the subspace spanned by the columns of
2. Endmember determination
Identify the columns of
Coefficients a and b depend on
• • • • • • • Terrain topography Reflectance of the surroudings Sun position (local time) Water-vapor Aerosols Gases Clouds
• Compute the eigendecomposition of the covariance matrix • Select the p eigenvalues, eigenvalues , for , corresponding to
• Take
p-dimensional
22
Dimensionality Reduction (unknown p and non-i.id. noise) NAPCNAPC-Noise adjusted principal components [Lee et al., 1990] MNFMNF-maximum noise fraction [Green et al., 1988]