Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
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Citations
Hyperspectral Remote Sensing Data Analysis and Future Challenges
Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]
Pixel-level image fusion
Hyperspectral Imaging: A Review on UAV-Based Sensors, Data Processing and Applications for Agriculture and Forestry
Hyperspectral Pansharpening: A Review
References
A new look at the statistical model identification
Estimating the Dimension of a Model
Compressed sensing
Principal Component Analysis
Nonlinear total variation based noise removal algorithms
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Frequently Asked Questions (20)
Q2. Why are independent Gamma distributions elected as priors for the spectra?
Because of the sparse nature of the chemical spectral components, independent Gamma distributions are elected aspriors for the spectra.
Q3. What constraints are used to solve a spectral unmixing problem?
When formulated as an optimization problem (e.g., implemented by the geometrical-based algorithms detailed in Section IV), spectral unmixing usually relies on algebraic constraints that are inherent to the observationspace : positivity, additivity and minimum volume.
Q4. What is the reason for the nonlinear mixing?
nonlinear mixing is usually due to physical interactions between the light scattered by multiple materials in the scene.
Q5. What is the effect of chance constraints on the fractional abundances?
RMVES accounts for the noise effects in the observations by employing chance constraints, which act as soft constraints on the fractional abundances.
Q6. What is the way to put in evidence the impact of the angles between the library vectors?
In order to put in evidence the impact of the angles between the library vectors, and therefore the mutual coherence of the library [187], in the unmixing results, the authors organize the library into two subsets; the minimum angle between any two spectral signatures is higher the 7 degrees in the first set and lower than 4 in the second set.
Q7. What are some of the kernels that are designed to be flexible?
Some of these kernels are designed to be sufficiently flexible to allow several nonlinearity degrees (using, e.g., radial basis functions or polynomials expansions) while others are physics-inspired kernels [55].
Q8. How can the authors use sparse processing with libraries?
it may become necessary to include distributions or tree structured representations into sparse processing with libraries.
Q9. Why have they been used in linear unmixing applications?
They have probably been the most 5 http://www.agc.army.mil/hypercubeoften used in linear hyperspectral unmixing applications, perhaps because of their light computational burden and clear conceptual meaning.
Q10. What is the recent approach to the spectral unmixing problem?
The spectral unmixing problem has recently been approached in a semi-supervised fashion, by assuming that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance [173]–[175] (e.g., spectra collected on the ground by a field spectro-radiometer).
Q11. How does the concept of thematic classification of hyperspectral images evolve?
as a prototypal task, thematic classification of hyperspectral images has recently motivated the development of a new class of algorithms that exploit both the spatial and spectral features contained in image.
Q12. Why are there many methods that have not been addressed in this manuscript?
Because of the high level of activity and limited space, there are many methods that have not been addressed directly in this manuscript.
Q13. What is the earliest work dealing with unmixing of multi-band images?
one of the earliest work dealing with linear unmixing of multi-band images (casted as a soft classification problem) explicitly attempts to highlight spatial correlations between neighboring pixels.
Q14. What is the way to find the boundary points of the data convex cone?
Convex cone analysis (CCA) [148], finds the boundary points of the data convex cone (it does not apply affine projection), what is very close to MV concept.
Q15. What is the difference between ICA and hyperspectral data?
ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them.
Q16. How do you get the estimates of the endmembers and fractional abundances?
The estimates of the endmembers and of the fractional abundances are obtained by a modification of the multiplicative update rules introduced in [147].
Q17. How can the authors penalize the volume of the recovered simplex?
According to the optimization perspective suggested above, penalizing the volume of the recovered simplex can be conducted by choosing an appropriate negative log-prior .
Q18. Why do the authors find that the CBPDN and CSR are often better than CLS and?
For this reason, and also due to the presence of noise and model mismatches, the authors have observed that the CBPDN and CSR often yields better unmixing results than CLS and FCLS.
Q19. How is the pixel correlation model adapted to unmix images?
In [199], abundance dependencies are modeled using Gaussian Markov random fields, which makes this approach particularly well adapted to unmix images with smooth abundance transition throughout the observed scene.
Q20. What is the alternating volume maximization (AVMAX) algorithm?
The alternating volume maximization (AVMAX) [126], inspired by N-FINDR, maximizes, in a cyclic fashion, the volume of the simplex defined by the endmembers with respect to only one endmember at one time.