A variable splitting augmented Lagrangian approach to linear spectral unmixing

By José M. Bioucas-Dias. 2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009

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This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed simplex identification via split augmented Lagrangian (SISAL). Following Craig's seminal ideas, hyperspectral linear unmixing amounts to finding the minimum volume simplex containing the hyperspectral vectors. This is a nonconvex optimization problem with convex constraints. In the proposed approach, the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. The obtained problem is solved by a sequence of augmented Lagrangian optimizations. The resulting algorithm is very fast and able so solve problems far beyond the reach of the current state-of-the art algorithms. The effectiveness of SISAL is illustrated with simulated data.

Subfields: Atmospheric Science, Media Technology

View Paper: https://www.semanticscholar.org/paper/c96d322ad45e5f412d20cf85b1d97b2c33267d53

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Citations in the corpus

Manifold Regularized Sparse NMF for Hyperspectral Unmixing (2013, background): “6) Experiment 6 (Generalization to Different Numbers of Endmembers): This experiment evaluates the performances of VCA-FCLS, L1/2-NMF, SISAL-FCLS, and GLNMF when the data are constituted of different numbers of endmembers.”
Fusing Hyperspectral and Multispectral Images via Coupled Sparse Tensor Factorization (2018, methodology): “The spectral dictionary S is initialized via simplex identiﬁcation split augmented Lagrangian (SISAL) [52] method, which efﬁciently identiﬁes a minimum volume simplex containing the LR-HSI spectral vectors.”
A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing (2014, background): “, soft constraints [41], chance constraints [43], and robust max-min volume [20].”
Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization (2011, methodology): “SISAL is the abbreviation of Simplex Identification via variable Splitting and Augmented Lagrangian, which can deal with outliers and is very efficient from the computational cost point of view.”
Sparse Unmixing of Hyperspectral Data (2011, background): “…[18], iterated constrained endmembers (ICE) [19], minimum volume constrained non-negative matrix factorization [20], spatial–spectral endmember extraction [21], sparsity-promoting ICE [22], minimum volume simplex analysis [23], and simplex identiﬁcation via split augmented Lagrangian [24].”
Hyperspectral Super-Resolution by Coupled Spectral Unmixing (2015, methodology): “Require: H, M, S, R Initialize E (0) with SISAL and˜A (0) with SUnSAL Initialize A (0) by upsampling˜A (0) k ← 0 while not converged do k ← k + 1 // low-resolution step: ˜ A ← A (k−1) S ; Estimate E (k) with (8a, 8b) // high-resolution step: ˜ E ← RE (k) ; Estimate A (k) with (9a, 9b) end while retu”
Hyperspectral and Multispectral Data Fusion: A comparative review of the recent literature (2017, methodology): “As a result, SISAL was used for the data sets #2, 5, 6 ,7, and 8, while VCA was used for the data sets #1, 3, and 4.”
Hyperspectral Remote Sensing Data Analysis and Future Challenges (2013, methodology): “This handicap was circumvented in the simplex identification via variable splitting and augmented Lagrangian (SISAL) [53], the minimum volume enclosing simplex (MVES) [54] by reformulating (3) with respect to M 1- instead of M.”
Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing (2010, unknown): “Therefore, ﬁnding the endmembers amounts to identifying the vertices of that simplex [1, 2, 19, 17, 4, 14, 21].”