Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing

By José M. Bioucas-Dias, Mário A. T. Figueiredo. Workshop on Hyperspectral Image and Signal Processing, 2010

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Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear mixtures of spectra, selected from large libraries, and the constrained basis pursuit denoising (CBPDN), which is a generalization of BP to admit modeling errors. In this paper, we introduce two new algorithms to efficiently solve these optimization problems, based on the alternating direction method of multipliers, a method from the augmented Lagrangian family. The algorithms are termed SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian) and C-SUnSAL (constrained SUnSAL). C-SUnSAL solves the CBP and CBPDN problems, while SUnSAL solves CLS as well as a more general version thereof, called constrained sparse regression (CSR). C-SUnSAL and SUnSAL are shown to outperform off-the-shelf methods in terms of speed and accuracy.

Subfields: Computational Mechanics, Media Technology

View Paper: https://www.semanticscholar.org/paper/14d1ead1d0ca380ccbafd00b807554816814230a

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Citations in the corpus

Sparse Unmixing of Hyperspectral Data (2011, methodology): “In this paper, we use the sparse unmixing algorithm via variable splitting and augmented Lagrangian (SUnSAL), introduced in [29], to solve problem (24).”
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers (2011, neutral): “ADMM has also been applied to a number of statistical problems, such as constrained sparse regression [18], sparse signal recovery [70], image restoration and denoising [72, 154, 134], trace norm regularized least squares minimization [174], sparse inverse covariance selection [178], the Dantzig sel”
Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing (2012, methodology): “To solve the problem in (8), we have modified the SUnSAL algorithm [45] following closely the methodology introduced in [62].”
Compressive Coded Aperture Spectral Imaging: An Introduction (2014, methodology): “This includes interior-point methods such as 1 , -magic software and gradient-descent methods like the sparse reconstruction via separable approximation (SpaRSA), the two-step iterative shrinkage/thresholding algorithm (TwIST), and the gradient projections for sparse reconstruction algorithm (GPSR) ”
Collaborative Sparse Regression for Hyperspectral Unmixing (2014, methodology): “To solve the optimization problem in (2), we use the Collaborative Sparse Unmixing via variable Splitting and Augmented Lagrangian (CLSUnSAL) algorithm [25], which is an ellaboration of the SUnSAL algorithm introduced in [26].”
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches (2012, neutral): “If we add the ANC to BP and BPDN problems, we have the constrained basis pursuit (CBP) and the constrained basis pursuit denoising (CBPDN) problems [184], respectively.”
Hyperspectral and Multispectral Data Fusion: A comparative review of the recent literature (2017, methodology): “Simplex identification via split augmented Lagrangian (SISAL) [63] is used to initialize the endmembers and sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) [64] is adopted to obtain initial abundances.”