A Novel Hierarchical Bayesian Approach for Sparse Semisupervised Hyperspectral Unmixing

Themelis, Konstantinos E.; Rontogiannis, Athanasios A.; Koutroumbas, Konstantinos

doi:10.1109/tsp.2011.2174052

Cited by 114 publications

(69 citation statements)

References 35 publications

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“…Finding the optimal solution of Equation (2) is an NP-hard [43], i.e., various subsets of the endmembers that are possibly present must be verified for each mixed pixel from a given spectral library. As a remedy, several efficient linear sparse techniques are proposed for the unmixing process, e.g., [4,5,17,18,26]. Minimizing the 1 -norm as approximation instead of the 0 -norm is one of the earliest methods proposed to avoid an exhaustive search for Equation (2) (e.g., see [44,45] and the references therein; see also [17,22,26,35,41,46,47] for unmixing techniques), as follows:…”

Section: Sparse Spectral Unmixingmentioning

confidence: 99%

“…Since the number of endmembers/materials present at each mixed pixel is normally scanty compared to the number of total endmembers in most applications, we can consider the problem of SU as a sparse unmixing problem [15][16][17][18][19][20][21][22][23]. Mathematically, the corresponding sparse problem is an 0 -norm problem and is an NP-hard problem due to the required exhaustive combinatorial search [24,25].…”

Section: Introductionmentioning

confidence: 99%

“…These may include iterative reweighted schemes (e.g., [27,28]), greedy algorithms [29,30], Bayesian learning algorithms [18], q regularization [31] and compressive sensing schemes [21,32]. Each of these methods has specific characteristics, e.g., the method proposed in [18] exploits Bayesian learning to control the parameters involved. Some algorithms have used better approximations of the 0 -norm, e.g., the p -norm is approximated as a weighted l 2 -norm in [33].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, we simply propose to increase σ exponentially. We compare our proposed method to several state-of-the-art methods [17,18,26,33] over both the synthetic data and real hyperspectral data. Our results show that our method results in a higher reconstruction signal-to-noise ratio (RSNR) for the fractional abundances than some state-of-the-art methods and outperforms them in the sense of the probability of success (PoS), except for the SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian) method [17,26].…”

Section: Introductionmentioning

confidence: 99%

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ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

et al. 2016

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Abstract:The goal of sparse linear hyperspectral unmixing is to determine a scanty subset of spectral signatures of materials contained in each mixed pixel and to estimate their fractional abundances. This turns into an 0 -norm minimization, which is an NP-hard problem. In this paper, we propose a new iterative method, which starts as an 1 -norm optimization that is convex, has a unique solution, converges quickly and iteratively tends to be an 0 -norm problem. More specifically, we employ the arctan function with the parameter σ ≥ 0 in our optimization. This function is Lipschitz continuous and approximates 1 -norm and 0 -norm for small and large values of σ, respectively. We prove that the set of local optima of our problem is continuous versus σ. Thus, by a gradual increase of σ in each iteration, we may avoid being trapped in a suboptimal solution. We propose to use the alternating direction method of multipliers (ADMM) for our minimization problem iteratively while increasing σ exponentially. Our evaluations reveal the superiorities and shortcomings of the proposed method compared to several state-of-the-art methods. We consider such evaluations in different experiments over both synthetic and real hyperspectral data, and the results of our proposed methods reveal the sparsest estimated abundances compared to other competitive algorithms for the subimage of AVIRIS cuprite data.

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Section: Sparse Spectral Unmixingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

et al. 2016

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“…Themelis et al presented a novel hierarchical Bayesian method for the sparse unmixing of HSIs [47] and selected suitable priors to ensure the non-negativity of the abundances and favor sparse solutions for the abundances. Given that the relaxation to the original 0 norm may introduce sensitive weighted parameters and additional calculation error, Xu et al thus developed a novel sparse unmixing method based on multi-objective optimization without any relaxation [48] that contains two correlative objectives: minimizing the reconstruction error and controlling the sparsity of abundance.…”

Section: Introductionmentioning

confidence: 99%

Sparse Unmixing of Hyperspectral Data with Noise Level Estimation

Mei

et al. 2017

Remote Sensing

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Abstract:Recently, sparse unmixing has received particular attention in the analysis of hyperspectral images (HSIs). However, traditional sparse unmixing ignores the different noise levels in different bands of HSIs, making such methods sensitive to different noise levels. To overcome this problem, the noise levels at different bands are assumed to be different in this paper, and a general sparse unmixing method based on noise level estimation (SU-NLE) under the sparse regression framework is proposed. First, the noise in each band is estimated on the basis of the multiple regression theory in hyperspectral applications, given that neighboring spectral bands are usually highly correlated. Second, the noise weighting matrix can be obtained from the estimated noise. Third, the noise weighting matrix is integrated into the sparse regression unmixing framework, which can alleviate the impact of different noise levels at different bands. Finally, the proposed SU-NLE is solved by the alternative direction method of multipliers. Experiments on synthetic datasets show that the signal-to-reconstruction error of the proposed SU-NLE is considerably higher than those of the corresponding traditional sparse regression unmixing methods without noise level estimation, which demonstrates the efficiency of integrating noise level estimation into the sparse regression unmixing framework. The proposed SU-NLE also shows promising results in real HSIs.Keywords: alternative direction method of multipliers (ADMM); hyperspectral image (HSI); sparse unmixing method based on noise level estimation (SU-NLE)

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Geometrical Methods – Illustration with Hyperspectral Unmixing

Bioucas‐Dias,

2023

Source Separation in Physical‐Chemical Sensing

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A Novel Hierarchical Bayesian Approach for Sparse Semisupervised Hyperspectral Unmixing

Cited by 114 publications

References 35 publications

ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

ℓ0-Norm Sparse Hyperspectral Unmixing Using Arctan Smoothing

Sparse Unmixing of Hyperspectral Data with Noise Level Estimation

Geometrical Methods – Illustration with Hyperspectral Unmixing

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