Recent developments in sparse hyperspectral unmixing

Iordache, Marian-Daniel; Bioucas-Dias, José M.

doi:10.1109/igarss.2010.5653075

Cited by 32 publications

(14 citation statements)

References 11 publications

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“…The convergence of the repeat process can be ensured by the Split Bregman algorithm, and the convergence of the whole algorithm is proved in Xu et al (2010). As ASC is critical (Iordache et al 2010b), we can set c = 0 in line 5.2 to easily discard it. The parameter λ is to keep the balance between the sparsity of the abundances and the residual of the least square term.…”

Section: Our Proposed Methodsmentioning

confidence: 99%

A novel l _1/2 sparse regression method for hyperspectral unmixing

Sun

Wu²,

Xiao³

et al. 2013

International Journal of Remote Sensing

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Hyperspectral unmixing (HU) is a popular tool in remotely sensed hyperspectral data interpretation, and it is used to estimate the number of reference spectra (end-members), their spectral signatures, and their fractional abundances. However, it can also be assumed that the observed image signatures can be expressed in the form of linear combinations of a large number of pure spectral signatures known in advance (e.g. spectra collected on the ground by a field spectro-radiometer, called a spectral library). Under this assumption, the solution of the fractional abundances of each spectrum can be seen as sparse, and the HU problem can be modelled as a constrained sparse regression (CSR) problem used to compute the fractional abundances in a sparse (i.e. with a small number of terms) linear mixture of spectra, selected from large libraries. In this article, we use the l 1/2 regularizer with the properties of unbiasedness and sparsity to enforce the sparsity of the fractional abundances instead of the l 0 and l 1 regularizers in CSR unmixing models, as the l 1/2 regularizer is much easier to be solved than the l 0 regularizer and has stronger sparsity than the l 1 regularizer (Xu et al. 2010). A reweighted iterative algorithm is introduced to convert the l 1/2 problem into the l 1 problem; we then use the Split Bregman iterative algorithm to solve this reweighted l 1 problem by a linear transformation. The experiments on simulated and real data both show that the l 1/2 regularized sparse regression method is effective and accurate on linear hyperspectral unmixing.

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Section: Our Proposed Methodsmentioning

confidence: 99%

A novel l _1/2 sparse regression method for hyperspectral unmixing

Sun

Wu²,

Xiao³

et al. 2013

International Journal of Remote Sensing

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“…A spectral unmixing method for a hyperspectral image based on sparse decomposition was proposed in Ref. 10. The redundant dictionary was trained by the spectral library samples, dependence on end member extraction accuracy, as done by other algorithms was avoided, and good results were obtained.…”

Section: Related Backgroundmentioning

confidence: 99%

“…Thus, any pixel curve can be represented by a combination of several atoms. Some researches 10 suggested that by redundant dictionary based sparse decomposition, the atoms of the trained redundant dictionary reflected the spectral features of the imaging materials. Most of the atoms were consistent with a certain spectral curve of the material.…”

Section: Principle Of Pixel Curve Based Sparse Decomposition Of the Hmentioning

confidence: 99%

Spatial resolution enhancement of hyperspectral images based on redundant dictionaries

Wang

Zhang

2015

J. Appl. Remote Sens

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Abstract. Spatial resolution enhancement of hyperspectral images is one of the key and difficult topics in the field of imaging spectrometry. The redundant dictionary based sparse representation theory is introduced, and a spatial resolution enhancement algorithm is proposed. In this algorithm, a pixel curve instead of a pixel patch is taken as the unit of processing. A pair of low-and high-resolution respective redundant dictionaries are joint trained, with the constraint that a pair of high-and low-resolution corresponded pixel curves can be sparse represented by same coefficients according to the respected dictionaries. In the process of super-resolution restoration, the low-resolution hyperspectral image is first sparse decomposed based on the low-resolution redundant dictionary and then the obtained coefficients are used to reconstruct the corresponding high-resolution image with respect to the high-resolution dictionary. The maximum a posteriori based constrained optimization is performed to further improve the quality of the reconstructed high-frequency information. Experimental results show that the pixel curve based sparse representation is more suitable for a hyperspectral image; the highly spectral correlations are better used for resolution enhancement. In comparison with the traditional bilinear interpolation method and other referenced super-resolution algorithms, the proposed algorithm is superior in both objective and subjective results.

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“…The mixture problem will seriously influence the efficiency of hyperspectral remote sensing information processing. There are two mixture models, named linear mixing and nonlinear mixing [1]. The linear mixture model (LSMM) assumes minimal secondary reflections and multiple scattering effects in the data collection procedure [2], and hence the measured spectra can be expressed as a This work has been supported by the National Natural Science Hyperspectral unmixing is a typical problem of blind source separation, as the collected mixed pixels, endmember signatures and corresponding proportions can be seen as the observations, mixing matrix and sources respectively.…”

Section: Introductionmentioning

confidence: 99%

Parallel optimization of hyperspectral unmixing based on sparsity constrained nonnegative matrix factorization

Wu¹,

Jie

et al. 2013

2013 IEEE International Geoscience and Remote Sensing Symposium - IGARSS

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1Hyperspectral unmixing is a typical problem of blind source separation, which can be solved by nonnegative matrix factorization (NMF). Sparsity based NMF will increase the efficiency of unmixing, but its computational complexity limits the possibility of utilizing it in time-critical applications. In this paper, method of parallel hyperspectral unmixing based on sparsity constrained nonnegative matrix factorization on Graphics Processing Units (CSNMF-GPU) is investigated and compared in terms of both accuracy and speed. The realization of the proposed method using Compute Unified Device Architecture (CUDA) on GPU are described and evaluated. The experimental results comparing with the serial implementations based on both simulated and real hyperspectral data demonstrate the effectiveness of the proposed parallel optimization approach.

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Recent developments in sparse hyperspectral unmixing

Cited by 32 publications

References 11 publications

A novel l _1/2 sparse regression method for hyperspectral unmixing

A novel l _1/2 sparse regression method for hyperspectral unmixing

Spatial resolution enhancement of hyperspectral images based on redundant dictionaries

Parallel optimization of hyperspectral unmixing based on sparsity constrained nonnegative matrix factorization

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Recent developments in sparse hyperspectral unmixing

Cited by 32 publications

References 11 publications

A novel l 1/2 sparse regression method for hyperspectral unmixing

A novel l 1/2 sparse regression method for hyperspectral unmixing

Spatial resolution enhancement of hyperspectral images based on redundant dictionaries

Parallel optimization of hyperspectral unmixing based on sparsity constrained nonnegative matrix factorization

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Resources

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A novel l _1/2 sparse regression method for hyperspectral unmixing

A novel l _1/2 sparse regression method for hyperspectral unmixing