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Manifold regularization for sparse unmixing of hyperspectral images

View Article: PubMed Central - PubMed

ABSTRACT

Background: Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression, ignore the intrinsic geometric structure in the hyperspectral data.

Results: In this paper, we propose a novel model, called manifold regularized collaborative sparse regression, by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model.

Conclusions: Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

No MeSH data available.


Evolution of the objective function (10) for SI-1 with  by using MCSUnADMM algorithm
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Fig3: Evolution of the objective function (10) for SI-1 with by using MCSUnADMM algorithm

Mentions: Table 2 reports the times of the MCSUnADMM, CLSUnSAL, TVSUnSAL, and SUnSAL algorithms for these two synthetic experiments with different SNRs when the stopping criterion (i.e., the maximum iteration number or the Frobenius norm of the pixel reconstruction errors, i.e. , less than ) is reached. As can been see from this table, the proposed MCSUnADMM algorithm converges faster than the other three algorithms to reach the minima of the objective function because of the use of the locally geometrical structure of the hyperspectral data introduced by the manifold regularization. Note that a proper and efficient regularization introduced to the model will benefit the descending of the objective function. However, it must be pointed out that the computational complexity of solving model (10) is a little higher than solving the models (6) and (8) in theory. Table 3 gives the computational times for the SI-1 and SI-2 experiments by all of the four algorithms when setting the maximum iteration number (to be 2000) as the stopping criterion. According to this table, we can see that the SUnSAL and CLSUnSAL algorithms need almost the same computational times, while the TVSUnSAL and the MCSUnADMM algorithms have almost the same computational times, which are higher than that of the SUnSAL and CLSUnSAL algorithms. This is consistent with the theoretical analysis of the complexity (Iordache et al. 2012, 2014a). In addition, Fig. 3 plots the evolution of the objective function (10) versus time in the SI-1 experiments with to illustrate the convergence of the proposed MCSUnADMM algorithm.Fig. 3


Manifold regularization for sparse unmixing of hyperspectral images
Evolution of the objective function (10) for SI-1 with  by using MCSUnADMM algorithm
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121117&req=5

Fig3: Evolution of the objective function (10) for SI-1 with by using MCSUnADMM algorithm
Mentions: Table 2 reports the times of the MCSUnADMM, CLSUnSAL, TVSUnSAL, and SUnSAL algorithms for these two synthetic experiments with different SNRs when the stopping criterion (i.e., the maximum iteration number or the Frobenius norm of the pixel reconstruction errors, i.e. , less than ) is reached. As can been see from this table, the proposed MCSUnADMM algorithm converges faster than the other three algorithms to reach the minima of the objective function because of the use of the locally geometrical structure of the hyperspectral data introduced by the manifold regularization. Note that a proper and efficient regularization introduced to the model will benefit the descending of the objective function. However, it must be pointed out that the computational complexity of solving model (10) is a little higher than solving the models (6) and (8) in theory. Table 3 gives the computational times for the SI-1 and SI-2 experiments by all of the four algorithms when setting the maximum iteration number (to be 2000) as the stopping criterion. According to this table, we can see that the SUnSAL and CLSUnSAL algorithms need almost the same computational times, while the TVSUnSAL and the MCSUnADMM algorithms have almost the same computational times, which are higher than that of the SUnSAL and CLSUnSAL algorithms. This is consistent with the theoretical analysis of the complexity (Iordache et al. 2012, 2014a). In addition, Fig. 3 plots the evolution of the objective function (10) versus time in the SI-1 experiments with to illustrate the convergence of the proposed MCSUnADMM algorithm.Fig. 3

View Article: PubMed Central - PubMed

ABSTRACT

Background: Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression, ignore the intrinsic geometric structure in the hyperspectral data.

Results: In this paper, we propose a novel model, called manifold regularized collaborative sparse regression, by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model.

Conclusions: Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

No MeSH data available.