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Scaled gradient-based algorithms for supervised hyperspectral image unmixing

Two scaled gradient iterative methods are proposed for estimating the abundances of the linear mixing model. The first method is obtained by including a normalization step in the scaled gradient method. The second method inspired by the fully constrained least squares algorithm includes the sum-to-one constraint in the observation model with an appropriate weighting parameter. The proposed algorithms are efficient alternative to the very popular Fully Constrained Least Square (FCLS) algorithm. One of the main advantages of FCLS is its computational cost since few iterations are required to ensure convergence to a local minimum of the least-squares criterion. However, the convergence of this algorithm to a global minimum of the LS criterion is not guarantied which is its main drawback.

Convergence of the SGM algorithms is illustrated in Fig. 1.
Convergence of SGM
Fig. 1. Normalized SGM estimates of the abundances versus the iteration number k for SNR = 15dB.

The abundance estimation procedure and the main results are detailed in a paper presented at the IEEE Statistical Signal Processing Workshop in 2009.

The corresponding Matlab codes are available below.

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