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Blind spectral unmixing based on sparse nonnegative matrix factorization.

Zuyuan Yang1, Guoxu Zhou, Shengli Xie

  • 1School of Electronic and Information Engineering, South China University of Technology, Guangzhou, 510641, China.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|October 5, 2010
PubMed
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This study introduces a novel S-measure constraint for Nonnegative Matrix Factorization (NMF) to improve spectral unmixing (SU). The NMF-SMC algorithm enhances abundance estimation without prior knowledge of sparsity or dimension reduction.

Area of Science:

  • Remote Sensing
  • Signal Processing
  • Data Analysis

Background:

  • Nonnegative Matrix Factorization (NMF) is a standard technique for blind spectral unmixing (SU).
  • Traditional sparsity constraints (L0/L1-norm) are ineffective for SU due to the sum-to-one abundance constraint.
  • Existing methods often require pure pixel assumptions or prior knowledge of sparsity levels.

Purpose of the Study:

  • To propose a novel S-measure for sparsity in SU that has physical significance.
  • To develop a gradient-based NMF algorithm (NMF-SMC) incorporating the S-measure constraint (SMC).
  • To address limitations of traditional NMF in spectral unmixing, particularly regarding abundance sparsity.

Main Methods:

  • A novel S-measure for signal vector sparseness is introduced.

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  • A gradient-based Nonnegative Matrix Factorization algorithm with S-measure constraint (NMF-SMC) is developed.
  • Simultaneous estimation of endmembers and abundances with adaptive learning rates is performed.

    • Main Results:

    • The proposed NMF-SMC algorithm effectively handles spectral unmixing without pure index assumptions.
    • It does not require prior knowledge of the exact abundance sparsity degree.
    • Experiments on synthetic and real-world hyperspectral data (AVIRIS, HYDICE) validate the method's effectiveness.

    Conclusions:

    • The S-measure constraint offers a physically meaningful approach to sparsity in spectral unmixing.
    • NMF-SMC provides a robust and effective solution for blind spectral unmixing.
    • The method avoids information loss from dimension reduction and simplifies prior assumptions.