Jun Zhang

Publications (3)5.99 Total impact

• Article: Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization

  Zuyuan Yang, Guoxu Zhou, Shengli Xie, Shuxue Ding, Jun-Mei Yang, Jun Zhang
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  ABSTRACT: Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.
  IEEE Transactions on Image Processing 05/2011; · 3.04 Impact Factor
• Article: Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization.

  Zuyuan Yang, Guoxu Zhou, Shengli Xie, Shuxue Ding, Jun-Mei Yang, Jun Zhang
  IEEE Transactions on Image Processing. 01/2011; 20:1112-1125.
• Article: Nonorthogonal Approximate Joint Diagonalization With Well-Conditioned Diagonalizers

  Guoxu Zhou, Shengli Xie, Zuyuan Yang, Jun Zhang
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  ABSTRACT: To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.
  IEEE Transactions on Neural Networks 12/2009; · 2.95 Impact Factor