Recently, L1-norm-based discriminant subspace learning has attracted much more attention in dimensionality reduction and machine learning. However, most existing approaches solve the column vectors of the optimal projection matrix one by one with greedy strategy. Thus, the obtained optimal projection matrix does not necessarily best optimize the corresponding trace ratio objective function, which is the essential criterion function for general supervised dimensionality reduction. In this paper, we propose a non-greedy iterative algorithm to solve the trace ratio form of L1-norm-based linear discriminant analysis. We analyze the convergence of our proposed algorithm in detail. Extensive experiments on five popular image databases illustrate that our proposed algorithm can maximize the objective function value and is superior to most existing L1-LDA algorithms.

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A new speckle suppression algorithm is proposed for high-resolution synthetic aperture radar (SAR) images. It is based on the nonlocal means (NLM) filter and the modified Aubert and Aujol (AA) model. This method takes the nonlocal Dirichlet function as a linear regularization item, which constructs the weight by measuring the similarity of images. Then, a new despeckling model is introduced by combining the regularization item and the data item of the AA model, and an iterative algorithm is proposed to solve the new model. The experiments show that, compared with the AA model, the proposed model has more effective performance in suppressing speckle; namely, ENL and DCV measures are 21.75% and 4.5% higher, respectively, than for NLM. Moreover, it also has better performance in keeping the edge information.