Sparse representation has been widely used in signal processing, pattern recognition and computer vision etc. Excellent achievements have been made in both theoretical researches and practical applications. However, there are two limitations on the application of classification. One is that sufficient training samples are required for each class, and the other is that samples should be uncorrupted. In order to alleviate above problems, a sparse and dense hybrid representation (SDR) framework has been proposed, where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific dictionary. SDR puts ℓ₁ constraint on the coefficients of class-specific dictionary. Nevertheless, it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary, which may lead to poor classification results. To overcome this disadvantage, an adaptive sparse and dense hybrid representation with non-convex optimization (ASDR-NO) is proposed in this paper. The trace norm is adopted in class-specific dictionary, which is different from general approaches. By doing so, the dictionary structure becomes adaptive and the representation ability of the dictionary will be improved. Meanwhile, a non-convex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization, which can be solved by iteratively reweighted nuclear norm (IRNN) algorithm. Extensive experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods.

中文翻译：

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非凸优化的自适应稀疏和密集混合表示

稀疏表示已广泛应用于信号处理，模式识别和计算机视觉等领域。在理论研究和实际应用中均取得了卓越的成就。但是，分类的应用存在两个限制。一个是每个班级都需要足够的训练样本，另一个是样本应该没有损坏。为了减轻上述问题，已经提出了稀疏和密集的混合表示（SDR）框架，其中训练字典被分解成特定于类别的字典和非特定于类别的字典。SDR放ℓ ₁特定类字典系数的约束。但是，它过分强调稀疏性，而忽略了特定于类的词典中的相关性信息，这可能导致较差的分类结果。为了克服这个缺点，本文提出了一种具有非凸优化的自适应稀疏和稠密混合表示（ASDR-NO）。跟踪规范在特定于类的字典中采用，这与常规方法不同。这样，词典结构变得自适应，并且词典的表示能力将得到提高。同时，在字典分解中使用非凸代理近似秩函数，以避免原始秩最小化的次优解，这可以通过迭代重新加权核范数（IRNN）算法来解决。