We consider the robust principal component analysis (RPCA) problem where the observed data are decomposed to a low-rank component and a sparse component. Conventionally, the matrix rank in RPCA is often approximated using a nuclear norm. Recently, RPCA has been formulated using the nonconvex $$\ell _{\gamma }$$ ℓ γ -norm, which provides a closer approximation to the matrix rank than the traditional nuclear norm. However, the low-rank component generally has sparse property, especially in the transform domain. In this paper, a sparsity-based regularization term modeled with $$\ell _1$$ ℓ 1 -norm is introduced to the formulation. An iterative optimization algorithm is developed to solve the obtained optimization problem. Experiments using synthetic and real data are utilized to validate the performance of the proposed method.

中文翻译：

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使用非凸秩近似和稀疏正则化器的鲁棒 PCA

我们考虑稳健主成分分析 (RPCA) 问题，其中将观察到的数据分解为低秩成分和稀疏成分。通常，RPCA 中的矩阵秩通常使用核范数来近似。最近，RPCA 已经使用非凸 $$\ell _{\gamma }$$ ℓ γ -norm 来制定，与传统的核范数相比，它提供了更接近矩阵秩的近似值。然而，低秩分量通常具有稀疏特性，尤其是在变换域中。在本文中，一个基于稀疏性的正则化项被引入到公式中，该正则化项以 $$\ell _1$$ ℓ 1 -norm 为模型。开发了迭代优化算法来解决所获得的优化问题。使用合成数据和真实数据的实验被用来验证所提出方法的性能。