Sparse and low-rank matrices recovery from incomplete and noisy measurement

作者：Yang Zhenzhen; Yang Zhen

来源：Journal of Computational Information Systems, 2013, 9(19): 7703-7710.

DOI：10.12733/jcis6857

• Alternating direction method of multipliers
• Low-rank matrices
• Matrix recovery
• Principle component analysis
• Sparse matrices

The problem of recovering sparse and low-rank matrices from a given matrix captures many applications. However, this recovery problem is NP-hard and thus not tractable in general. Recently, it has been shown that this NP-hard problem can be well approached via heuristically solving a convex relaxation problem where the ?1-norm and the nuclear norm are used to induce sparse and low-rank structures, respectively. To capture more applications, this paper studies the recovery problem in a more general setting: the matrix is acquired by compressed measurement and the measurement is corrupted by Gaussian noise. The separable structure of the new model enables us to solve the involved subproblems more efficiently by splitting the multipliers function. Hence, an implementable numerical algorithm which called accelerated alternating direction method of multipliers (AADMM) is proposed to solve the novel model. Our experimental results show that AADMM is surprisingly efficient for solving the new recovery model.

• 出版日期2013
• 单位南京邮电大学