Convex Relaxation Algorithm for a Structured Simultaneous Low-Rank and Sparse Recovery Problem

2015 ◽  
Vol 3 (3) ◽  
pp. 363-379 ◽  
Author(s):  
Le Han ◽  
Xiao-Lan Liu
Author(s):  
Xuan Vinh Doan ◽  
Stephen Vavasis

AbstractLow-rank matrix recovery problem is difficult due to its non-convex properties and it is usually solved using convex relaxation approaches. In this paper, we formulate the non-convex low-rank matrix recovery problem exactly using novel Ky Fan 2-k-norm-based models. A general difference of convex functions algorithm (DCA) is developed to solve these models. A proximal point algorithm (PPA) framework is proposed to solve sub-problems within the DCA, which allows us to handle large instances. Numerical results show that the proposed models achieve high recoverability rates as compared to the truncated nuclear norm method and the alternating bilinear optimization approach. The results also demonstrate that the proposed DCA with the PPA framework is efficient in handling larger instances.


2020 ◽  
Vol 532 ◽  
pp. 170-189
Author(s):  
Yu-Bang Zheng ◽  
Ting-Zhu Huang ◽  
Xi-Le Zhao ◽  
Tai-Xiang Jiang ◽  
Teng-Yu Ji ◽  
...  

2019 ◽  
Vol 5 (5) ◽  
pp. 51 ◽  
Author(s):  
Marco Donald Migliore ◽  
Fulvio Schettino ◽  
Daniele Pinchera ◽  
Mario Lucido ◽  
Gaetano Panariello

A method to filter out the contribution of interference sources in array diagnosis is proposed. The interference-affected near field measured on a surface is treated as a (complex-data) image. This allows to use some modern image processing algorithms. In particular, two strategies widely used in image processing are applied. The first one is the reduction of the amount of information by acquiring only the innovation part of an image, as currently happens in video processing. More specifically, a differential measurement technique is used to formulate the estimation of the array excitations as a sparse recovery problem. The second technique has been recently proposed in video denoising, where the image is split into a low-rank and high-rank part. In particular, in this paper the interference field is filtered out using sparsity as discriminant adopting a mixed minimum ℓ 1 norm and trace norm minimization algorithm. The methodology can be applied to both near and far field measurement ranges. It could be an alternative to the systematic use of anechoic chambers for antenna array testing.


2016 ◽  
Vol 33 (01) ◽  
pp. 1650003
Author(s):  
Li Cui ◽  
Lu Liu ◽  
Di-Rong Chen ◽  
Jian-Feng Xie

In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix [Formula: see text] can be exactly recovered from the linear measurement [Formula: see text] via some Schatten [Formula: see text] norm minimization. Moreover it is shown that the explicit bound on exponent [Formula: see text] in the Schatten [Formula: see text] norm minimization can be exactly extracted.


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