+ Site Statistics
+ Search Articles
+ Subscribe to Site Feeds
EurekaMag Most Shared ContentMost Shared
EurekaMag PDF Full Text ContentPDF Full Text
+ PDF Full Text
Request PDF Full TextRequest PDF Full Text
+ Follow Us
Follow on FacebookFollow on Facebook
Follow on TwitterFollow on Twitter
Follow on LinkedInFollow on LinkedIn

+ Translate

Matrix Completion Based on Non-convex Low Rank Approximation

Matrix Completion Based on Non-convex Low Rank Approximation

IEEE Transactions on Image Processing 2018

Without any prior structure information, Nuclear Norm Minimization (NNM), a convex relaxation for Rank Minimization (RM), is a widespread tool for matrix completion and relevant low rank approximation problems. Nevertheless, the result derivated by NNM generally deviates the solution we desired, because NNM ignores the difference between different singular values. In this paper, we present a non-convex regularizer and utilize it to construct two matrix completion models. In order to solve the constructed models efficiently, we develop an efficient optimization method with convergence guarantee, which can achieve faster convergence speed compared to conventional approaches. Particularly, we show that the proposed regularizer as well as optimization method are suitable for other RM problems, such as subspace clustering based on low rank representation. Extensive experimental results on real images demonstrate that the constructed models provide significant advantages over several state-of-the-art matrix completion algorithms. In addition, we implement numerous experiments to investigate the convergence speed of developed optimization method.

(PDF emailed within 0-6 h: $19.90)

Accession: 066026169

Download citation: RISBibTeXText

PMID: 30571624

DOI: 10.1109/TIP.2018.2886712

Related references

A non-convex tensor rank approximation for tensor completion. Applied Mathematical Modelling 48: 410-422, 2017

Compressive Sampling Photoacoustic Microscope System based on Low Rank Matrix Completion. Biomedical Signal Processing and Control 26: 58-63, 2016

Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion. Magnetic Resonance in Medicine 72(4): 959-970, 2015

Non-Convex Low-Rank Approximation for Image Denoising and Deblurring. Ieice Transactions on Information and Systems E99.D(5): 1364-1374, 2016

Rank-One Matrix Completion With Automatic Rank Estimation via L1-Norm Regularization. IEEE Transactions on Neural Networks and Learning Systems: -, 2018

Rank adaptive atomic decomposition for low-rank matrix completion and its application on image recovery. Neurocomputing 145: 374-380, 2014

Fast raypath separation based on low-rank matrix approximation in a shallow-water waveguide. Journal of the Acoustical Society of America 143(4): El271-El271, 2018

Glass Reflection Removal Using Co-Saliency-Based Image Alignment and Low-Rank Matrix Completion in Gradient Domain. IEEE Transactions on Image Processing 27(10): 4873-4888, 2018

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit. Sensors 18(12): -, 2018

An efficient matrix bi-factorization alternative optimization method for low-rank matrix recovery and completion. Neural Networks 48: 8-18, 2014

Correlated spatio-temporal data collection in wireless sensor networks based on low rank matrix approximation and optimized node sampling. Sensors 14(12): 23137-23158, 2014

Convex Coupled Matrix and Tensor Completion. Neural Computation: 1-33, 2018

A Novel Riemannian Metric Based on Riemannian Structure and Scaling Information for Fixed Low-Rank Matrix Completion. IEEE Transactions on Cybernetics (): -, 2016

Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation. IEEE Transactions on Neural Networks and Learning Systems 30(2): 474-485, 2018

The approximation of one matrix by another of lower rank. Psychometrika 1(3): 211-218, 1936