The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm
Open accessAbstract
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm-based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to use a family of nonconvex surrogates of L0-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then, we propose to solve the problem by an iteratively re-weighted nuclear norm (IRNN) algorithm. IRNN iteratively solves a weighted singular value thresholding problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that the IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low rank matrix recovery compared with the state-of-the-art convex algorithms.
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Normalized cuts and image segmentation
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
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Tensor Decompositions and Applications
Kolda, T. G., & Bader, B. W. (2009) · SIAM Review · doi:10.1137/07070111x · Cited by 10,301
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Robust Face Recognition via Sparse Representation
Wright, J., Yang, A. Y., Ganesh, A., Sastry, S. S., & Ma, Y. (2009) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2008.79 · Cited by 9,388
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Robust principal component analysis?
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A Singular Value Thresholding Algorithm for Matrix Completion
Cai, J.-F., Candès, E. J., & Shen, Z. (2010) · SIAM Journal on Optimization · doi:10.1137/080738970 · Cited by 5,809
Image Super-Resolution Via Sparse Representation
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Cited by
Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm
Zhang, L., & Peng, Z. (2019) · Remote Sensing · doi:10.3390/rs11040382 · Cited by 759
Dai, Y., & Wu, Y. (2017) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2017.2700023 · Cited by 615
Metadata
- Authors
- Lu, C., Tang, J., Yan, S., & Lin, Z.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2016-02
- Volume
- 25
- Issue
- 2
- Pages
- 829-839
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W1860736741
- Cited by
- 307
- References
- 37
- FWCI
- 13.41
- Type
- journal article
- Language
- en
- Open access
- green
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- Lu, C., Tang, J., Yan, S., & Lin, Z. (2016). Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm. IEEE Transactions on Image Processing. https://doi.org/10.1109/tip.2015.2511584
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