Matrix Recipes for Hard Thresholding Methods

作者: Anastasios Kyrillidis , Volkan Cevher

DOI: 10.1007/S10851-013-0434-7

关键词:

摘要: In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class hard thresholding methods. We provide strategies on how to up these via basic ingredients different configurations achieve complexity vs. accuracy tradeoffs. Moreover, study acceleration schemes memory-based techniques randomized, ∈-approximate matrix projections decrease computational costs in process. For most configurations, theoretical analysis that guarantees convergence under mild problem conditions. Simulation results demonstrate notable performance improvements as compared state-of-the-art both terms reconstruction complexity.

参考文章(52)
Amir Beck, Marc Teboulle, A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems Fixed-point algorithms for inverse problems in science and engineering, 2011, ISBN 978-1-4419-9568-1, págs. 33-48. pp. 33- 48 ,(2011) , 10.1007/978-1-4419-9569-8_3
Zhouchen Lin, Arvind Ganesh, John Wright, Leqin Wu, Minming Chen, Yi Ma, None, Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix Coordinated Science Laboratory, University of Illinois at Urbana-Champaign. ,(2009)
Inderjit S. Dhillon, Prateek Jain, Raghu Meka, Guaranteed Rank Minimization via Singular Value Projection neural information processing systems. ,vol. 23, pp. 937- 945 ,(2010)
Yi-Kai Liu, Universal low-rank matrix recovery from Pauli measurements arXiv: Quantum Physics. ,(2011)
Oleg Kuybeda, Gabriel A. Frank, Alberto Bartesaghi, Mario Borgnia, Sriram Subramaniam, Guillermo Sapiro, A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography Journal of Structural Biology. ,vol. 181, pp. 116- 127 ,(2013) , 10.1016/J.JSB.2012.10.010
Laura Balzano, John C. S. Lui, Jun He, Online Robust Subspace Tracking from Partial Information arXiv: Information Theory. ,(2011)
Petros Drineas, Ravi Kannan, Michael W. Mahoney, Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix SIAM Journal on Computing. ,vol. 36, pp. 158- 183 ,(2006) , 10.1137/S0097539704442696
Xiaoxiao Shi, Philip S. Yu, Limitations of matrix completion via trace norm minimization ACM SIGKDD Explorations Newsletter. ,vol. 12, pp. 16- 20 ,(2011) , 10.1145/1964897.1964902
Anastasios Kyrillidis, Volkan Cevher, Combinatorial selection and least absolute shrinkage via the Clash algorithm international symposium on information theory. pp. 2216- 2220 ,(2012) , 10.1109/ISIT.2012.6283847