New regularization method and iteratively reweighted algorithm for sparse vector recovery
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Motivated by the study of regularization for sparse problems, we propose a new regularization method for sparse vector recovery. We derive sufficient conditions on the well-posedness of the new regularization, and design an iterative algorithm, namely the iteratively reweighted algorithm (IR-algorithm), for efficiently computing the sparse solutions to the proposed regularization model. The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length. Finally, we present numerical examples to illustrate the features of the new regularization and algorithm.
Key wordsregularization method iteratively reweighted algorithm (IR-algorithm) sparse vector recovery
Chinese Library ClassificationO24
2010 Mathematics Subject Classification49K35 90C06
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Thanks to Prof.Mingjun LAI for many enlightening discussions with us on lq minimization, to Prof.Rong HUANG for his guidance during my post-doctoral research period, to Dr.Yangyang XU for his contributions to Theorem 3 and lone-term communication on sparse vector recovery with nonconvex models, and to Dr.Housen LI for his careful reading of the manuscript.
- DONG, J., XUE, Z. C., GUAN, J., HAN, Z. F., and WANG, W. W. Low rank matrix completion using truncated nuclear norm and sparse regularizer. Signal Processing: Image Communication, 68, 76–87 (2018)Google Scholar
- ENGL, H. W. and RAMLAU, R. Regularization of inverse problems. Encyclopedia of Applied and Computational Mathematics, Springer, Heidelberg (2015)Google Scholar
- ARJOUNE, Y., KAABOUCH, N., GHAZI, H. E., and TAMTAOUI, A. Compressive sensing: performance comparison of sparse recovery algorithms. 2017 IEEE 7th Annual Computing and Communication Workshop and Conference (CCWC), IEEE, Las Vegas (2017)Google Scholar
- FAZEL, M. Matrix Rank Minimization with Applications, Ph.D. dissertation, Stanford University, California (2002)Google Scholar
- NEEDELL, D. Noisy signal recovery via iterative reweighted L 1-minimization. 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, IEEE, Pacific Grove (2009)Google Scholar
- XU, W. Y., KHAJEHNEJAD, M. A., AVESTIMEHR, S., and HASSIBI, B. Breaking through the thresholds: an analysis for iterative reweighted l 1 minimization via the Grassmann angle framework. ICASSP 2010: IEEE International Conference on Acoustics, Speech and Signal, IEEE, Texas (2009)Google Scholar
- BERTSEKAS, D. P., NEDIĆC, A., and OZDAGLAR, A. E. Convex Analysis and Optimization, Athena Scietific and Tsinghua University Press, Beijing (2006)Google Scholar