Abstract
Recently, He et al. proposed a modified Peaceman–Rachford splitting method (MPRSM) for separable convex programming, which includes compressive sensing (CS) as a special case. In this paper, we further study MPRSM for CS, and regularize its first subproblem by the proximal regularization. Thus the computational load of the subproblem is substantially alleviated. That is, it is easy enough to have a closed-form solution for CS. Convergence of the new method can be guaranteed under the same assumptions as MPRSM. Finally, numerical results, including comparisons with MPPSM are reported to demonstrate the efficiency of the new method.
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Acknowledgments
The authors gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers. This work was supported by the Foundation of Zaozhuang University Grants No. 2014YB03, Shandong Province Statistical Research Project No. 20143038, and the domestic visiting scholar project funding of Shandong Province outstanding young teachers in higher schools.
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Sun, M., Liu, J. A proximal Peaceman–Rachford splitting method for compressive sensing. J. Appl. Math. Comput. 50, 349–363 (2016). https://doi.org/10.1007/s12190-015-0874-x
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DOI: https://doi.org/10.1007/s12190-015-0874-x