Abstract
We study the computational properties of solving a constrained L 1-L 2 minimization via a difference of convex algorithm (DCA), which was proposed in our previous work [13,19] to recover sparse signals from a under-determined linear system. We prove that the DCA converges to a stationary point of the nonconvex L 1-L 2 model. We clarify the relationship of DCA to a convex method, Bregman iteration [20] for solving a constrained L 1 minimization. Through experiments, we discover that both L 1 and L 1-L 2 obtain better recovery results from more coherent matrices, which appears unknown in theoretical analysis of exact sparse recovery. In addition, numerical studies motivate us to consider a weighted difference model L 1-αL 2 (α > 1) to deal with ill-conditioned matrices when L 1-L 2 fails to obtain a good solution.
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Lou, Y., Osher, S., Xin, J. (2015). Computational Aspects of Constrained L 1-L 2 Minimization for Compressive Sensing. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_15
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DOI: https://doi.org/10.1007/978-3-319-18161-5_15
Publisher Name: Springer, Cham
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