Accelerated Schemes for the $L_1/L_2$ Minimization

Abstract

In this paper, we consider the $L_1/L_2$ minimization for sparse recovery and study its relationship with the $L_1$-$\alpha L_2$ model. Based on this relationship, we propose three numerical algorithms to minimize this ratio model, two of which work as adaptive schemes and greatly reduce the computation time. Focusing on two adaptive schemes, we discuss their connection to existing approaches and analyze their convergence. The experimental results demonstrate the proposed approaches are comparable to the state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. Lastly, we reveal some empirical evidence on the exact $L_1$ recovery under various combinations of sparsity, coherence, and dynamic ranges, which calls for theoretical justification in the future.

arXiv comment10 pages

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Cited by in corpus (4)

• A Novel Regularization Based on the Error Function for Sparse Recovery
• Minimizing L1 over L2 norms on the gradient
• Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum
• Analysis of The Ratio of ${\ell }_1$ and ${\ell }_2$ Norms in Compressed Sensing