Accelerated Schemes for the $L_1/L_2$ Minimization
Chao Wang, Ming Yan, Yaghoub Rahimi, Yifei Lou
Abstract
In this paper, we consider the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> minimization for sparse recovery and study its relationship with the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -αL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 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 the two adaptive schemes, we discuss their connection to existing approaches and analyze their convergence. The experimental results demonstrate that the proposed algorithms are comparable to 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> recovery under various combinations of sparsity, coherence, and dynamic ranges, which calls for theoretical justification in the future.