In this article, we propose a new projection-type algorithm for solving ${\ell }_1-{\ell }_2$ minimization. Compared with the proposed method by Feng and Wang (2018), a new stepsize rule is introduced which has allowed the algorithms to work without any prior information about operator norms. Under suitable conditions, the convergence and linear convergence rate of the designed algorithm are established. Several examples on signal processing and image restoration are given to illustrate the effectiveness and competitiveness of our algorithm.

中文翻译：

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一种线性收敛算法，无需先验算子范数，用于求解 ℓ1−ℓ2 最小化

在本文中，我们提出了一种新的投影型算法来解决 ${\ell }_1-{\ell }_2$最小化。与 Feng 和 Wang (2018) 提出的方法相比，引入了一种新的步长规则，该规则允许算法在没有任何关于算子规范的先验信息的情况下工作。在合适的条件下，建立了所设计算法的收敛性和线性收敛速度。给出了几个信号处理和图像恢复的例子来说明我们算法的有效性和竞争力。