In this paper, we study ℓ 1 − αℓ 2 (0 < α ⩽ 1) minimization methods for signal and image reconstruction with impulsive noise removal. The data fitting term is based on ℓ 1 fidelity between the reconstruction output and the observational data, and the regularization term is based on ℓ 1 − αℓ 2 nonconvex minimization of the reconstruction output or its total variation. Theoretically, we show that under the generalized restricted isometry property that the underlying signal or image can be recovered exactly. Numerical algorithms are also developed to solve the resulting optimization problems. Experimental results have shown that the proposed models and algorithms can recover signal or images under impulsive noise degradation, and their performance is better than that of the existing methods.

中文翻译：

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− 1 −αℓ2最小化方法，用于去除脉冲噪声的信号和图像

在本文中，我们研究了用于去除脉冲噪声的信号和图像重建的ℓ1-αℓ2（0 <α⩽1）最小化方法。数据拟合项基于重建输出和观测数据之间的ℓ1保真度，正则化项基于重建输出或其总变化的ℓ1-αℓ2非凸最小化。从理论上讲，我们证明了在广义受限等距特性下，可以准确地恢复基础信号或图像。还开发了数值算法来解决由此产生的优化问题。实验结果表明，所提出的模型和算法能够在脉冲噪声降级的情况下恢复信号或图像，其性能优于现有方法。