In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established for both constrained and unconstrained models. The practical algorithms via both the iteratively reweighted $\ell_1$ and the difference of convex functions algorithms are presented. Numerical experiments are conducted to illustrate the improvement provided by the proposed approach in various scenarios. Its practical application in magnetic resonance imaging (MRI) reconstruction is studied as well.

翻译：在本文中,我们根据普遍误差功能提出了一个新的稀有回收方法。引入的处罚功能涉及形状和比例参数,使其非常灵活。理论分析的结果是:空空间财产、球形部分属性和有限的可视性系数,对受限制和不受限制的模型都是如此。介绍了通过迭代再加权$@ell_1美元的实际算法和convex函数算法的差异。进行了数值实验,以说明各种情景中拟议方法所提供的改进。还研究了其在磁共振成像(MRI)重建中的实际应用。