This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively preserving the most significant contributions to the signal while promoting sparsity. We present models for both noise-free and noisy scenarios, and rigorously prove the existence of solutions for each case. To solve these models, we adopt a linearization approach inspired by the difference of convex functions algorithm. Our experimental results demonstrate the superiority of our method over state-of-the-art approaches in sparse signal recovery across various circumstances, particularly in support detection.

翻译：本文提出了一种基于有序L1/L2最小化的稀疏信号恢复新方法。该方法为绝对值较小的索引分配更高权重，而绝对值较大的索引分配较低权重，从而在促进稀疏性的同时有效保留信号中最重要的贡献。我们针对无噪声和有噪声场景分别建立了模型，并严格证明了每种情况下解的存在性。为求解这些模型，我们采用了一种受凸函数差分算法启发的线性化方法。实验结果表明，在多种情境下，尤其在支撑检测方面，我们的方法优于当前最先进的稀疏信号恢复技术。