Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our method attains linear convergence. In practice, extensive empirical results verify the advantages of our method.

翻译：最近,关于所学的迭代递减临界值算法(LISTA)的研究引起了越来越多的注意,许多实验以及一些理论证明LIPA在解决稀有的编码问题方面的效率很高,然而,现有的ListA方法都是序列连接。为了解决这一问题,我们提议建立一个具有剩余结构和理论保障的新的基于超高级的ListA(ELISTA),特别是我们的算法也可以在某种程度上为Res-Net提供解释性。从理论的角度来看,我们证明我们的方法实现了线性趋同。在实践中,广泛的实证结果可以验证我们的方法的优点。