  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.
