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Recently, the paradigm of unfolding iterative algorithms into finite-lengthfeed-forward neural networks has achieved a great success in the area of sparserecovery. Benefit from available training data, the learned networks haveachieved state-of-the-art performance in respect of both speed and accuracy.However, the structure behind sparsity, imposing constraint on the support ofsparse signals, is often an essential prior knowledge but seldom considered inthe existing networks. In this paper, we aim at bridging this gap.Specifically, exploiting the iterative reweighted $\ell_1$ minimization (IRL1)algorithm, we propose to learn the cluster structured sparsity (CSS) byrewegihting adaptively. In particular, we first unfold the Reweighted IterativeShrinkage Algorithm (RwISTA) into an end-to-end trainable deep architecturetermed as RW-LISTA. Then instead of the element-wise reweighting, the globaland local reweighting manner are proposed for the cluster structured sparselearning. Numerical experiments further show the superiority of our algorithmagainst both classical algorithms and learning-based networks on differenttasks.

Learning Cluster Structured Sparsity by Reweighting