  Recently, the paradigm of unfolding iterative algorithms into finite-length
feed-forward neural networks has achieved a great success in the area of sparse
recovery. Benefit from available training data, the learned networks have
achieved state-of-the-art performance in respect of both speed and accuracy.
However, the structure behind sparsity, imposing constraint on the support of
sparse signals, is often an essential prior knowledge but seldom considered in
the 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) by
rewegihting adaptively. In particular, we first unfold the Reweighted Iterative
Shrinkage Algorithm (RwISTA) into an end-to-end trainable deep architecture
termed as RW-LISTA. Then instead of the element-wise reweighting, the global
and local reweighting manner are proposed for the cluster structured sparse
learning. Numerical experiments further show the superiority of our algorithm
against both classical algorithms and learning-based networks on different
tasks.
