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Deep unfolding methods---for example, the learned iterative shrinkagethresholding algorithm (LISTA)---design deep neural networks as learnedvariations of optimization methods. These networks have been shown to achievefaster convergence and higher accuracy than the original optimization methods.In this line of research, this paper develops a novel deep recurrent neuralnetwork (coined reweighted-RNN) by the unfolding of a reweighted$\ell_1$-$\ell_1$ minimization algorithm and applies it to the task ofsequential signal reconstruction. To the best of our knowledge, this is thefirst deep unfolding method that explores reweighted minimization. Due to theunderlying reweighted minimization model, our RNN has a differentsoft-thresholding function (alias, different activation functions) for eachhidden unit in each layer. Furthermore, it has higher network expressivity thanexisting deep unfolding RNN models due to the over-parameterizing weights.Importantly, we establish theoretical generalization error bounds for theproposed reweighted-RNN model by means of Rademacher complexity. The boundsreveal that the parameterization of the proposed reweighted-RNN ensures goodgeneralization. We apply the proposed reweighted-RNN to the problem of videoframe reconstruction from low-dimensional measurements, that is, sequentialframe reconstruction. The experimental results on the moving MNIST datasetdemonstrate that the proposed deep reweighted-RNN significantly outperformsexisting RNN models.

Interpretable Deep Recurrent Neural Networks via Unfolding Reweighted  $\ell_1$-$\ell_1$ Minimization: Architecture Design and Generalization  Analysis