# Designing recurrent neural networks by unfolding an l1-l1 minimization algorithm

## TL;DR

This paper introduces a novel RNN architecture derived from unfolding an l1-l1 minimization algorithm, specifically designed for sequential signal reconstruction, leveraging sparsity in signals and their differences.

## Contribution

The paper presents a new RNN model based on unfolding a proximal gradient method for l1-l1 minimization, tailored for sparse sequential signal reconstruction.

## Key findings

- Outperforms state-of-the-art RNN models in video frame reconstruction from compressive measurements.
- Demonstrates the effectiveness of unfolding optimization algorithms into neural network architectures.
- Leverages sparsity in signals and their differences for improved reconstruction accuracy.

## Abstract

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and that the difference between consecutive signal representations is also sparse. We evaluate the proposed model in the task of reconstructing video frames from compressive measurements and show that it outperforms several state-of-the-art RNN models.