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Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds

This repository is for LISTA networks with weight coupling and/or support selection structures introduced in the following paper:

Xiaohan Chen*, Jialin Liu*, Zhangyang Wang and Wotao Yin "Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds", accepted as spotlight oral at NIPS 2018. The preprint version is here.

*: These authors contributed equally and are listed alphabetically.

The code is tested in Linux environment (Tensorflow: 1.10.0, CUDA9.0) with Titan 1080Ti GPU.

Introduction

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the power of neural networks. In this work, we study unfolded ISTA (Iterative Shrinkage Thresholding Algorithm) for sparse signal recovery. We introduce a weight structure that is necessary for asymptotic convergence to the true sparse signal. With this structure, unfolded ISTA can attain a linear convergence, which is better than the sublinear convergence of ISTA/FISTA in general cases. Furthermore, we propose to incorporate thresholding in the network to perform support selection, which is easy to implement and able to boost the convergence rate both theoretically and empirically. Extensive simulations, including sparse vector recovery and a compressive sensing experiment on real image data, corroborate our theoretical results and demonstrate their practical usefulness.

Citation

If you find our code helpful in your resarch or work, please cite our paper.

@article{chen2018theoretical,
  title={Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds},
  author={Chen, Xiaohan and Liu, Jialin and Wang, Zhangyang and Yin, Wotao},
  journal={arXiv preprint arXiv:1808.10038},
  year={2018}
}

About

[NeurIPS'18, Spotlight oral] "Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds", by Xiaohan Chen*, Jialin Liu*, Zhangyang Wang and Wotao Yin.

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