Learned Interpretable Residual Extragradient ISTA for Sparse Coding

2021/06/22 by Lin Kong, Kong, Lin, Wei Sun +7
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2106.11970

openalex publication_date 2021/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our method attains linear convergence. In practice, extensive empirical results verify the advantages of our method.

Citations

• Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures
• Least angle regression
• From Bayesian Sparsity to Gated Recurrent Nets
• Learned D-AMP: Principled Neural Network based Compressive Image\n Recovery
• Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds
• Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation
• Deep Network Classification by Scattering and Homotopy Dictionary Learning

Related

• Learned ISTA with Error-based Thresholding for Adaptive Sparse Coding
• Learning step sizes for unfolded sparse coding
• Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds
• Hyperparameter Tuning is All You Need for LISTA
• Learned Greedy Method (LGM): A Novel Neural Architecture for Sparse\n Coding and Beyond