# Learned ISTA with Error-based Thresholding for Adaptive Sparse Coding

arXiv: https://arxiv.org/abs/2112.10985 · HTML: https://mlsanity.com/paper/2112.10985/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Learning step sizes for unfolded sparse coding](https://mlsanity.com/paper/1905.11071/) (2019)
- [Maximal Sparsity with Deep Networks?](https://mlsanity.com/paper/1605.01636/) (2016)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)

## Built on by (most cited first, 2 of 2)

- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Tunable Domain Adaptation Using Unfolding](https://mlsanity.com/paper/2603.26931/) (2026)

## Abstract (arXiv)

Drawing on theoretical insights, we advocate an error-based thresholding (EBT) mechanism for learned ISTA (LISTA), which utilizes a function of the layer-wise reconstruction error to suggest a specific threshold for each observation in the shrinkage function of each layer. We show that the proposed EBT mechanism well disentangles the learnable parameters in the shrinkage functions from the reconstruction errors, endowing the obtained models with improved adaptivity to possible data variations. With rigorous analyses, we further show that the proposed EBT also leads to a faster convergence on the basis of LISTA or its variants, in addition to its higher adaptivity. Extensive experimental results confirm our theoretical analyses and verify the effectiveness of our methods.