# Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation

arXiv: https://arxiv.org/abs/2507.02084 · HTML: https://mlsanity.com/paper/2507.02084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 2 Jul 2025.

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

- [Between hard and soft thresholding: optimal iterative thresholding algorithms](https://mlsanity.com/paper/1804.08841/) (2018)
- [Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling](https://mlsanity.com/paper/2002.11546/) (2020)
- [Local Linear Convergence of ISTA and FISTA on the LASSO Problem](https://mlsanity.com/paper/1501.02888/) (2015)
- [Gradient descent with nonconvex constraints: local concavity determines convergence](https://mlsanity.com/paper/1703.07755/) (2017)
- [Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing](https://mlsanity.com/paper/1408.6890/) (2014)

## Abstract (arXiv)

The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter λ. Despite that the adaptive ISTA is a successful practical algorithm, few theoretical results exist. In this paper, we present the theoretical analysis on the adaptive ISTA with the thresholding strategy of estimating noise level by median absolute deviation. We show properties of the fixed points of the algorithm, including scale equivariance, non-uniqueness, and local stability, prove the local linear convergence guarantee, and show its global convergence behavior.