# Adaptive Regularization of Some Inverse Problems in Image Analysis

arXiv: https://arxiv.org/abs/1705.03350 · HTML: https://mlsanity.com/paper/1705.03350/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2017.

## Built on by (most cited first, 4 of 4)

- [An Adaptive Framework for Learning Unsupervised Depth Completion](https://mlsanity.com/paper/2106.03010/) (2021)
- [Monitored Distillation for Positive Congruent Depth Completion](https://mlsanity.com/paper/2203.16034/) (2022)
- [Heteroscedastic Uncertainty Estimation Framework for Unsupervised Registration](https://mlsanity.com/paper/2312.00836/) (2023)
- [Adaptive Correspondence Scoring for Unsupervised Medical Image Registration](https://mlsanity.com/paper/2312.00837/) (2023)

## Abstract (arXiv)

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.