Adaptive Regularization of Some Inverse Problems in Image Analysis

TL;DR

This paper introduces an adaptive regularization scheme with Huber loss for inverse image analysis problems, dynamically balancing data fidelity and regularization during optimization to improve results.

Contribution

It proposes a novel adaptive regularization method using Huber loss and an efficient ADMM algorithm for various image analysis tasks.

Findings

Effective in segmentation, motion estimation, and denoising

Adaptive scheme improves convergence and results

Validated on synthetic and real images

Abstract

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.