Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems

TL;DR

This paper introduces an adaptive regularization scheme within a variational framework for imaging problems, dynamically balancing data fidelity and regularization locally at each pixel to improve results.

Contribution

It proposes a novel adaptive regularization method integrated into the ADMM framework, enhancing robustness and effectiveness over static regularization in various imaging tasks.

Findings

Superior qualitative and quantitative results compared to constant regularization.

Robustness demonstrated across denoising, segmentation, and motion estimation.

Adaptive regularization effectively controls local image features.

Abstract

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are considered as optimal solutions of the energy functionals that mainly consist of data fidelity, regularization and a control parameter for their trade-off. We presents an algorithm to determine the relative weight between data fidelity and regularization based on the residual that measures how well the observation fits the model. Our adaptive regularization scheme is designed to locally control the regularization at each pixel based on the assumption that the diversity of the residual of a given imaging model spatially varies. The energy optimization is presented in the alternating direction method of multipliers (ADMM) framework where the adaptive regularization is iteratively applied along with mathematical analysis of the proposed algorithm. We demonstrate the robustness and effectiveness of our adaptive regularization through experimental results presenting that the qualitative and quantitative evaluation results of each imaging task are superior to the results with a constant regularization scheme. The desired properties, robustness and effectiveness, of the regularization parameter selection in a variational framework for imaging problems are achieved by merely replacing the static regularization parameter with our adaptive one.