Multiresolution Adaptive Block-Coordinate Forward-Backward for Image Reconstruction

TL;DR

This paper introduces an adaptive multiresolution block coordinate Forward-Backward algorithm for image restoration that dynamically balances updates across scales based on local image features, improving efficiency across different blur and noise levels.

Contribution

It proposes a novel adaptive multiresolution strategy that automatically adjusts scale updates in image reconstruction, overcoming limitations of fixed schemes in varying degradation conditions.

Findings

Automatically adapts to different blur and noise levels

Balances coarse and fine updates based on local image features

Improves convergence efficiency in image restoration

Abstract

Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose effectiveness in moderate-blur or noise-dominated regimes. In this work, we propose an adaptive multiresolution block coordinate Forward-Backward algorithm for image restoration. Multiresolution block selection is driven by the local magnitude of the proximal update via a stochastic non-smooth Gauss-Southwell rule applied to the wavelet decomposition of the image. This adaptive selection strategy dynamically balances updates across scales, emphasizing coarse or fine blocks according to the degradation regime. As a result, the proposed method automatically adapts to varying blur and noise levels without relying on a predefined hierarchical update scheme.