Learning spatially varying regularisation parameters of low regularity for image reconstruction

2026-08-25

AI Summary

本文探讨了通过学习空间变化的正则化参数来改善图像重建中边缘和细节保留的问题，特别是结合深度神经网络的方法。

Abstract

In this chapter, we review and discuss the regularity properties of spatially adaptive regularisation weight functions used in variational image reconstruction. Incorporating such weights into classical model-based regularisers, such as Total Variation (TV) and Total Generalised Variation (TGV), allows the regularisation strength to vary across the image and adapt to local image content. When appropriately estimated, these weights can thus significantly improve edge and detail preservation in the reconstructions. We review the existing theoretical literature on this topic for different regularity classes, including constant, continuous, and piecewise constant functions. Our discussion is motivated by recent work on hybrid image reconstruction methods that combine model-based regularisation with deep neural networks to learn highly adaptive regularisation weights. In particular, we discuss how the structural properties of these weights influence the reconstruction from both theoretical and practical perspectives. Through representative examples in image denoising and magnetic resonance imaging (MRI) reconstruction, we demonstrate that the learned weights are often of low regularity and can adapt not only to the image structure but also to the specific noise realisation. We conclude by highlighting several directions for future research on this topic.

Problem

• spatially varying regularisation
• image reconstruction
• local image content
• noise realisation

Innovation

• spatially adaptive regularisation
• low regularity weights
• hybrid image reconstruction
• deep neural networks
• image denoising