Deep unrolling for learning optimal spatially varying regularisation parameters for Total Generalised Variation

TL;DR

This paper introduces a deep unrolling framework that learns spatially varying TGV regularisation parameters for inverse imaging problems, leading to improved image reconstruction quality in denoising and MRI tasks.

Contribution

It extends deep unrolling to TGV regularisation, jointly training CNNs with unrolled algorithms to adaptively learn spatially varying parameters for better image reconstruction.

Findings

Significant improvements in image quality over scalar TGV parameters.

Learned parameter maps show structured patterns near edges.

Method outperforms unsupervised spatially varying parameter approaches.

Abstract

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional neural network (CNN) inferring the two spatially varying TGV parameters with an unrolled algorithmic scheme that solves the corresponding variational problem. The two subnetworks are jointly trained end-to-end in a supervised fashion and as such the CNN learns to compute those parameters that drive the reconstructed images as close to the ground truth as possible. Numerical results in image denoising and MRI reconstruction show a significant qualitative and quantitative improvement compared to the best TGV scalar parameter case as well as to other approaches employing spatially varying parameters computed by unsupervised methods. We also observe that the inferred spatially varying parameter maps have a consistent structure near the image edges, asking for further theoretical investigations. In particular, the parameter that weighs the first-order TGV term has a triple-edge structure with alternating high-low-high values whereas the one that weighs the second-order term attains small values in a large neighbourhood around the edges.