Generalized Hessian-Schatten Norm Regularization for Image Reconstruction

TL;DR

This paper introduces a new regularization method called GHSN for image reconstruction, combining Hessian-Schatten norm and TGV advantages, and develops an ADMM-based optimization algorithm to improve imaging inverse problem solutions.

Contribution

The paper proposes the GHSN regularization, integrating Hessian-Schatten norm and TGV concepts, along with a novel ADMM-based optimization method for enhanced image recovery.

Findings

GHSN outperforms traditional regularizations in reconstruction quality.

The proposed method effectively stabilizes inverse imaging problems.

Experimental results demonstrate improved image fidelity.

Abstract

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging process. In the past decades, total variation regularization, especially second-order total variation (TV-2) regularization played a dominant role in the literature. Two forms of generalizations, namely Hessian-Schatten norm (HSN) regularization, and total generalized variation (TGV) regularization, have been recently proposed and have become significant developments in the area of regularization for imaging inverse problems owing to their performance. Here, we develop a novel regularization for image recovery that combines the strengths of these well-known forms. We achieve this by restricting the maximization space in the dual form of HSN in the same way that TGV is obtained from TV-2. We name the new regularization as the generalized Hessian-Schatten norm regularization (GHSN), and we develop a novel optimization method for image reconstruction using the new form of regularization based on the well-known framework called alternating direction method of multipliers (ADMM). We demonstrate the strength of the GHSN using some reconstruction examples.