# PET-MRI Joint Reconstruction by Joint Sparsity Based Tight Frame Regularization

## TL;DR

This paper introduces a novel PET-MRI joint reconstruction model using tight frame regularization and joint sparsity, improving image quality by accounting for different regularities of PET and MRI data.

## Contribution

It proposes a non-convex joint sparsity model with a proximal alternating minimization algorithm and proves its global convergence, advancing PET-MRI image reconstruction techniques.

## Key findings

- Achieves better reconstruction performance than existing models
- Utilizes a non-convex balanced approach for different image regularities
- Provides a convergence proof based on Kurdyka-Lojasiewicz property

## Abstract

Recent technical advances lead to the coupling of PET and MRI scanners, enabling to acquire functional and anatomical data simultaneously. In this paper, we propose a tight frame based PET-MRI joint reconstruction model via the joint sparsity of tight frame coefficients. In addition, a non-convex balanced approach is adopted to take the different regularities of PET and MRI images into account. To solve the nonconvex and nonsmooth model, a proximal alternating minimization algorithm is proposed, and the global convergence is present based on Kurdyka-Lojasiewicz property. Finally, the numerical experiments show that the our proposed models achieve better performance over the existing PET-MRI joint reconstruction models.