CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization

TL;DR

This paper introduces a novel CT image reconstruction method using data-driven tight frames in the spatial-Radon domain, improving the recovery of subtle structures by adaptively learning sparsity priors.

Contribution

It presents a new joint reconstruction model that combines data-driven tight frames with Radon domain inpainting, providing superior image quality over existing models.

Findings

Outperforms previous models in recovering subtle image structures

Uses adaptive tight frames learned from data for optimal sparse approximation

Provides convergence analysis for the proposed algorithm

Abstract

This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and that of the data-driven tight frames for image denoising \cite{cai2014data}. It is different from existing models in that both CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments showed that the SRD-DDTF model is superior to the model by \cite{Dong2013X} especially in recovering some subtle structures in the images.