Efficient Low Dose X-ray CT Reconstruction through Sparsity-Based MAP Modeling

TL;DR

This paper introduces an efficient sparsity-based MAP model for low dose X-ray CT reconstruction, significantly reducing computation time and error, enabling fast high-quality image recovery from limited projections.

Contribution

It formulates a weighted compressive sensing model for low dose CT and proposes a fast algorithm using pseudo polar Fourier transform and rebinning, improving efficiency and accuracy.

Findings

Reconstruction error reduced by an order of magnitude.

High-quality 512x512 images reconstructed in less than 20 seconds.

Method applicable to fan beam and helical cone beam CT scans.

Abstract

Ultra low radiation dose in X-ray Computed Tomography (CT) is an important clinical objective in order to minimize the risk of carcinogenesis. Compressed Sensing (CS) enables significant reductions in radiation dose to be achieved by producing diagnostic images from a limited number of CT projections. However, the excessive computation time that conventional CS-based CT reconstruction typically requires has limited clinical implementation. In this paper, we first demonstrate that a thorough analysis of CT reconstruction through a Maximum a Posteriori objective function results in a weighted compressive sensing problem. This analysis enables us to formulate a low dose fan beam and helical cone beam CT reconstruction. Subsequently, we provide an efficient solution to the formulated CS problem based on a Fast Composite Splitting Algorithm-Latent Expected Maximization (FCSA-LEM) algorithm. In the proposed method we use pseudo polar Fourier transform as the measurement matrix in order to decrease the computational complexity; and rebinning of the projections to parallel rays in order to extend its application to fan beam and helical cone beam scans. The weight involved in the proposed weighted CS model, denoted by Error Adaptation Weight (EAW), is calculated based on the statistical characteristics of CT reconstruction and is a function of Poisson measurement noise and rebinning interpolation error. Simulation results show that low computational complexity of the proposed method made the fast recovery of the CT images possible and using EAW reduces the reconstruction error by one order of magnitude. Recovery of a high quality 512$\times$ 512 image was achieved in less than 20 sec on a desktop computer without numerical optimizations.