Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction

TL;DR

This paper introduces a relaxed linearized augmented Lagrangian method for X-ray CT image reconstruction, achieving approximately twice the speed of existing algorithms by leveraging over-relaxation techniques.

Contribution

It presents a novel relaxed linearized AL algorithm with proven faster convergence and demonstrates its effectiveness in accelerating CT image reconstruction.

Findings

The proposed method is about twice as fast as existing algorithms.

It maintains image quality with negligible additional computation.

The algorithm is effective on both simulated and real CT data.

Abstract

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.