A constrained, total-variation minimization algorithm for low-intensity X-ray CT

TL;DR

This paper introduces a novel iterative reconstruction algorithm for low-intensity X-ray CT that employs constrained total-variation minimization to improve resolution and reduce noise compared to traditional methods.

Contribution

The paper presents a new algorithm combining Fourier upsampling and TV-minimization for high-resolution low-intensity CT reconstruction, optimized for structure at detector-bin scales.

Findings

Lower noise levels at equivalent contrast compared to FBP

Effective resolution recovery at detector-bin scale

Algorithm converges within 100 iterations

Abstract

Purpose: We develop an iterative image-reconstruction algorithm for application to low-intensity computed tomography (CT) projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector-bin width. Method: Recovering the resolution on the scale of a detector bin, requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV-minimization, as suggested by compressive sensing. The presented pseudo-code for solving constrained, TV-minimization is designed to yield an accurate solution to this optimization problem within 100 iterations. Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire, to test resolution. The proposed algorithm is compared with filtered back-projection (FBP). Conclusion: The algorithm may have some advantage over FBP in that the resulting noise-level is lowered at equivalent contrast levels of the wire.