A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT

Abstract

Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient μ(r, E)at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp–Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.

Implementation of a Framelet-Based Spectral Reconstruction for Multi-Slice Spiral CT

“…In our previous work [14,15], I 0 (E) is constant for all X-ray beams. Here we assume I 0 (E) varies with respect to positions of X-ray beams and take bowtie filtering into consideration.…”

“…In this section we extend the framelet-based spectral reconstruction algorithm from fan-beam geometry [14][15][16][17][18] to multi-slice spiral scanning with the bowtie filtering making it more practical in clinical applications.…”

“…In this section, we compare the computational time of the proposed algorithm with that of the fan beam spectral reconstruction algorithm [14]. Experiments with both algorithms are conducted on the Xeon Gold 6242R @3.1 GHz/NVIDIA Quadro RTX 8000 workstation in the same operating environment.…”

“…In our previous method [14], the reconstruction process were all realized in the environment of MATLAB and running on the CPU without any acceleration technologies. Besides, it only reconstructs a central slice from the rebined fanbeam projections.…”

“…Besides, for a hospital, adding a new spectral CT scanner to its lab which has facilitated a conventional CT scanner involves practical issues in cost and space. Recently, a framelet-based iterative reconstruction algorithm is proposed to solve the spectral CT reconstruction problem from the aspect of software in the current CT hardware platform [14][15][16][17][18] by our group. The key technique is the sparse representation of X-ray attenuation coefficients in a framelet system.…”