Abstract
The total variation (TV) regularized reconstruction methods for computed tomography (CT) may lead to staircase effects in the reconstructed images because of using the TV regularization. This paper develops a total fractional-order variation regularized CT reconstruction method, aiming at overcoming the weakness of the reconstruction methods based on the TV. Specifically, we propose an optimization model for CT reconstruction, including a fidelity term, a regularization term, and a constraint term. Here, the regularization is a total fractional-order variation arising from the fractional derivative of the underlying solution. To address the nondifferentiability of the resulting model, we introduce a fixed-point characterization for its solution through the proximity operators of the nondifferentiable functions. Based on the characterization, we further develop a fixed-point iterative scheme to solve the resulting model and provide convergence analysis of the developed scheme. Numerical experiments are presented to demonstrate that the developed method outperforms the TV regularized reconstruction method in terms of suppressing noise for CT reconstruction.
Highlights
Computed tomographic (CT) technology provides patients’ anatomical information through reconstruction of measured X-ray intensities
CT reconstruction methods based on the total variation (TV) regularization can effectively suppress noise and preserve edges of the reconstructed images
We develop an optimization model based on the anisotropic TVα for CT reconstruction problem. e underlying model includes a fidelity term with differentiability and two nondifferentiable terms
Summary
Computed tomographic (CT) technology provides patients’ anatomical information through reconstruction of measured X-ray intensities (projection data). E conventional total variation (TV) regularized reconstruction methods may lead to staircase effects in the reconstructed images due to the use of the TV regularization. To overcome the weakness of these methods, this paper investigates a total fractional-order variation regularized CT reconstruction method. CT reconstruction methods based on the TV regularization can effectively suppress noise and preserve edges of the reconstructed images. Fractional derivative-based regularization methods are studied for overcoming the difficulty of the TV in image processing [8,9,10,11]. E goal of the paper is to develop a regularized CT reconstruction method with a TFV regularization for improving the quality of the reconstructed images.
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