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Nonconvex weighted variational metal artifacts removal via convergent primal-dual algorithms

Lianfang Wang, Zhangling Chen, Zhifang Liu, Yutong Li, Yunsong Zhao, Hongwei Li, Huibin Chang

TL;DR

This paper proposes a nonconvex weighted variational approach for metal artifact reduction, in lieu of employing a binary function with zeros in the metal trace, an adaptive weight function is designed in the Radon domain, with zeros in the overlapping regions of multiple disjoint metals as well as areas of highly attenuated projections.

Abstract

Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis. Inpainting the metal trace directly in the Radon domain for the extant variational method leads to strong edge diffusion and potential inherent artifacts. With normalization based on pre-segmentation, the inpainted outcome can be notably ameliorated. However, its reconstructive fidelity is heavily contingent on the precision of the presegmentation, and highly accurate segmentation of images with metal artifacts is non-trivial in actuality. In this paper, we propose a nonconvex weighted variational approach for metal artifact reduction. Specifically, in lieu of employing a binary function with zeros in the metal trace, an adaptive weight function is designed in the Radon domain, with zeros in the overlapping regions of multiple disjoint metals as well as areas of highly attenuated projections, and the inverse square root of the measured projection in other regions. A nonconvex L1-alpha L2 regularization term is incorporated to further enhance edge contrast, alongside a box-constraint in the image domain. Efficient first-order primal-dual algorithms, proven to be globally convergent and of low computational cost owing to the closed-form solution of all subproblems, are devised to resolve such a constrained nonconvex model. Both simulated and real experiments are conducted with comparisons to other variational algorithms, validating the superiority of the presented method. Especially in comparison to Reweighted JSR, our proposed algorithm can curtail the total computational cost to at most one-third, and for the case of inaccurate pre-segmentation, the recovery outcomes by the proposed algorithms are notably enhanced.

Nonconvex weighted variational metal artifacts removal via convergent primal-dual algorithms

TL;DR

This paper proposes a nonconvex weighted variational approach for metal artifact reduction, in lieu of employing a binary function with zeros in the metal trace, an adaptive weight function is designed in the Radon domain, with zeros in the overlapping regions of multiple disjoint metals as well as areas of highly attenuated projections.

Abstract

Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis. Inpainting the metal trace directly in the Radon domain for the extant variational method leads to strong edge diffusion and potential inherent artifacts. With normalization based on pre-segmentation, the inpainted outcome can be notably ameliorated. However, its reconstructive fidelity is heavily contingent on the precision of the presegmentation, and highly accurate segmentation of images with metal artifacts is non-trivial in actuality. In this paper, we propose a nonconvex weighted variational approach for metal artifact reduction. Specifically, in lieu of employing a binary function with zeros in the metal trace, an adaptive weight function is designed in the Radon domain, with zeros in the overlapping regions of multiple disjoint metals as well as areas of highly attenuated projections, and the inverse square root of the measured projection in other regions. A nonconvex L1-alpha L2 regularization term is incorporated to further enhance edge contrast, alongside a box-constraint in the image domain. Efficient first-order primal-dual algorithms, proven to be globally convergent and of low computational cost owing to the closed-form solution of all subproblems, are devised to resolve such a constrained nonconvex model. Both simulated and real experiments are conducted with comparisons to other variational algorithms, validating the superiority of the presented method. Especially in comparison to Reweighted JSR, our proposed algorithm can curtail the total computational cost to at most one-third, and for the case of inaccurate pre-segmentation, the recovery outcomes by the proposed algorithms are notably enhanced.
Paper Structure (25 sections, 11 theorems, 92 equations, 18 figures, 2 tables, 2 algorithms)

This paper contains 25 sections, 11 theorems, 92 equations, 18 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Polychromatic X-ray CT and related variational reconstruction methods
  4. Anisotropic-isotropic regularization
  5. The proposed variational method for MAR
  6. A nonconvex weighted MAR with a box-constraint
  7. Primal-dual optimization for the penalized model
  8. Preconditioned primal-dual hybrid gradient
  9. Fully-splitting primal-dual hybrid gradient
  10. Convergence analysis
  11. Convergence of Algorithm \ref{['Pre Pdhg']}
  12. Convergence of Algorithm \ref{['Pdhg']}.
  13. Numerical experiments
  14. Experimental settings
  15. Tests on various weight functions
  16. ...and 10 more sections

Key Result

Proposition 4.1

For all $k \ge 0$, we have

Figures (18)

  • Figure 1: (a) The measured projection data. (b) The reconstructed image $u_a$ by the analysis model (\ref{['CG reconstruct']}) (4600 Hounsfield Units (HU) window, 1300 HU level). (c) The overlap area $\Omega_t$. (d) The metal image.
  • Figure 2: Flowchart of the proposed CT image reconstruction with reduced metal artifacts.
  • Figure 3: Energy spectrum $\mathcal{S}_0(E)$
  • Figure 4: Comparison of the different weights. The first row is the reference image and the result of NCAT phantom in models (\ref{['mask weight model']}) and (\ref{['non multiplier ']}), respectively (4600 HU window, 1300 HU level). The second row is the reconstruction result of the head phantom in model (\ref{['mask weight model']}) and the selection of $O_m$ or $\Omega_t$ as the mask region in (\ref{['non multiplier ']}) from left to right (4200 HU window, 1100 HU level).
  • Figure 5: The third row represents the variation curve of Hounsfield Units (HU) corresponding to the positions of the red lines in the reconstructed images (\ref{['hbbb']})-(\ref{['tvline']}). From left to right, it shows the horizontal profile and the vertical profile. The remaining two rows correspond to the real metal-free image, the CG reconstruction image, the reconstruction result of model (\ref{['mask weight model']}), and the reconstruction result of model (\ref{['non multiplier ']}) (4600 HU window, 1300 HU level).
  • ...and 13 more figures

Theorems & Definitions (18)

  • Definition 1
  • Proposition 4.1
  • Lemma 4.1
  • Lemma 4.2
  • Lemma 4.3
  • Lemma 4.4
  • Theorem 4.1
  • Lemma 4.5
  • Lemma 4.6
  • Lemma 4.7
  • ...and 8 more