Department of Computer Science, Faculty of Computers and Information, Suez University, Suez, Egypt.
Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt.
PLoS One. 2022 Jun 28;17(6):e0268410. doi: 10.1371/journal.pone.0268410. eCollection 2022.
Ring artifact elimination is one of the popular problems in computed tomography (CT). It appears in the reconstructed image in the form of bright or dark patterns of concentric circles. In this paper, based on the compressed sensing theory, we propose a method for eliminating the ring artifact during the image reconstruction. The proposed method is based on representing the projection data by a sum of two components. The first component contains ideal correct values, while the latter contains imperfect error values causing the ring artifact. We propose to minimize some sparsity-induced norms corresponding to the imperfect error components to effectively eliminate the ring artifact. In particular, we investigate the effect of using different sparse models, i.e. different sparsity-induced norms, on the accuracy of the ring artifact correction. The proposed cost function is optimized using an iterative algorithm derived from the alternative direction method of multipliers. Moreover, we propose improved versions of the proposed algorithms by incorporating a smoothing penalty function into the cost function. We also introduce angular constrained forms of the proposed algorithms by considering a special case as follows. The imperfect error values are constant over all the projection angles, as in the case where the source of ring artifact is the non-uniform sensitivity of the detector. Real data and simulation studies were performed to evaluate the proposed algorithms. Results demonstrate that the proposed algorithms with incorporating smoothing penalty and their angular constrained forms are effective in ring artifact elimination.
环形伪影消除是计算机断层扫描（CT）中的一个常见问题。它以同心圆环的亮暗图案形式出现在重建图像中。在本文中，我们基于压缩感知理论，提出了一种在图像重建过程中消除环形伪影的方法。该方法基于将投影数据表示为两个分量的和。第一个分量包含理想的正确值，而后者包含导致环形伪影的不完美误差值。我们建议最小化与不完美误差分量相对应的某些稀疏诱导范数，以有效地消除环形伪影。特别是，我们研究了使用不同稀疏模型（即不同的稀疏诱导范数）对环形伪影校正准确性的影响。所提出的代价函数通过从交替方向乘子法（ADMM）推导出的迭代算法进行优化。此外，我们通过在代价函数中加入平滑惩罚函数，提出了所提出算法的改进版本。我们还通过考虑以下特殊情况，引入了所提出算法的角度约束形式。在这种情况下，环形伪影的源是非探测器的均匀灵敏度，因此不完美误差值在所有投影角度上都是常数。进行了真实数据和模拟研究以评估所提出的算法。结果表明，具有平滑惩罚的所提出算法及其角度约束形式在消除环形伪影方面是有效的。
