Zhang Lingli
Chongqing Key Laboratory of Complex Data Analysis & Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing, China.
Chongqing Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, China.
J Xray Sci Technol. 2021;29(4):645-662. doi: 10.3233/XST-200833.
Since the stair artifacts may affect non-destructive testing (NDT) and diagnosis in the later stage, an applicable model is desperately needed, which can deal with the stair artifacts and preserve the edges. However, the classical total variation (TV) algorithm only considers the sparsity of the gradient transformed image. The objective of this study is to introduce and test a new method based on group sparsity to address the low signal-to-noise ratio (SNR) problem.
This study proposes a weighted total variation with overlapping group sparsity model. This model combines the Gaussian kernel and overlapping group sparsity into TV model denoted as GOGS-TV, which considers the structure sparsity of the image to be reconstructed to deal with the stair artifacts. On one hand, TV is the accepted commercial algorithm, and it can work well in many situations. On the other hand, the Gaussian kernel can associate the points around each pixel. Quantitative assessments are implemented to verify this merit.
Numerical simulations are performed to validate the presented method, compared with the classical simultaneous algebraic reconstruction technique (SART) and the state-of-the-art TV algorithm. It confirms the significantly improved SNR of the reconstruction images both in suppressing the noise and preserving the edges using new GOGS-TV model.
The proposed GOGS-TV model demonstrates its advantages to reduce stair artifacts especially in low SNR reconstruction because this new model considers both the sparsity of the gradient image and the structured sparsity. Meanwhile, the Gaussian kernel is utilized as a weighted factor that can be adapted to the global distribution.
由于阶梯伪影可能会影响后期的无损检测（NDT）及诊断，因此迫切需要一种适用的模型，该模型能够处理阶梯伪影并保留边缘。然而，经典的全变分（TV）算法仅考虑梯度变换图像的稀疏性。本研究的目的是引入并测试一种基于组稀疏性的新方法，以解决低信噪比（SNR）问题。
本研究提出了一种具有重叠组稀疏性的加权全变分模型。该模型将高斯核与重叠组稀疏性结合到TV模型中，记为GOGS-TV，其考虑了待重建图像的结构稀疏性以处理阶梯伪影。一方面，TV是公认的商业算法，并且在许多情况下都能很好地工作。另一方面，高斯核可以关联每个像素周围的点。通过定量评估来验证这一优点。
进行了数值模拟以验证所提出的方法，并与经典的同时代数重建技术（SART）和最新的TV算法进行比较。结果证实，使用新的GOGS-TV模型在抑制噪声和保留边缘方面，重建图像的SNR有显著提高。
所提出的GOGS-TV模型显示出其在减少阶梯伪影方面的优势，特别是在低SNR重建中，因为该新模型既考虑了梯度图像的稀疏性又考虑了结构稀疏性。同时，高斯核被用作加权因子，可适应全局分布。
