Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization
Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization
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DOI：
10.1118/1.4947485
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发表时间：
2016-05-01
期刊：
影响因子：
3.8
通讯作者：
Zhu, Lei
中科院分区：
文献类型：
--
作者：
Harms, Joseph;Wang, Tonghe;Zhu, Lei
目的：双能CT （Dual-energy CT， DECT）将CT图像分解为物质图像，拓展了CT成像的应用。然而，通过直接矩阵反演进行分解会导致较大的噪声放大，限制了DECT的定量使用。他们的团队之前开发了一种基于边缘保持正则化（PWLS-EPR）的惩罚加权最小二乘优化的噪声抑制算法。在本文中，作者使用相同的惩罚加权最小二乘优化框架，但采用基于相似度的正则化（PWLS-SBR）来提高方法的性能，通过保持更均匀的噪声功率谱（NPS），大大提高了分解图像的质量。方法：PWLS-SBR的设计是基于对相似材料的像素进行平均得到低噪声图像。对于每个像素，作者通过比较CT值来计算其与邻域其他像素的相似性。使用经验高斯模型，如果相邻像素的CT值与感兴趣像素的CT值接近或远离，则作者为其分配高/低相似值。这些相似值以矩阵形式组织，使得相似矩阵与图像向量的乘法可以减少图像噪声。在高能量和低能CT图像上计算相似矩阵并取平均。在PWLS-SBR中，作者加入了一个正则化项，通过相似矩阵乘法最小化无噪声和有噪声图像之间差的L-2范数。PWLS-SBR利用了初始CT图像的所有像素信息，而不仅仅是位于边缘或边缘附近的像素信息，因此优于先前开发的PWLS-EPR，这一点得到了对幻影和头颈部患者的对比研究的支持。结果：在Catphan (c) 600幻影的线对切片上，PWLS-SBR优于PWLS-EPR，即使在噪声标准偏差（STD）降低90%的情况下，仍保持8 lp/cm的空间分辨率，与原始CT图像相当。在拟人化头部幻影上观察到类似的空间分辨率性能。此外，PWLS-SBR的结果表明，由于保留了图像NPS，图像质量得到了显著提高。在Catphan (c) 600幻影上，使用PWLS-SBR的NPS与直接矩阵反演的NPS相关性为93%，而使用PWLS-EPR的NPS相关性降至-52%。电子密度测量研究表明，PWLS-SBR具有较高的精度。在7种不同材料上，利用PWLS-SBR对分解后的材料图像计算得到的电子密度的均方根误差（RMSE）为1.20%，而PWLS-EPR的均方根误差（RMSE）为2.21%。在对头颈部患者的研究中，PWLS-SBR显示，在图像质量与CT图像相当的材料图像上，噪声STD降低了3倍，而在PWLS-EPR结果中，精细结构丢失。此外，PWLS-SBR能更好地保持组织图像的低对比度。结论：作者提出了一种优化框架的正则化项的改进，该框架对带有噪声抑制的DECT进行迭代图像域分解。正则化项避免了图像梯度的计算，并基于像素相似度。该方法不仅实现了较高的分解精度，而且在NPS和空间分辨率上都有改进。(C) 2016年美国医学物理学家协会。
Purpose: Dual-energy CT (DECT) expands applications of CT imaging in its capability to decompose CT images into material images. However, decomposition via direct matrix inversion leads to large noise amplification and limits quantitative use of DECT. Their group has previously developed a noise suppression algorithm via penalized weighted least-square optimization with edge-preservation regularization (PWLS-EPR). In this paper, the authors improve method performance using the same framework of penalized weighted least-square optimization but with similarity-based regularization (PWLS-SBR), which substantially enhances the quality of decomposed images by retaining a more uniform noise power spectrum (NPS).Methods: The design of PWLS-SBR is based on the fact that averaging pixels of similar materials gives a low-noise image. For each pixel, the authors calculate the similarity to other pixels in its neighborhood by comparing CT values. Using an empirical Gaussian model, the authors assign high/low similarity value to one neighboring pixel if its CT value is close/far to the CT value of the pixel of interest. These similarity values are organized in matrix form, such that multiplication of the similarity matrix to the image vector reduces image noise. The similarity matrices are calculated on both high- and low-energy CT images and averaged. In PWLS-SBR, the authors include a regularization term to minimize the L-2 norm of the difference between the images without and with noise suppression via similarity matrix multiplication. By using all pixel information of the initial CT images rather than just those lying on or near edges, PWLS-SBR is superior to the previously developed PWLS-EPR, as supported by comparison studies on phantoms and a head-and-neck patient.Results: On the line-pair slice of the Catphan (c) 600 phantom, PWLS-SBR outperforms PWLS-EPR and retains spatial resolution of 8 lp/cm, comparable to the original CT images, even at 90% reduction in noise standard deviation (STD). Similar performance on spatial resolution is observed on an anthropomorphic head phantom. In addition, results of PWLS-SBR show substantially improved image quality due to preservation of image NPS. On the Catphan (c) 600 phantom, NPS using PWLS-SBR has a correlation of 93% with that via direct matrix inversion, while the correlation drops to -52% for PWLS-EPR. Electron density measurement studies indicate high accuracy of PWLS-SBR. On seven different materials, the measured electron densities calculated from the decomposed material images using PWLS-SBR have a root-mean-square error (RMSE) of 1.20%, while the results of PWLS-EPR have a RMSE of 2.21%. In the study on a head-and-neck patient, PWLS-SBR is shown to reduce noise STD by a factor of 3 on material images with image qualities comparable to CT images, whereas fine structures are lost in the PWLS-EPR result. Additionally, PWLS-SBR better preserves low contrast on the tissue image.Conclusions: The authors propose improvements to the regularization term of an optimization framework which performs iterative image-domain decomposition for DECT with noise suppression. The regularization term avoids calculation of image gradient and is based on pixel similarity. The proposed method not only achieves a high decomposition accuracy, but also improves over the previous algorithm on NPS as well as spatial resolution. (C) 2016 American Association of Physicists in Medicine.