Zeng Gengsheng L
Department of Engineering, Weber State University, 1447 Edvalson Street, Ogden, UT 84408, USA.
Department of Radiology and Imaging Sciences, University of Utah, 729 Arapeen Drive, Salt Lake City, UT 84108, USA.
Chin J Acad Radiol. 2019 Jul;1(1):13-24. doi: 10.1007/s42058-019-00006-1. Epub 2019 Apr 11.
It is rather controversial whether it is justified to use an unmatched projector/backprojector pair in an iterative image reconstruction algorithm. One common concern of using an unmatched projector/backprojector pair is that the optimal solution cannot be reached. This concern is misleading and must be clarified. We define a figure-of-merit in the image domain as the distance between the reconstructed image and the true image, as the normalized mean-squared-error (NMSE). The NMSE is used to determine whether an unmatched matched projector/backprojector pair can provide a better image than a matched projector/backprojector pair. Hot and cold lesion's contrast-to-noise ratio is also used as an alternative secondary figure-of-merit for algorithm comparison. Computer-generated counterexamples are used to test the performance for matched and unmatched projection/backprojection pairs for different reconstruction algorithms. The projectors are ray-driven, and the backprojectors are ray-driven and pixel-driven. For the attenuation-free data examples, the unmatched pixel-driven backprojector outperforms the matched ray-driven backprojector. For the attenuated data example, the matched ray-driven backprojector performs better. The ray-driven backprojector can be slightly improved by using an attenuation coefficient that is larger than the true one; in this case the backprojector becomes unmatched. Unmatched projector/backprojector pairs are fairly flexible. If the backprojector is properly chosen, good results can be obtained. However, we have not found a general rule to select a good backprojector.
在迭代图像重建算法中使用不匹配的投影仪/反投影仪对是否合理，这颇具争议。使用不匹配的投影仪/反投影仪对的一个常见担忧是无法达到最优解。这种担忧具有误导性，必须予以澄清。我们在图像域中将一个品质因数定义为重建图像与真实图像之间的距离，即归一化均方误差（NMSE）。NMSE用于确定不匹配的投影仪/反投影仪对是否能比匹配的投影仪/反投影仪对提供更好的图像。热病变和冷病变的对比度噪声比也用作算法比较的替代二级品质因数。使用计算机生成的反例来测试不同重建算法中匹配和不匹配的投影/反投影对的性能。投影仪是射线驱动的，反投影仪是射线驱动和像素驱动的。对于无衰减数据示例，不匹配的像素驱动反投影仪优于匹配的射线驱动反投影仪。对于衰减数据示例，匹配的射线驱动反投影仪表现更好。通过使用大于真实值的衰减系数，射线驱动反投影仪的性能可以略有提高；在这种情况下，反投影仪就变得不匹配了。不匹配的投影仪/反投影仪对相当灵活。如果正确选择反投影仪，可以获得良好的结果。然而，我们尚未找到选择良好反投影仪的通用规则。
