Department of Physics, Royal Institute of Technology, SE-10691, Stockholm, Sweden.
Med Phys. 2017 Sep;44(9):e242-e254. doi: 10.1002/mp.12322.
In spectral CT, basis material decomposition is commonly used to generate a set of basis images showing the material composition at each point in the field of view. The noise in these images typically contains anticorrelations between the different basis images, which leads to increased noise in each basis image. These anticorrelations can be removed by changing the basis functions used in the material decomposition, but the resulting basis images can then no longer be used for quantitative measurements. Recent studies have demonstrated that reconstruction methods which take the anticorrelations into account give reduced noise in the reconstructed image. The purpose of this work is to analyze an analytically solvable denoising model problem and investigate its effect on the noise level and bias in the image as a function of spatial frequency.
A denoising problem with a quadratic regularization term is studied as a mathematically tractable model for such a reconstruction method. An analytic formula for the resulting image in the spatial frequency domain is presented, and this formula is applied to a simple mathematical phantom consisting of an iodinated contrast agent insert embedded in soft tissue. We study the effect of the denoising on the image in terms of its transfer function and the visual appearance, the noise power spectrum and the Fourier component correlation coefficient of the resulting image, and compare the result to a denoising problem which does not model the anticorrelations in the image.
Including the anticorrelations in the noise model of the denoising method gives 3-40% lower noise standard deviation in the soft-tissue image while leaving the iodine standard deviation nearly unchanged (0-1% difference). It also gives a sharper edge-spread function. The studied denoising method preserves the noise level and the anticorrelated structure at low spatial frequencies but suppresses the noise and removes the anticorrelations at higher spatial frequencies. Cross-talk between images gives rise to artifacts at high spatial frequencies.
Modeling anticorrelations in a denoising problem can decrease the noise level in the basis images by removing anticorrelations at high spatial frequencies while leaving low spatial frequencies unchanged. In this way, basis image cross-talk does not lead to low spatial frequency bias but it may cause artifacts at edges in the image. This theoretical insight will be useful for researchers analyzing and designing reconstruction algorithms for spectral CT.
在光谱 CT 中，通常使用基物质分解来生成一组基图像，以显示视野中每个点的物质组成。这些图像中的噪声通常包含不同基图像之间的反相关，这导致每个基图像中的噪声增加。通过改变物质分解中使用的基函数可以去除这些反相关，但得到的基图像则不能再用于定量测量。最近的研究表明，考虑到反相关的重建方法可以降低重建图像中的噪声。本研究的目的是分析一个可解析求解的去噪模型问题，并研究其对图像中噪声水平和偏差随空间频率变化的影响。
研究了具有二次正则化项的去噪问题，作为这种重建方法的数学上可解模型。给出了空间频率域中所得图像的解析公式，并将该公式应用于由嵌入软组织中的碘造影剂插入物组成的简单数学体模。我们从图像的传递函数和视觉外观、噪声功率谱和所得图像的傅里叶分量相关系数的角度研究了去噪的影响，并将结果与不模拟图像中反相关的去噪问题进行了比较。
在去噪方法的噪声模型中包含反相关会使软组织图像的噪声标准偏差降低 3-40%，而碘的标准偏差几乎不变（差异为 0-1%）。它还给出了更锐利的边缘扩展函数。所研究的去噪方法在保留低空间频率的噪声水平和反相关结构的同时，抑制了高空间频率的噪声并去除了反相关。图像之间的串扰会在高空间频率产生伪影。
在去噪问题中模拟反相关可以通过去除高空间频率的反相关来降低基图像的噪声水平，而不改变低空间频率。这样，基图像的串扰不会导致低空间频率的偏差，但可能会在图像的边缘产生伪影。这种理论见解对于分析和设计光谱 CT 重建算法的研究人员将是有用的。
