Little Kevin J, La Rivière Patrick J
Department of Radiology, The University of Chicago, Chicago, Illinois 60637.
Med Phys. 2015 Mar;42(3):1307-20. doi: 10.1118/1.4907968.
With the goal of producing a less computationally intensive alternative to fully iterative penalized-likelihood image reconstruction, our group has explored the use of penalized-likelihood sinogram restoration for transmission tomography. Previously, we have exclusively used a quadratic penalty in our restoration objective function. However, a quadratic penalty does not excel at preserving edges while reducing noise. Here, we derive a restoration update equation for nonquadratic penalties. Additionally, we perform a feasibility study to extend our sinogram restoration method to a helical cone-beam geometry and clinical data.
A restoration update equation for nonquadratic penalties is derived using separable parabolic surrogates (SPS). A method for calculating sinogram degradation coefficients for a helical cone-beam geometry is proposed. Using simulated data, sinogram restorations are performed using both a quadratic penalty and the edge-preserving Huber penalty. After sinogram restoration, Fourier-based analytical methods are used to obtain reconstructions, and resolution-noise trade-offs are investigated. For the fan-beam geometry, a comparison is made to image-domain SPS reconstruction using the Huber penalty. The effects of varying object size and contrast are also investigated. For the helical cone-beam geometry, we investigate the effect of helical pitch (axial movement/rotation). Huber-penalty sinogram restoration is performed on 3D clinical data, and the reconstructed images are compared to those generated with no restoration.
We find that by applying the edge-preserving Huber penalty to our sinogram restoration methods, the reconstructed image has a better resolution-noise relationship than an image produced using a quadratic penalty in the sinogram restoration. However, we find that this relatively straightforward approach to edge preservation in the sinogram domain is affected by the physical size of imaged objects in addition to the contrast across the edge. This presents some disadvantages of this method relative to image-domain edge-preserving methods, although the computational burden of the sinogram-domain approach is much lower. For a helical cone-beam geometry, we found applying sinogram restoration in 3D was reasonable and that pitch did not make a significant difference in the general effect of sinogram restoration. The application of Huber-penalty sinogram restoration to clinical data resulted in a reconstruction with less noise while retaining resolution.
Sinogram restoration with the Huber penalty is able to provide better resolution-noise performance than restoration with a quadratic penalty. Additionally, sinogram restoration with the Huber penalty is feasible for helical cone-beam CT and can be applied to clinical data.
为了开发一种计算强度低于完全迭代惩罚似然图像重建的替代方法，我们团队探索了将惩罚似然正弦图恢复用于透射断层扫描。此前，我们在恢复目标函数中仅使用了二次惩罚。然而，二次惩罚在保留边缘同时降低噪声方面表现不佳。在此，我们推导了非二次惩罚的恢复更新方程。此外，我们进行了一项可行性研究，以将我们的正弦图恢复方法扩展到螺旋锥束几何结构和临床数据。
使用可分离抛物替代法（SPS）推导非二次惩罚的恢复更新方程。提出了一种计算螺旋锥束几何结构正弦图退化系数的方法。使用模拟数据，分别采用二次惩罚和保边缘的Huber惩罚进行正弦图恢复。在正弦图恢复后，使用基于傅里叶的解析方法获得重建图像，并研究分辨率-噪声权衡。对于扇束几何结构，与使用Huber惩罚的图像域SPS重建进行比较。还研究了物体大小和对比度变化的影响。对于螺旋锥束几何结构，我们研究了螺旋 pitch（轴向移动/旋转）的影响。对3D临床数据进行Huber惩罚正弦图恢复，并将重建图像与未进行恢复时生成的图像进行比较。
我们发现，通过在正弦图恢复方法中应用保边缘的Huber惩罚，重建图像在分辨率-噪声关系方面比在正弦图恢复中使用二次惩罚生成的图像更好。然而，我们发现这种在正弦图域中相对直接的边缘保留方法除了受边缘对比度影响外，还受成像物体的物理大小影响。这表明该方法相对于图像域边缘保留方法存在一些缺点，尽管正弦图域方法的计算负担要低得多。对于螺旋锥束几何结构，我们发现三维应用正弦图恢复是合理的，并且pitch在正弦图恢复的总体效果上没有显著差异。将Huber惩罚正弦图恢复应用于临床数据可得到噪声更小同时保留分辨率的重建图像。
与二次惩罚恢复相比，Huber惩罚正弦图恢复能够提供更好的分辨率-噪声性能。此外，Huber惩罚正弦图恢复对于螺旋锥束CT是可行的，并且可以应用于临床数据。
