Penalized-likelihood sinogram restoration for computed tomography
Penalized-likelihood sinogram restoration for computed tomography
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DOI：
10.1109/tmi.2006.875429
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发表时间：
2006-08-01
影响因子：
10.6
通讯作者：
Vargas, Phillip A.
中科院分区：
文献类型：
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作者：
La Riviere, Patrick J.;Bian, Junguo;Vargas, Phillip A.
我们将计算机断层扫描（CT）正弦图预处理制定为统计恢复问题，其目标是从一组噪声、退化测量中获得重建所需的线积分的最佳估计。 CT 测量数据会受到多种因素的影响（包括光束硬化和离焦辐射），除非经过适当校正，否则会在重建图像中产生伪影。目前，此类影响可通过一系列正弦图预处理步骤来解决，包括对离焦辐射进行去卷积校正，这些步骤可能会放大噪声。噪声本身通常通过重建内核的变迹来减轻，这有效地忽略了测量统计数据，尽管在高噪声情况下有时会应用对数据统计数据进行松散建模的自适应滤波方法。作为替代方案，我们提出了一种通用成像模型，将退化的测量结果与理想线积分的正弦图相关联，并建议通过迭代优化基于统计的目标函数来估计这些线积分。我们考虑三种不同的策略来估计理想线积分集，一种是基于对已针对单材料束硬化进行校正的理想“单色”线积分的直接估计，一种是基于对可以容易地映射到单色线积分的理想“多色”线积分的估计，一种是基于对理想透射强度的估计，从中可以容易地估计理想的单色线积分。前两种方法涉及惩罚泊松似然目标函数的最大化，而第三种方法涉及应用于透射强度域的二次惩罚加权最小二乘（PWLS）目标的最小化。我们发现，在考虑用于筛查 CT 的典型低曝光水平下，基于泊松似然的方法优于 PWLS 目标以及基于自适应滤波和反卷积的标准方法。在较高的暴露水平下，这些方法的表现都相似。
We formulate computed tomography (CT) sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. CT measurement data are degraded by a number of factors-including beam hardening and off-focal radiation-that produce artifacts in reconstructed images unless properly corrected. Currently, such effects are addressed by a sequence of sinogram-preprocessing steps, including deconvolution corrections for off-focal radiation, that have the potential to amplify noise. Noise itself is generally mitigated through apodization of the reconstruction kernel, which effectively ignores the measurement statistics, Although in high-noise situations adaptive filtering methods that loosely model data statistics are sometimes applied. As an alternative, we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function. We consider three different strategies for estimating the set of ideal line integrals, one based on direct estimation of ideal "monochromatic" line integrals that have been corrected for single-material beam hardening, one based on estimation of ideal "polychromatic" line integrals that can be readily mapped to monochromatic line integrals, and one based on estimation of ideal transmitted intensities, from which ideal, monochromatic line integrals can be readily estimated. The first two approaches involve maximization of a penalized Poisson-likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares (PWLS) objective applied in the transmitted intensity domain. We find that at low exposure levels typical of those being considered for screening CT, the Poisson-likelihood based approaches outperform the PWLS objective as well as a standard approach based on adaptive filtering followed by deconvolution. At higher exposure levels, the approaches all perform similarly.