Blind X-Ray CT Image Reconstruction From Polychromatic Poisson Measurements
Blind X-Ray CT Image Reconstruction From Polychromatic Poisson Measurements
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DOI：
10.1109/tci.2016.2523431
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发表时间：
2016-06-01
影响因子：
5.4
通讯作者：
Dogandzic, Aleksandar
中科院分区：
文献类型：
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作者：
Gu, Renliang;Dogandzic, Aleksandar
我们开发了一个框架，用于重建在盲型场景下的多色计算机断层扫描（CT）测量中稀疏的图像，在盲方案中，在该场景中，检查对象的材料和入射 - 能源谱的材料尚不清楚。假设我们希望重建的对象由单个材料组成，我们通过将积分变量从光子能量从光子能量更改为质量衰减，从衰减到单个未知的质量分支谱函数中；所得的测量方程式具有拉普拉斯融合形式。然后，使用阶的B条件将质量分配光谱扩展为基础函数。我们考虑一个泊松噪声模型，并建立相应的对数可能性（NLL）功能相对于密度图和质量分支谱谱参数的两种函数的条件。我们得出了一种块坐标下降算法，以最大程度地减少惩罚的NLL目标函数，其中惩罚项可确保使用CONVEX施加的质量分配样条系数的非负性和非负性和非负和梯度映射率总变化（电视）规范；由此产生的目标函数是Biconvex。该算法在Nesterovs近端梯度（NPG）步骤和有限的内存Broyden-Fletcher-Goldfarb-Shanno之间交替使用，分别具有盒子约束（L-BFGSB）迭代，分别更新图像和质量增强频谱参数。我们证明了目标函数的kurdyka-lojasiewicz属性，这对于在BICONVEX优化问题中建立块坐标下降方案的局部收敛很重要。我们的框架适用于其他NLL和信号 - 符号惩罚，例如2-D离散小波变换（DWT）图像系数的lognormal nll和L（1）范围。使用模拟和实际X射线CT数据进行的数值实验证明了该方案的性能。
We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incident-energy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurement-model parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown mass-attenuation spectrum function; the resulting measurement equation has the Laplace-integral form. The mass-attenuation spectrum is then expanded into basis functions using B-splines of order one. We consider a Poisson noise model and establish conditions for biconvexity of the corresponding log-likelihood (NLL) function with respect to the densitymap and mass-attenuation spectrum parameters. We derive a block-coordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure non-negativity of the mass-attenuation spline coefficients and non-negativity and gradient-map sparsity of the densitymap image, imposed using a convex total-variation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterovs proximal-gradient (NPG) step and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGSB) iteration for updating the image and mass-attenuation spectrum parameters, respectively. We prove the Kurdyka-Lojasiewicz property of the objective function, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Our framework applies to other NLLs and signal-sparsity penalties, such as lognormal NLL and l(1) norm of 2-D discrete wavelet transform (DWT) image coefficients. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme.