多能X射线断层成像的材料分离正则化器
Material-separating regularizer for multi-energy X-ray tomography
AI总结：
针对双能X射线断层成像中两种材料的分离重建，提出结合非负约束与内积惩罚项的正则化器，并采用预条件内点法求解，实验表明其优于联合全变分方法。
摘要：
本文考虑双能X射线断层成像，其成像目标由两种不同材料组成。假设这些材料在空间上可能相互交织，但在任何给定位置仅存在一种材料。此外，选择两种X射线能量，使得两种材料的衰减系数在光谱依赖性上存在明显差异。针对从两种材料重建各自断层图像的反问题，提出了一种新型正则化器。该正则化器结合了（a）非负约束和（b）包含两种材料图像之间内积的惩罚项，从而促进在给定像素中至多存在一种材料。推导了一种预条件内点法，用于最小化该正则化泛函。使用数字体模进行的数值测试表明，新算法在正确材料表征像素方面优于基线方法——联合全变分正则化。尽管该方法仅在二维设置下对两种材料和两种能量进行了测试，但该方法可轻松推广到三维和更多材料的情况。材料数量只需与成像中使用的能量数量相匹配即可。
英文摘要：
Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material present. Further, two X-ray energies are chosen so that there is a clear difference in the spectral dependence of the attenuation coefficients of the two materials. A novel regularizer is presented for the inverse problem of reconstructing separate tomographic images for the two materials. A combination of two things, (a) non-negativity constraint, and (b) penalty term containing the inner product between the two material images, promotes the presence of at most one material in a given pixel. A preconditioned interior point method is derived for the minimization of the regularization functional. Numerical tests with digital phantoms suggest that the new algorithm outperforms the baseline method, Joint Total Variation regularization, in terms of correctly material-characterized pixels. While the method is tested only in a two-dimensional setting with two materials and two energies, the approach readily generalizes to three dimensions and more materials. The number of materials just needs to match the number of energies used in imaging.
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