The attenuated X-ray transform arises from the image reconstruction in single photon emission computed tomography. The theory of attenuated X-ray transforms is so far incomplete and many questions remain open. In this paper, we are pursuing the inversion of the attenuated X-ray transforms with nonnegative varying attenuation functions μ. By the symmetric attenuated X-ray transform $A_{\mu }$ on plane and the method of convolution-backprojection, we obtain the inversion formulas of the attenuated X-ray transforms with nonnegative attenuation functions μ, satisfying some decaying and smoothing conditions on plane.

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衰减 X 射线变换的反演 - 卷积反投影方法

衰减的 X 射线变换源于单光子发射计算机断层扫描中的图像重建。迄今为止，衰减 X 射线变换的理论还不完善，许多问题仍然悬而未决。在本文中，我们正在研究具有非负变化衰减函数μ的衰减 X 射线变换的反演。通过对称衰减 X 射线变换${\mathrm{一种}}_{\mu }$在平面上和卷积反投影的方法，我们得到了具有非负衰减函数μ的衰减X射线变换的反演公式，满足平面上的一些衰减和平滑条件。