An Exact Radon Formula for Lambertian Tomography

被引:0
|
作者
Jean-Baptiste Bellet
机构
[1] CNRS,Université de Lorraine
[2] IECL,undefined
来源
Journal of Mathematical Imaging and Vision | 2022年 / 64卷
关键词
Inverse optics; Radon transform; Lambertian diffusion; Tomography; 44A12; 78A46;
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摘要
This paper, based on an extension of the Radon transform on distributions, is a mathematical contribution to the field of tomographic imaging in optics. Indeed, we tackle the reconstruction of a Lambertian convex reflector using tomography. In a bi-dimensional setup, we prove that the Lambert’s cosine law can be exactly inverted by an original Radon formula. The associated reconstruction contains the geometry and the physics of the problem: it is a Radon measure supported by the reflector, and its density is the inverse of the albedo. Surprisingly, the Radon transform from X-ray transmission tomography, extended on distributions, permits here to invert reflected radiances in optics.
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页码:939 / 947
页数:8
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