An Exact Radon Formula for Lambertian Tomography

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.