To local reconstruction from the spherical mean Radon transform, and A flag representation for a n-dimensional convex body

We will discuss two recently published articles.

1. To local reconstruction from the spherical mean Radon transform, Journal of Mathematical Analysis and Applications, 470 (2019) 102–117

The article suggests a new approach for the inversion of the spherical mean Radon transform in 2D with detectors on a line. We present a new inversion formula to recover an unknown function. Our reconstruction formula has the benefit of being local.

2. A flag representation for a n-dimensional convex body, The Journal of Geometric Analysis, https://doi.org/10.1007/s12220-018-00102-1

The cosine representation of a centrally symmetric convex body plays a fundamental role in integral geometry. In the article, one new flag representation for the support function of an origin symmetric n-dimensional convex body in terms of surface curvature functions of the body is found generalizing the cosine representation.