Atmosphere Ocean Science Student Seminar

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Abel inverse transform encountered in an AOS project

Speaker: Han Wang, PhD Candidate

Location: Warren Weaver Hall 1314

Date: Friday, March 1, 2019, 3:30 p.m.

Synopsis:

This is an informal talk on our experiences of treating the Abel inverse transform, an inverse problem that we encountered in a research project analyzing track data measurements. In words, the Abel inverse transform reconstructs an isotropic 2D function f(x,y), from its projection along a certain axis. Calculating the projection of f(x,y) along a chosen axis is straightforward and numerically well-conditioned. Reconstructing f(x,y) from its projection, on the contrary, is numerically ill-conditioned.

Solving the Abel inverse problem has been an important topic in image analysis useful in applications such as computer tomography, and new algorithms are still being developed. I will describe how the Abel inverse problem showed up in our research about track data, why it is ill-conditioned, what are some popular reconstruction methods, and how we found our way around the Abel inverse problem in our research eventually.