Research
Interests in Brief
My primary research interests are applied mathematics problems related to medical imaging. In particular, the mathematics involved generally consists of the following;
- Complex analysis of one variable
- Differential geometry
- Partial differential equations
- Algorithms and Numerical Analysis
My research has primarily used results from classical harmonic analysis and geometric function theory to obtain filtered backprojection (FBP) reconstruction formulae for attenuated ray transforms over curves in 2 dimensional settings. Medical imaging merges many extremely difficult "pure" math topics with challenges in algorithm design, instrument design, data analysis, image analysis, histology, classical physics and modeling. It's a vibrant and well-mixed field where several disciplines merge.
The Inverse Problems group at Columbia's APAM
While I was a graduate student, I was a member of Columbia University's (roughly weekly) meeting group on inverse problems. It was a great way to share ideas with some very talented quick thinkers.