I am interested in the mathematics surrounding inverse problems, this includes: differential geometry, micro-local analysis, partial differential equations, probability, and applied functional analysis. I like mathematical problems that intertwine with other fields of science like physics, computer science and biology. My research is focus on stability and reconstruction for different types of inverse problems. I use micro-local analysis to understand the inverse operators and to exploit the underlying geometry of the problem, by doing so you are able to extract information that allows a stable reconstruction of solutions under certain regularity conditions
I have work in problem that include:
- hybrid inverse problems and medical imaging.
- image visualization perception.
- inverse hyperbolic stability.