I am interested in three different but related areas: computed imaging/inverse problems, data assimilation, and machine learning. Below are my current research projects.
1. Computed imaging:
We study the mathematical and computational foundation of several computed imaging methods, such as thermo/photo-acoustic tomography, X-ray tomography, ultrasound tomography, SAR, SONAR. The research involves several areas of mathematics: partial differential equations (PDEs), microlocal analysis, integral geometry, functional analysis, approximation theory, scientific computing, numerical optimization, and numerical linear algebra.
This research has been supported by two NSF grants: DMS 1212125 (expired) and DMS 1616904 (active).
2. Imaging and Data Assimilation for Ocean Acoustics:
We use the stochastic methods to solve large scale forward and inverse problems arising in monitoring the ocean.
3. Deep learning for biomedical image analysis
We use the deep learning techniques to study the retina diseases and cancer diagnostics. This is carried out under the Healthcare Image Modeling group at the Center for Mathematical Modeling Complex Interaction (CMCI) at the University of Idaho.
For perspective students
I am recruiting both graduate and undergraduate students. If you are a motivated student at U of I and interested in my research, just stop by my office for a chat. For undergrad students, the following majors are most expected: mathematics, computer sciences, electrical engineering, and mechanical engineering.
If you are considering applying for the graduate program in mathematics at the U of I and interested in my research, you are welcome to contact me. I will try my best to support your application, as long as your background is strong enough and suitable for my research. However, please keep in mind that the decision is made by the graduate committee, not me.
List of students advised:
1) Daniel Schmalz (Undergraduate, currently ECE graduate student at GATECH): Numerical linear algebra and optimization methods for photoacoustic tomography
2) Jonah Bartrand (Undergraduate): Wave propagationg in photoacoustic tomography
3) Tuan Pham (Graduate, MS): Microlocal anlaysis for photoacoustic tomography
4) Daniel Furman (Undergraduate): Stochastic optimization for ocean acoustic imaging
4) Bailey Lind-Trefts (Undergraduate): Deep learning for retina image analysis