My research is the field of applied analysis, focusing on inverse problems, specifically medical imaging problems, and signal processing. I am currently collaborating on developing algorithms for low-rank tensor recovery, support recovery and signal reconstruction for the multiple measurement vector (MMV) problem in signal processing, and applying a multi-criteria decision-making framework (drawing on tools from statistics) to problems in airport gate availability. I am also starting a collaboration on using data analysis tools to analyze the evolution of natural language in response to cultural stimuli. In the summer of 2018 I worked with a team of three undergraduates on alternative methods for generating a reduced basis to use in the hyDOT forward problem. For my dissertation, I investigated the forward and inverse problems for hyperspectral diffuse optical tomography and worked on a team applying a multi-criteria decision-making framework to problems in the power market. For my master's degree I worked on an imaging problem in the geosciences.
Publications
Conference (Research) Presentations
International Conference of the IEEE Engineering in Medicine and Biology Society July 2019 Ignite Session speaker, and poster presentation: “Fast Hyperspectral Diffuse Optical Imaging Method with Joint Sparsity.”
MAA MD-DC-VA Sectional Meeting April 2019 Contributed talk: “Streaming isn’t Just for Netflix: How to Deal with Corrupt Signals in Medical Imaging.”
AMS Spring Central and Western Joint Sectional Meeting March 2019
Special Session, Sparsity, Randomness, and Optimization (invited by organizers): “Application of Stochastic Algorithms for Multiple Measurement Vectors to the Hyperspectral Diffuse Optical Tomography Problem.”
Joint Mathematics Meetings January 2019 Special Session, Statistical, Variational, and Learning Techniques in Image Analysis and their Applications to Biomedical, Hyperspectral, and Other Imaging: “Application of Stochastic Algorithms for Multiple Measurement Vectors to the Hyperspectral Diffuse Optical Tomography Problem.”
Hood College Math Seminar and Stevenson University STEMinar Series October, February 2017
“Can you Reconstruct a Tiger from its Stripes? The Mathematical Reconstruction of a Medical Image”
Joint Mathematics Meetings January 2016 AMS Contributed Paper Session: “Towards a Better Image: The Hyperspectral Diffuse Optical Tomography Inverse Problem”
Publications
- N. Durgin, R. Grotheer, C. Huang, S. Li, A. Ma, D. Needell, and J. Qin. "Sparse randomized Kaczmarz for support recovery of jointly sparse corrupted multiple measurement vectors." Research in Data Science. Springer, Cham, 2019. 1-14.
- N. Durgin, R. Grotheer, C. Huang, S. Li, A. Ma, D. Needell, and J. Qin. “Compressed anomaly detection with multiple mixed observations.” Research in Data Science. Springer, Cham, 2019. 211-237.
- S.C. Gray, T. Massaro, I. Chen, C. Edholm, R. Grotheer, Y. Zheng, and H. Chang. “A county-level analysis of persons living with HIV in the southern United States.” AIDS Care, 28(2), 2016.
- T. Khan, J. Reneke, R. Grotheer and T. Strauss. "Decision making using a multi-criteria approach in a wholesale electrical power market." Power Systems Conference (PSC), 2015 Clemson University. IEEE, 2015.
- B.H. Hokr, C.D. Clark, III, R. E. Grotheer, and R.J. Thomas. “Higher-order wide-angle split-step spectral method for non-paraxial beam propagation.” Optics Express 21, 15815-15825 (2013).
- N. Durgin, R. Grotheer, C. Huang, S. Li, A. Ma, D. Needell, and J. Qin. “Fast Hyperspectral Diffuse Optical Imaging Method with Joint Sparsity”. Proceedings of the 41stAnnual International Conference of the IEEE Engineering in Medicine and Biology Society.
- N. Durgin, R. Grotheer, C. Huang, S. Li, A. Ma, D. Needell, and J. Qin. “Jointly Sparse MMV Signal Recovery with Prior Information.” Proceedings of the 2019 Asilomar Conference on Signals, Systems, and Computers.
Conference (Research) Presentations
International Conference of the IEEE Engineering in Medicine and Biology Society July 2019 Ignite Session speaker, and poster presentation: “Fast Hyperspectral Diffuse Optical Imaging Method with Joint Sparsity.”
MAA MD-DC-VA Sectional Meeting April 2019 Contributed talk: “Streaming isn’t Just for Netflix: How to Deal with Corrupt Signals in Medical Imaging.”
AMS Spring Central and Western Joint Sectional Meeting March 2019
Special Session, Sparsity, Randomness, and Optimization (invited by organizers): “Application of Stochastic Algorithms for Multiple Measurement Vectors to the Hyperspectral Diffuse Optical Tomography Problem.”
Joint Mathematics Meetings January 2019 Special Session, Statistical, Variational, and Learning Techniques in Image Analysis and their Applications to Biomedical, Hyperspectral, and Other Imaging: “Application of Stochastic Algorithms for Multiple Measurement Vectors to the Hyperspectral Diffuse Optical Tomography Problem.”
Hood College Math Seminar and Stevenson University STEMinar Series October, February 2017
“Can you Reconstruct a Tiger from its Stripes? The Mathematical Reconstruction of a Medical Image”
Joint Mathematics Meetings January 2016 AMS Contributed Paper Session: “Towards a Better Image: The Hyperspectral Diffuse Optical Tomography Inverse Problem”