Rahul Parhi

About

I am an Assistant Professor of Electrical and Computer Engineering (ECE) at the University of California, San Diego (UCSD), which I joined in 2024. From 2022 to 2024, I was a Postdoctoral Researcher at the École Polytechnique Fédérale de Lausanne (EPFL), hosted by Michael Unser. I completed my Ph.D. in Electrical Engineering in 2022 at the University of Wisconsin–Madison (UW–Madison), where I was supervised by Robert D. Nowak. I completed my undergraduate studies at the University of Minnesota, Twin Cities (UMN) in 2018, where I received a B.S. in Mathematics and a B.S. in Computer Science.

I am interested in the interplay between functional and harmonic analysis and data science—broadly defined—and their applications to problems in signal processing, machine learning, statistics, and optimization. In particular, my research focuses on the following areas:

• foundations of neural networks and deep learning
  • mathematical characterizations of functions and representations learned from data
  • approximation properties of neural networks
  • nonparametric function estimation with neural networks
• mathematics of data science
  • sparsity and compressed sensing
  • optimal recovery and minimax estimation
  • wavelet-based signal processing and statistics
• functional and harmonic analysis
  • Radon transforms and their generalizations
  • wavelets, their generalizations, and other kinds of space-scale or time-frequency analysis
  • optimization problems over Banach spaces and more general topological vector spaces

For more detailed information about my research, you can take a look at my:

• CV (pdf)
• Publication list (pdf)
• List of talks (pdf)