Research

Current research problems

Most of the problems I am currently thinking about involve finding submatrices of the DFT matrix with certain properties. Recall that the DFT matrix (of size $N$) is defined as

\[\mathcal{F} = (e^{2\pi i mn/N})_{m,n=0}^{N-1}.\]

Say we pick certain columns $J\subseteq \{0,1,2,\ldots,N-1\}$ of $\mathcal{F}$, how do we pick rows $I$ such that the submatrix of $\mathcal{F}$ with rows $I$ and columns $J$ has certain desirable properties. Which choice of $J$ would enable us to pick a suitable $I$ ? See this for a summary of key results on this theme.

For prospective students: Working on these problems involves drawing from multiple fields in mathematics, including linear algebra, probability (concentration inequalities), number theory, additive combinatorics, convex optimization and duality. In case you are interested, you can reach me via email.

Apart from this, my group is also involved in some problems in machine learning.

Publications on Fourier Analysis

• Fast DFT Computation for Signals with Structured Support
  Charantej Reddy P, Aditya Siripuram, Brad Osgood
  arXiv preprint arXiv:2211.15299 (2022).
• Computing the Discrete Fourier Transform of signals with spectral frequency support
  PC Reddy, VSSP Tej, A Siripuram, B Osgood
  2021 IEEE International Symposium on Information Theory (ISIT), 2381-2386 (online)
• Convolution idempotents with a given zero-set
  A Siripuram, B Osgood
  IEEE Transactions on Signal Processing 68, 4773-4781 (online)
• Some results on convolution idempotents
  PC Reddy, A Siripuram, B Osgood
  2020 IEEE International Symposium on Information Theory (ISIT), 1462-1467 (online)
• Discrete sampling: A graph theoretic approach to orthogonal interpolation
  A Siripuram, WD Wu, B Osgood
  IEEE Transactions on Information Theory 65 (12), 8119-8130 (online)
• LP relaxations and fuglede’s conjecture
  A Siripuram, B Osgood
  2018 IEEE International Symposium on Information Theory (ISIT), 2525-2529(online)
• Discrete sampling and interpolation: Universal sampling sets for discrete bandlimited spaces
  B Osgood, A Siripuram, W Wu
  IEEE transactions on information theory 58 (7), 4176-4200 (online)

Other work (including collaborations)

• Graph learning under spectral sparsity constraints
  B Subbareddy, A Siripuram, J Zhang
  ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• A channel coding perspective of collaborative filtering
  ST Aditya, O Dabeer, BK Dey
  IEEE Transactions on Information Theory 57 (4), 2327-2341
• A channel coding perspective of recommendation systems
  ST Aditya, O Dabeer, BK Dey
  2009 IEEE International Symposium on Information Theory, 319-323
• FlexCast: Graceful wireless video streaming
  S Aditya, S Katti
  Proceedings of the 17th annual international conference on Mobile computing and networking
• Perceptually Guided Adversarial Perturbations
  P Charantej Reddy, A Siripuram, SS Channappayya
  arXiv e-prints, arXiv: 2106.12731
• Sparse Bayesian learning for acoustic source localization
  R Pandey, S Nannuru, A Siripuram
  ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)