Azita Mayeli
CUNY Graduate School and University Center, NY·Mathematics & Statistics
Pulling the clear parts out of a noisy signal is central to MRI scans, wireless networks and scientific imaging. This works best when a signal can be isolated at once in space (or time) and in frequency.
- Fields
Mathematics & Statistics
Engineering
- Topics
spatio-spectral limiting operators
harmonic analysis
spectral analysis
- Grants
- 1 known grant, through Jul 2028
What they work on
- Develop Gaussian wave packet systems, which extend wavelets and Gabor systems using translations, modulations and dilations, to analyze multi-dimensional signals.
- Characterize the spectral properties of spatio-spectral limiting operators on balls and smooth domains, and test their stability on shapes with small holes or gaps.
- Build radial wave packets for discs to enable fast interpolation and integration in signal processing, and extend the framework to discrete-time signals.
More about the research
Spatio-spectral limiting operators (SSLOs) are mathematical tools that do exactly this. In one dimension they are well understood, but in higher dimensions many questions remain open.
Why it matters
Better mathematical tools for isolating signals in space and frequency could lead to sharper MRI scans, more reliable wireless communication and faster, more accurate data reconstruction. Clinicians, communication engineers and scientists who rely on multi-dimensional imaging and signal processing may benefit from these methods.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Dominique Maldague
University of California-Los Angeles, CA·Mathematics & Statistics
Study special cases of the Mizohata-Takeuchi conjecture in the plane. This conjecture bounds how waves can concentrate along tubes, and the work will use high-low decoupling together with new geometric insights about weights and wave packets.
Svetlana Jitomirskaya
University of California-Berkeley, CA·Mathematics & Statistics
Develop non-perturbative Green's function estimates for lattice quasiperiodic operators when the frequency parameter is restricted to a submanifold of a torus.
Weilin Li
CUNY City College, NY·Mathematics & Statistics
Construct objective functions for continuous parameter estimation whose informative minima lie close to the true parameters and have large basins of attraction, so standard local optimization methods can locate them efficiently.
The school
CUNY Graduate School and University Center: 1 labs on PI Pages, $81M a year on research, 356 research doctorates a year.
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