Student Analysis Seminar

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Uncertainty is Possibility: Uncertainty Principles and Signal Recovery

Speaker: Chen Li, NYU Courant

Location: Warren Weaver Hall 517

Date: Tuesday, December 2, 2025, 11 a.m.

Synopsis:

The Heisenberg uncertainty principle stipulates that a function and its Fourier transform cannot both have preponderance of mass on small intervals. We will present a couple of generalizations of the classical uncertainty principle from intervals to arbitrary (measurable) sets due to Donoho and Stark (1989). We will then demonstrate that even impossibility results have positive consequences by showing how the Donoho-Stark uncertainty principles can be used to justify various (sparse) signal recovery practices.