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Colloquium speaker: Prof. Dorsa Ghoreishi, Saint Louis University

Title: Vector recovery using phase retrieval and saturation recovery

Abstract: Frames, like orthonormal bases, give a continuous, linear, and stable reconstruction formula for vectors in a Hilbert space. However, frames allow for redundancy, and this makes frames much more adaptable for theory and applications. Phase retrieval is one of the applications of frame theory that has been used in X-ray crystallography and coherent diffraction imaging where only the intensity of each linear measurement of a signal is available and the phase information is lost. In this talk, I will focus on a real-world application in which the sensors are set up such that any measurement above and below a certain threshold would be clipped as the sensor gets saturated. We study the recovery of a vector from such measurements which is called declipping or saturation recovery. I will discuss vector recovery methods in phase retrieval and saturation recovery.

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