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Geometric Analysis of Phase Retrieval

Offered By: BIMSA via YouTube

Tags

Geometric Analysis Courses Signal Processing Courses Fourier Analysis Courses Least Squares Courses Nonconvex Optimization Courses

Course Description

Overview

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Explore the geometric analysis of phase retrieval in this 52-minute lecture by John Wright at ICBS2024. Delve into the generalized phase retrieval (GPR) problem, examining whether it's possible to recover a complex signal from its Fourier magnitudes or reconstruct a length-n complex vector from a set of m measurements. Investigate the effectiveness of nonconvex heuristics in practical GPR applications and the theoretical explanations behind their success. Learn about a least-squares formulation for GPR that exhibits a benign geometric structure under certain conditions, including the absence of spurious local minimizers and negative curvature around saddle points. Discover how this structure enables efficient global minimization using iterative optimization methods without special initialization. Gain insights into the connections between GPR and other optimization problems with similar geometric properties, such as dictionary learning and deconvolution.

Syllabus

John Wright: A Geometric Analysis of Phase Retrieval #ICBS2024


Taught by

BIMSA

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