STFT Phase Retrieval - Robustness and Generative Priors - IPAM at UCLA

Explore a comprehensive lecture on STFT Phase retrieval, focusing on robustness and generative priors. Delve into the non-convex inverse problem of signal reconstruction from intensity measurements, with applications in diffraction imaging and audio processing. Examine the use of Gabor frames in phase retrieval, discussing stable and efficient reconstruction methods. Investigate how generative models can regularize the phase retrieval problem, introduce prior information about signal classes, and reduce required measurements. Learn about injectivity, stability, and challenges in Gabor phase retrieval, as well as algorithms for structured frames. Discover the polarization approach, adaptive measurement design, and the incorporation of prior information in sparse phase retrieval and generative priors.

Intro
Example: diffraction imaging with masks
Masked Fourier phase retrieval
Frames: definition
Phase retrieval with frames
Phase retrieval with shifting window: application example
Gabor frames and phase retrieval applications
Injectivity of phase retrieval
Stability of phase retrieval
Stability using frame order statistics
Challenges of Gabor phase retrieval
Phase retrieval algorithm for structured frames
Idea of the polarization approach
Polarization identity
Polarization approach: phase propagation algorithm
How large should set E be?
Reconstruction in the case of noisy measurements
Adaptive measurement design
Prior information
Sparse phase retrieval
Generative priors