Continuous-Domain Phase Retrieval in Dimension One
Available
Master Semester Project
Bachelor Project
Project: 00474

We consider the problem of recovering a complex-valued continuous-domain signal f from magnitude-only linear measurements. The project's goal is to develop and benchmark a coarse-to-fine (multiscale) numerical solver for this problem when f is itself a continuous-domain object discretized at increasing resolution. Rather than solving the non-convex phase retrieval problem directly at full resolution — where basins of attraction shrink and spectral initialization becomes costly — this project develops a coarse-to-fine multiscale solver: recover f cheaply at a coarse scale via Wirtinger Flow, then propagate the solution up the resolution hierarchy, using each prolonged coarse estimate as a warm start for local descent at the next scale. The central numerical questions are how the prolongation error and per-level sample count control the probability that a coarse recovery successfully seeds the next scale, and how the resulting continuation scheme compares — in sample complexity, iteration count, and empirical recovery probability — to standard single-scale Wirtinger Flow with spectral initialization at full resolution.
- Supervisors
- Vincent Guillemet, vincent.guillemet@epfl.ch, EPFL