Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers

arXiv:2509.15026v2 Announce Type: replace-cross Abstract: We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem. Strong theoretical guarantees have been established for idealized random measurements, defining the sampling ratio required for signal recovery. However, these results neglect signal priors, which can fundamentally shift these limits, potentially enabling reconstruction with far fewer measurements and simpler models. We evaluate a variety of image priors in the context of severe undersampling with physically-grounded random measurement models. Our results show that these priors enable accurate recovery well below the weak recovery limit, the theoretical threshold required for recovery better than a random guess.

Source: arXiv cs.LG | 2026-07-02