Learned priors break phase retrieval limit below theoretical threshold
New research shows image priors enable signal recovery with far fewer measurements than theory predicts.
Phase retrieval is a classic inverse problem: reconstructing a signal from its magnitude-only measurements, common in imaging like X-ray crystallography. Theoretical guarantees exist for idealized random measurements, defining a 'weak recovery limit' — the sampling ratio below which reconstruction is no better than random guess. However, these guarantees ignore signal priors (e.g., natural image statistics). The EPFL team challenges this by introducing learned regularizers — neural-network-based priors that capture realistic image structures.
They evaluate various image priors under severely undersampled, physically realistic measurement models. Their key finding: these priors enable accurate recovery far below the classical weak recovery limit. This suggests that leveraging learned regularizers fundamentally changes the theoretical landscape, potentially reducing the number of measurements needed in practical applications like microscopy or astronomical imaging. The work highlights a gap between theory and practice, and offers a path to more efficient sensing systems.
- Standard weak recovery limits assume no signal priors; learned regularizers break that bound.
- EPFL team demonstrated accurate recovery with fewer measurements than the random-guess threshold.
- Priors enable simpler models (fewer sensors) for real-world phase retrieval tasks.
Why It Matters
Enables more efficient imaging (X-ray, microscopy) with fewer measurements, reducing cost and acquisition time.