Uniform recovery over all signals

Establish a uniform recovery guarantee for the minimum-norm Gauss–Newton method for coded diffraction phase retrieval that holds simultaneously for all target signals, rather than separately for each fixed signal.

Background

The paper proves convergence guarantees for the minimum-norm Gauss–Newton method under resampled and fixed-data coded diffraction patterns, but the probabilistic results are stated for each fixed target signal. A uniform guarantee would require the convergence analysis to hold simultaneously over the signal class, strengthening the current fixed-signal results.

References

Several questions remain open. First, our guarantees hold for each fixed signal $\star$, rather than simultaneously for all $\star$. Extending the analysis to a uniform recovery guarantee would be of interest.

— The Gauss--Newton Method for Phase Retrieval from Coded Diffraction Patterns  (2610.18021 - Huang et al., 13 Oct 2026) in Section 6, “Conclusions and discussion”