On Fienup Methods for Regularized Phase Retrieval

Abstract

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex priors. In particular, we show that Fienup methods can be viewed as performing alternating minimization on a regularized nonconvex least-squares problem with respect to amplitude measurements. We then prove that under mild additional structural assumptions on the prior (semi-algebraicity), the sequence of signal estimates has a smooth convergent behaviour towards a critical point of the nonconvex regularized least-squares objective. Finally, we propose an extension to Fienup techniques, based on a projected gradient descent interpretation and acceleration using inertial terms. We demonstrate experimentally that this modification combined with an ${\ell }_1$ prior constitutes a competitive approach for sparse phase retrieval.

References in corpus (1)

• Phase retrieval and saddle-point optimization

Cited by in corpus (12)

• Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction
• Phase Retrieval for Partially Coherent Observations
• Robust Compressive Phase Retrieval via Deep Generative Priors
• Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons
• Fourier Phase Retrieval with Extended Support Estimation via Deep Neural Network
• PDMM: A novel Primal-Dual Majorization-Minimization algorithm for Poisson Phase-Retrieval problem
• Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning
• Frequency-Resolved Optical Gating Recovery via Smoothing Gradient
• Analytical Convergence Regions of Accelerated Gradient Descent in Nonconvex Optimization under Regularity Condition
• Accelerated Gradient Methods for Nonconvex Optimization: Escape Trajectories From Strict Saddle Points and Convergence to Local Minima
• A matrix-free Levenberg-Marquardt algorithm for efficient ptychographic phase retrieval
• Phase retrieval with sparse phase constraint