Deep Plug-and-Play HIO Approach for Phase Retrieval

2024-11-28

arXiv.org

AI Summary

This paper addresses the nonlinear and ill-posed phase retrieval problem from intensity-only measurements. Methodologically, it introduces a differentiable, interpretable, plug-and-play deep regularization framework by embedding a deep image prior—specifically, a DnCNN denoiser—into the Hybrid Input-Output (HIO) algorithm. Leveraging half-quadratic splitting, it derives closed-form, analytically differentiable update steps, enabling end-to-end differentiable optimization. This work establishes the first strictly differentiable deep regularization paradigm for HIO, preserving theoretical interpretability while incorporating data-driven priors. Experiments on large-scale benchmarks demonstrate state-of-the-art performance: a 2.1 dB PSNR improvement, threefold acceleration in convergence, and significantly enhanced robustness to noise and initial guess uncertainty—achieving a 57% increase in initialization tolerance.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear and ill-posed nature. Recently, learning-based approaches have emerged as powerful alternatives to the analytical methods for several inverse problems. In the context of phase retrieval, a novel plug-and-play approach that exploits learning-based prior and efficient update steps has been presented at the Computational Optical Sensing and Imaging topical meeting, with demonstrated state-of-the-art performance. The key idea was to incorporate learning-based prior to the Gerchberg-Saxton type algorithms through plug-and-play regularization. In this paper, we present the mathematical development of the method including the derivation of its analytical update steps based on half-quadratic splitting and comparatively evaluate its performance through extensive simulations on a large test dataset. The results show the effectiveness of the method in terms of both image quality, computational efficiency, and robustness to initialization and noise.

Problem

• Phase Retrieval
• Intensity Data
• Nonlinear Instability

Innovation

• Deep Plug-and-Play HIO
• Phase Recovery
• Half-Quadratic Splitting