DLMMPR:Deep Learning-based Measurement Matrix for Phase Retrieval

2025-11-16

AI Summary

This work addresses the challenge of jointly designing measurement matrices and reconstruction algorithms in phase retrieval. To this end, it introduces learnable optimization into the parameterization of measurement matrices for the first time, proposing an end-to-end trainable framework. Methodologically, it constructs a differentiable measurement matrix architecture integrated with subgradient descent and proximal mapping modules, enabling joint optimization of measurement strategy and reconstruction algorithm, while supporting robust phase recovery under multiple noise models (e.g., Gaussian, Poisson, and mixed noise). Experimental results demonstrate that the proposed method significantly outperforms DeepMMSE and PrComplex in terms of PSNR and SSIM across all tested noise conditions, maintaining consistently high performance. This validates the feasibility and superiority of co-optimizing measurement design and reconstruction in phase retrieval.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

This paper pioneers the integration of learning optimization into measurement matrix design for phase retrieval. We introduce the Deep Learning-based Measurement Matrix for Phase Retrieval (DLMMPR) algorithm, which parameterizes the measurement matrix within an end-to-end deep learning architecture. Synergistically augmented with subgradient descent and proximal mapping modules for robust recovery, DLMMPR's efficacy is decisively confirmed through comprehensive empirical validation across diverse noise regimes. Benchmarked against DeepMMSE and PrComplex, our method yields substantial gains in PSNR and SSIM, underscoring its superiority.

Problem

• Designing optimized measurement matrices for phase retrieval using deep learning
• Integrating subgradient descent and proximal mapping for robust signal recovery
• Improving reconstruction quality under various noise conditions through learned optimization

Innovation

• Deep learning optimizes measurement matrix design
• End-to-end architecture parameterizes the measurement matrix
• Subgradient descent and proximal mapping enhance recovery robustness