基于深度学习测量矩阵的去模糊相位恢复

Deep Learning Measurement Matrix for Deblurring Phase Retrieval

摘要: 光学成像系统中由相位缺失、 高斯噪声以及物理退化引起的模糊效应，本文提出了一种基于深度 学习的去模糊相位恢复算法(DLMMPR-DB)。 首先，本文将模糊相位恢复问题建模为含噪非线 性观测方程的正则化优化模型，并利用循环矩阵的对角化特性，推导出频域加速的次梯度显式表 达式。 在此基础上，本文在DLMMPR 框架中引入模糊算子建模，设计了包含模糊核建模、频域 梯度计算、 梯度更新及稀疏先验约束的四阶段端到端网络架构。 该网络通过空域与频域的交替计 算，有效解捐了去模糊与相位恢复的复杂关联。 实验结果表明，DLMMPR-DB 算法在处理高度 退化的成像数据时，能够显著提升信号重建的PSNR 与SSIM 指标，在保持较低计算复杂度的同 时，实现了精度与效率的平衡。

Abstract: To address the blur effects caused by phase loss, Gaussian noise, and physical degrada- tions in optical imaging systems, this paper proposes a deep learning-based deblurring phase retrieval algorithm, termed DLMMPR-DB. First, the deblurring phase retrieval problem is formulated as a regularized optimization model involving a noisy nonlinear observation equation. By leveraging the diagonalization property of circulant matrices, an explicitly expressed subgradient is derived in the frequency domain to accelerate the computation. Building upon this, we introduce blur operator modeling into the DLMMPR framework and design a four-stage end-to-end network architecture, which consists of a blur kernel modeling layer, a frequency-domain gradient calculation layer, a gradient descent update layer, and a sparse prior constraint layer. Through alternat- ing computations between the spatial and frequency domains, the network effectively decouples the complex correlation between deblurring and phase retrieval. Experi- mental results demonstrate that the proposed DLMMPR-DB algorithm significantly improves reconstruction performance in terms of PSNR and SSIM when processing highly degraded imaging data. While maintaining low computational complexity, the algorithm achieves an optimal balance between reconstruction accuracy and efficiency.