prDeep: Robust Phase Retrieval with a Flexible Deep Network (1803.00212v2)

Abstract: Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models. A MatConvNet implementation of prDeep is available at https://github.com/ricedsp/prDeep.

• The paper introduces prDeep, a novel phase retrieval method combining robust optimization via the RED framework with a deep learning denoiser (DnCNN).
• prDeep leverages the prRED algorithm, an adaptation of Regularization by Denousing, which provides flexibility across various measurement models including Fourier measurements.
• Experimental evaluation shows prDeep offers superior robustness in noisy environments and flexibility in handling diverse system models compared to existing phase retrieval algorithms.

prDeep: Robust Phase Retrieval with a Flexible Deep Network

Phase retrieval (PR) algorithms serve as essential tools in computational imaging, addressing the challenge of reconstructing signals from phaseless measurements. The paper "prDeep: Robust Phase Retrieval with a Flexible Deep Network" presents prDeep, a novel approach combining robust phase retrieval with a deep learning component to address the limitations faced by traditional algorithms in noisy environments.

Problem Definition and Challenges

The PR problem is defined as recovering a vectorized signal $x$ from measurements $y$ in the form $y = |\mathbf{A} x| + w$, where $\mathbf{A}$ is the measurement matrix, and $w$ represents the noise. PR is a well-known problem in various applications such as microscopy, crystallography, astronomical imaging, and inverse scattering. However, traditional PR algorithms often have diminished performance under noisy conditions or are limited by the measurement models they support, typically confined to Gaussian or coded diffraction patterns.

Technical Contributions

The paper introduces two primary technical contributions. Firstly, it adapts the Regularization by Denoising (RED) framework for phase retrieval, resulting in the prRED algorithm. prRED leverages the flexibility of RED, accommodating various measurement models including Fourier measurements, and significantly improving robustness to noise. Secondly, the authors combine prRED with the DnCNN convolutional neural network, forming prDeep, a powerful solution for PR challenges. DnCNN acts as a denoiser within RED, enabling prDeep to utilize learned priors effectively.

Experimental Evaluation

Through simulation tests, prDeep demonstrates superior robustness in noisy environments and flexibility in handling diverse system models compared to existing PR algorithms. The comparisons are carried out using coded diffraction patterns and Fourier measurements, with prDeep consistently outperforming traditional methods in terms of reconstruction quality and computational efficiency in scenarios with high levels of Poisson noise.

Implications and Future Directions

The integration of neural networks within a traditional optimization framework, showcased by prDeep, highlights the potential of combining deep learning with established algorithmic approaches to enhance robustness and performance across various PR scenarios. This paper sets a precedent for future research in adapting complex signal priors via deep learning models for broader inverse problems in computational imaging.

An important future direction is extending prDeep to manage complex-valued targets, expanding its applicability and further leveraging the strengths of deep learning in solving PR problems efficiently. Additionally, refining the initialization process and exploring alternative neural network architectures may yield further improvements in computational speed and reconstruction fidelity.

Overall, prDeep marks a significant advancement in phase retrieval, demonstrating the efficacy of deep learning-assisted optimization approaches in overcoming longstanding challenges associated with noise and measurement model limitations.