Low Photon Count Phase Retrieval Using Deep Learning (1806.10029v1)

Abstract: Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to recover objects illuminated with weak light and demonstrate better performance than with the classical Gerchberg-Saxton phase retrieval algorithm for equivalent signal over noise ratio. Prior knowledge about the object is implicitly contained in the training data set and feature detection is possible for a signal over noise ratio close to one. We apply this principle to a phase retrieval problem and show successful recovery of the object's most salient features with as little as one photon per detector pixel on average in the illumination beam. We also show that the phase reconstruction is significantly improved by training the neural network with an initial estimate of the object, as opposed as training it with the raw intensity measurement.

• The paper demonstrates using deep neural networks (DNNs) for phase retrieval in challenging low-light conditions heavily affected by shot noise.
• DNNs significantly outperform the traditional Gerchberg-Saxton algorithm, successfully reconstructing objects with average photon counts as low as one per detector pixel.
• This research has practical implications for improving low-light imaging systems in fields like remote sensing, medical imaging, and microscopy.

Low Photon Count Phase Retrieval Using Deep Learning

The paper "Low Photon Count Phase Retrieval Using Deep Learning" presents an experimental demonstration of using deep neural networks (DNNs) for phase retrieval under conditions of low light intensity, significantly affected by shot noise. This research tackles a recurrent challenge in imaging systems, particularly the retrieval of phase information when illumination power is minimal. In low-light scenarios, the intensification of shot noise requires effective regularization techniques to enhance image reconstruction. Traditional algorithms like Gerchberg-Saxton struggle under these conditions, prompting the exploration of alternative methods.

Key Findings

The paper introduces a DNN-based approach that utilizes prior knowledge embedded within training datasets to effectively retrieve salient object features even when the signal-to-noise ratio (SNR) approaches unity. It demonstrates that DNNs outperform the Gerchberg-Saxton algorithm in reconstructing objects when the photon count on average is as low as one per detector pixel. The findings suggest that DNN training can further be enhanced by using an initial object estimate, rather than relying solely on raw intensity measurements.

Experimental Approach

The authors implemented two sets of databases for training: Integrated Circuit (IC) layouts, which represent a constrained feature set, and the ImageNet dataset, which embodies more diverse image features. Experiments involved capturing images under various noise levels, where the photon count ranged from 1050 down to 0.25 photons per pixel on average. The optical setup utilized a spatial light modulator (SLM) to impart phase shifts to the illuminating beam, and results showed significant diffusion of noise effects using DNNs compared to traditional methods.

Numerical Analysis

Quantitative measurements using the Pearson correlation coefficient (PCC) confirmed that the DNN reconstructions could achieve better visual quality than established methods, even in scenarios of minimum photon detection. The "physics-informed" method, which incorporates knowledge of Fresnel propagation within the training phase, demonstrated superior performance across all photon levels compared to the "end-to-end" method. Both approaches consistently outperformed the classical Gerchberg-Saxton algorithm, affirming the efficiency of deep learning in adaptive regularization.

Practical and Theoretical Implications

This research has practical implications for enhancing imaging systems that operate in low-light environments, such as remote sensing, medical imaging, and microscopy. Theoretical contributions include advancing the understanding of adaptive regularization methods using DNNs to process shot noise. Future developments might focus on optimizing DNN architectures to further improve phase estimation fidelity and expand applicability to broader classes of imaging challenges.

Future Prospects

As DNNs continue to evolve, incorporating deeper layers and more sophisticated learning procedures, there can be substantial benefits in resolving ill-posed problems characterized by intrinsic noise. The adaptability of deep learning models in bridging the gap between measurement and ground truth through implicit prior knowledge encapsulates potential for breakthroughs in AI-assisted image processing domains, paving the way for enhanced precision in scientific and technological imaging applications. This paper lays foundational work for utilizing AI in complex image reconstruction tasks and encourages the integration of physical laws into DNN training paradigms for improved outcomes.