Poster R17 - Deep image prior-based untrained neural network for single-shot quantitative phase gradient microscopy

Introduction: Quantitative phase imaging (QPI) has become a promising label-free imaging technique due to its ability to provide quantified optical thickness information of transparent objects. QPI measures the phase delay of the object, a product of the refractive index and physical thickness, closely connected to cellular morphology and chemical features. This promotes in-depth understanding of cellular dynamics, such as cell-mass transport, growth rate, and cell death.
Single-shot quantitative phase gradient microscopy (ss-QGPM) enables quantitative phase imaging with only single intensity acquisition based on a conventional differential interference contrast (DIC) microscopy. In ss-QGPM, a quarter-wave plate and polarization camera, which features a polarization filter array arranged in front of CMOS array, replace the analyzer in a DIC microscope. This configuration allows for the phase gradient recovery from a single intensity acquisition, and subsequent application of a dedicated least-squares algorithm reconstruct the quantitative phase image.
Deep neural networks (DNNs) have recently demonstrated significant potential in solving nonlinear inverse problems. By utilizing large datasets and end-to-end training, DNNs have become powerful tools for quantitative phase imaging, providing high-accuracy phase retrieval . However, the performance of these networks is heavily dependent on the consistency between training and experimental datasets. An innovative approach involves untrained neural network (UNN), inspired by the deep image prior (DIP), which have shown promise in integrating a physical model with a DNN to overcome this challenge. Here, we propose a UNN-based phase retrieval for ss-QPGM that facilitates quantitative phase imaging by incorporating a numerical forward imaging model without requiring ground-truth data.

Materials and

Methods: Figure 1(a) illustrates the schematic of single-shot quantitative phase gradient microscopy (ss-QGPM). In this setup, a quarter-wave plate replaces the analyzer in a conventional differential interference contrast (DIC) microscope, and a polarization camera (PCMOS) is used to compute multiple phase-shifted images from a single intensity measurement. The raw intensity image is decomposed into four distinct directional polarization images (0°, 45°, 90°, 135°) through a polarization demosaicing process. From these decomposed images, the phase gradient can be computed using a conventional phase-shifting algorithm.
Figure 1(b) depicts the phase retrieval process using a deep image prior-inspired untrained neural network (UNN) approach for quantitative phase reconstruction. The input to the UNN is the phase gradient computed from the raw intensity measurements. An encoder-decoder style U-net model is employed to estimate the reconstructed phase as an output. The estimated quantitative phase is subsequently passed through the nonlinear forward imaging model to generate the estimated phase gradient. The loss between the estimated phase gradient and the measured phase gradient is computed and the weights of the U-net model are updated iteratively. A combination of mean-square-error (MSE) and total-variation loss function is used for iteratively training the model. Notably, the training does not involve any large training data, hence, it needs to be trained for each image separately.

Results, Conclusions, and Discussions: To assess the validity of the proposed UNN-based ss-QGPM imaging method, we used a phase target. Figure 2 shows the representative UNN-based phase-retrieved image of the phase target and profiles along the blue lines. We adopted Tikhonov regularization, a common approach for solving ill-posed problems, to compare the results of both methods. The phase profiles recovered by the conventional Tikhonov regularization method and the expected phase delays are presented for comparison, indicated by red lines and black dashed lines, respectively. The UNN-based ss-QGPM produced an accurate phase image, while the Tikhonov regularization method exhibited large errors, particularly in the high-frequency features of objects and the background.
We presented a self-supervised learning method based on UNN to reconstruct quantitative phase images from a single intensity acquisition in ss-QPGM. The proposed method achieved high-accuracy phase imaging over both low- and high-spatial frequency information. We demonstrated phase imaging for a pre-calibrated phase target, comparing it to the traditional image reconstruction method. The proposed method can be applied to learning-based models to increase phase retrieval efficiency for larger datasets, enabling the monitoring of live cellular dynamics.
In conclusion, our UNN-based ss-QPGM, approach offers a robust and accurate solution for quantitative phase imaging. By leveraging the strengths of self-supervised learning and model-based learning approaches, this method enhances the phase retrieval performance and provides reliable imaging for various applications, including live cell mass transportation, and drug response.

Acknowledgements (Optional): This research was supported by the National Institutes of Health under award number P41EB031772.