Low-light phase retrieval with implicit generative priors

TL;DR

This work addresses low-dose phase retrieval for CDI by introducing LoDIP, a single-image method that couples a high-dose static region with implicit generative priors to suppress shot noise while preserving resolution. The forward model incorporates the static region via $Y = \left| \mathcal{F}(X+U) \right|^2$, and reconstruction is achieved by optimizing over a CNN-based generator $g_{\mathbf{W}}$ with the constraint $(1-S_{0}) \odot X = 0$, effectively regularizing the inverse problem in a data-scarce regime. Across simulated natural images, biological cells, and experimental data, LoDIP outperforms or matches state-of-the-art methods (e.g., HIO-stat, GPS) in PSNR, SSIM, and $R_F$, while enabling robust single-pattern reconstructions at very low photon counts. The approach promises practical impact for dose-sensitive imaging domains, such as biological specimens and organic materials, by delivering high-quality reconstructions with minimal data requirements and tuning.

Abstract

Phase retrieval (PR) is fundamentally important in scientific imaging and is crucial for nanoscale techniques like coherent diffractive imaging (CDI). Low radiation dose imaging is essential for applications involving radiation-sensitive samples. However, most PR methods struggle in low-dose scenarios due to high shot noise. Recent advancements in optical data acquisition setups, such as in-situ CDI, have shown promise for low-dose imaging, but they rely on a time series of measurements, making them unsuitable for single-image applications. Similarly, data-driven phase retrieval techniques are not easily adaptable to data-scarce situations. Zero-shot deep learning methods based on pre-trained and implicit generative priors have been effective in various imaging tasks but have shown limited success in PR. In this work, we propose low-dose deep image prior (LoDIP), which combines in-situ CDI with the power of implicit generative priors to address single-image low-dose phase retrieval. Quantitative evaluations demonstrate LoDIP's superior performance in this task and its applicability to real experimental scenarios.

Figures (7)

• Figure 1: Examples from the simulated data at different levels of illumination of the sample region as measured in photons per pixel (Np/px). [Left] The first two columns are the diffraction pattern and the image sample without a static structure. [Right] And the last two columns are the same sample with a static region. [Top] The first row has a high illumination of 80k Np/px on both the sample and the static region. [Bottom] Whereas the second row has a high illumination of 80k Np/px on the static region and a low illumination of 800 Np/px on the sample. At lower illumination levels (bottom row), the sample exhibits significantly reduced pixel values. Lesser illumination results in higher presence of Poisson noise. Thus different illumination levels correspond to different levels of noise.
• Figure 2: Coherent Diffraction Imaging (CDI) employs a coherent X-ray beam directed at a sample, capturing the resulting diffraction pattern on a 2D detector. A computational algorithm is then applied to reconstruct the desired sample image. (Left) Inspired by in-situ CDI lo2018situ, LoDIP introduces two modifications to the CDI setup. First, it involves imaging the sample alongside a static region. Secondly, the static region is exposed to a high radiation dose, while the sample's exposure is significantly reduced. A customized sample grid and holder is used with an attenuator placed on top of the sample to reduce the incident radiation dose on the sample. (Center) In the computational step, LoDIP takes both the diffraction pattern and an estimated reconstruction of the static region as inputs, generating a sample reconstruction as its output. (Right) LoDIP uses the output of an implicit generative model $g_{w}$ as an estimate of the sample $\hat{X}$ and iteratively updates the generator parameters $w$ to refine the estimate.
• Figure 3: Experimental Results on simulated data. Left: Reconstruction of Low Resolution Set images for 800 Np/pixel (Top rows) and 80 Np/pixel (Bottom rows). Right: Reconstruction of High Resolution Set images for 800 Np/pixel (Top rows) and 80 Np/pixel (Bottom rows). Each image shows a zoomed-in view of only the sample region.
• Figure 4: Experimental Results on biological cell sample. (Top row) Reconstruction at 800 Np/pixel. (Bottom row) Reconstruction at 80 Np/pixel).
• Figure 5: Comparison of FRC values for GPS and LoDIP reconstructions on biological cell at 800 Np/px and 80 Np/px.