Generalizable Holographic Reconstruction via Amplitude-Only Diffusion Priors

TL;DR

Phase retrieval in inline holography is ill-posed due to nonlinear amplitude–phase coupling. The authors introduce an off-the-shelf diffusion-prior approach trained only on amplitude data to jointly recover amplitude and phase from diffraction intensities, using a predictor–corrector sampler with decoupled likelihood gradients for amplitude and phase. The method generalizes robustly across object shapes, imaging configurations, and even cross-modality scenarios, including lensless on-chip imaging, without ground-truth phase data for training. This diffusion-based framework offers a scalable, cost-effective solution for nonlinear inverse problems in coherent imaging and has potential applications beyond holography to other diffraction and holographic modalities.

Abstract

Phase retrieval in inline holography is a fundamental yet ill-posed inverse problem due to the nonlinear coupling between amplitude and phase in coherent imaging. We present a novel off-the-shelf solution that leverages a diffusion model trained solely on object amplitude to recover both amplitude and phase from diffraction intensities. Using a predictor-corrector sampling framework with separate likelihood gradients for amplitude and phase, our method enables complex field reconstruction without requiring ground-truth phase data for training. We validate the proposed approach through extensive simulations and experiments, demonstrating robust generalization across diverse object shapes, imaging system configurations, and modalities, including lensless setups. Notably, a diffusion prior trained on simple amplitude data (e.g., polystyrene beads) successfully reconstructs complex biological tissue structures, highlighting the method's adaptability. This framework provides a cost-effective, generalizable solution for nonlinear inverse problems in computational imaging, and establishes a foundation for broader coherent imaging applications beyond holography.

Figures (9)

• Figure 1: Overall schemtic of the proposed method.a. The object domain comprises both amplitude and phase components, whereas the measurement domain contains only diffraction intensity patterns. b. During training, low-dimensional amplitude images are used to learn a diffusion prior $S_{\theta^*}$, without requiring paired phase information. c. At inference time, the proposed method operates as an off-the-shelf model for complex amplitude reconstruction, demonstrating strong generalization across object shapes, imaging hardware, and even cross-modality scenarios.
• Figure 2: Reconstructed complex amplitudes given diffraction intensities.a. The proposed method effectively reconstructs the object field of polystyrene beads, regardless of the sample-to-sensor distance, using only two diffraction intensities. The scale bar in the full field of view indicates 10$\mu$m and the scale bar in insets indicates 1$\mu$m. b, c. The object amplitude and phase profiles along the white dotted lines on insets in a. d. The proposed method also works with tissue sections, even for the types that are not shown by the model during the training. The scale bar in the full field of view indicates 20$\mu$m and the scale bar in insets indicates 2$\mu$m. e, f. The object amplitude and phase profiles along the white dotted lines on insets in d. Red, Yellow: ours, Blue: Ground Truth.
• Figure 3: Reconstruction comparison with the existing methods. The target tissue section is the human appendix. The profile on the left-bottom side denotes the phase profile along a white dotted line on each field of view. a. Diffraction intensity measured at $15mm$. The scale bar indicates 20$\mu$m. b. Multi-height reconstruction. c. Deep Decoder reconstruction. d. Ground truth is measured by the off-axis holography. f. Deep Image Prior reconstruction. g. Proposed method reconstruction.
• Figure 4: Shape generalization capacity of the proposed method.a. An example of polystyrene bead amplitude for the training and tissue section diffraction intensity for the inference. b. The proposed method trained on bead amplitudes generates random bead amplitude images for both amplitude and phase without conditions (the top row). However, the method generates tissue complex amplitude when conditions are given for the inference (the bottom row). c, d. Reconstructed phases of the small bowel and appendix by the proposed method trained with bead amplitude. The scale bar indicates 20$\mu$m. e, f. Phase profile along the white dotted line on c and d.The insets correspond to the white box in the full field of view.
• Figure 5: Analaysis of shape generalization of the proposed method.a. The proposed method reconstructs the object field where the diffraction intensities are synthesized by incorporating distinct amplitude and phase pairs. b. Ablation Study: Comparison of the reconstructed complex amplitude corresponding to the synthesized measurement. The reconstruction is shown for: (Top) A randomly initialized diffusion model (i.e., without a diffusion prior), and (Bottom) Applying the Tweedie's formula during the reconstruction procedure to estimate the clean phase image $\hat{x}_0^p$. c. Visualization of the sampling trajectory for the proposed method and the two ablation cases detailed in b (w/o diffusion prior and w/ tweedie for phase).