🔬 optics

YOSO: single-frame Gerchberg-Saxton phase retrieval with AI-based data augmentation for in-line holography

YOSO is a single-frame phase retrieval framework for digital in-line holographic microscopy that utilizes AI-based data augmentation to generate multi-height datasets from a single hologram, enabling efficient and generalizable reconstruction via the Gerchberg-Saxton algorithm without the need for patch-and-stitch procedures.

Original authors: Julianna Winnik, Adam Walocha, Wojciech Ogonowski, Wiktor Forjasz, Piotr Arcab, Mikołaj Rogalski, Aleksandra Rutkowska, Marzena Stefaniuk, José Ángel Picazo-Bueno, Vicente Micó, Maciej Trusiak, Maria

Published 2026-05-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Julianna Winnik, Adam Walocha, Wojciech Ogonowski, Wiktor Forjasz, Piotr Arcab, Mikołaj Rogalski, Aleksandra Rutkowska, Marzena Stefaniuk, José Ángel Picazo-Bueno, Vicente Micó, Maciej Trusiak, Maria Cywińska

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to take a photo of a transparent object, like a jellyfish or a human cell, using a very special camera. The problem is, these objects don't block light; they only bend it slightly. To a standard camera, they look invisible.

In the world of Digital In-Line Holography (DIHM), scientists use a trick: they take a picture of the object slightly out of focus. This creates a messy, blurry pattern of light and dark rings (like ripples in a pond). Hidden inside this mess is the shape of the object, but you need a mathematical "decoder" to reveal it.

The traditional decoder, called the Gerchberg-Saxton (GS) algorithm, is very good, but it has a catch: it usually needs two photos taken at different distances to work perfectly. Taking two photos slows things down and makes the equipment complicated. If you only have one photo, the decoder gets confused and produces a "ghost" image (a twin image) that ruins the picture.

Enter YOSO (You Only Shot Once).

The Magic Trick: The AI Assistant

YOSO is a new system that lets you get a perfect 3D reconstruction from just one blurry photo. Here is how it works, using a simple analogy:

Imagine you are trying to guess what a cake looks like inside, but you can only see the top layer.

The Problem: You have one photo of the cake (the hologram). You need a second photo of the cake from a slightly different angle to figure out the 3D shape.
The AI's Job: Instead of taking a second photo, you ask a super-smart AI assistant (a Deep Neural Network) to imagine what that second photo would look like.
The Training: Before you use it, you teach this AI by showing it thousands of computer-generated examples of flowers and natural scenes. You show it: "Here is what this flower looks like from distance A. Now, here is what it looks like from distance B." The AI learns the rules of how light bends (diffraction) without ever seeing a real flower.
The Result: When you give the AI your single blurry photo of a cell, it instantly "dreams up" the second blurry photo that would have been taken at a different distance.

Putting It All Together

Once the AI creates this "imaginary" second photo, YOSO takes the real photo and the AI-generated photo and feeds them into the trusted, old-school Gerchberg-Saxton decoder. Because the decoder now has two photos (one real, one AI-made), it can easily remove the "ghost" images and reveal the clear, sharp 3D structure of the object.

Why YOSO is Special

The paper highlights a few clever features that make YOSO stand out:

It's Fast to Train: Other similar AI systems take all day (18 hours) to learn. YOSO uses a specific type of brain-like architecture (called a multi-scale ResNet) that learns the rules of light in under 2 hours on a standard computer. It's like a student who can master a subject in an afternoon instead of a whole semester.
It Doesn't Need to Cut and Paste: Many AI systems are like a photocopier that can only copy small pieces of paper at a time. You have to cut a large photo into tiny squares, copy them one by one, and tape them back together (a "patch-and-stitch" process). YOSO is like a wide-angle scanner; it can look at a tiny 256-pixel image to learn, but then instantly process a massive, full-size hologram in one go without cutting it up.
It Fills the Gaps Naturally: When computers process images, they often have to add empty borders (padding) to do the math. Traditional methods fill these borders with black or copy the edge pixels, which creates fake artifacts. YOSO is "physics-aware." It knows how light waves behave, so it fills those borders with the correct "ripples" of light, making the math work perfectly.
It Works on Thick Objects: Because YOSO doesn't force the object to be flat, it works great on 3D things like a mouse brain slice or swimming sperm cells. It can even let you "refocus" the image later, as if you were adjusting the focus knob on a microscope after the photo was already taken.

What They Tested It On

The researchers didn't just test this on perfect computer simulations. They tried it on:

A test target (like a ruler for microscopes) to check sharpness.
Human cheek cells (flat cells stuck to a slide).
Mouse brain slices (thick, complex tissue).
Human sperm (swimming, 3D cells).

In every case, YOSO successfully removed the "ghost" images and revealed clear details, proving that you can get high-quality 3D data from a single snapshot using this AI-assisted trick. The code and data are now open for anyone to use.

1. Problem Statement

Digital In-Line Holographic Microscopy (DIHM) is a compact, lensless (or lens-based) imaging technique that retrieves phase information from defocused intensity patterns. However, it faces significant challenges:

The Twin-Image Effect: Single-frame DIHM suffers from the overlap of the true image and a conjugate (twin) image, degrading reconstruction quality.
Single-Frame Limitation: Traditional high-quality phase retrieval (e.g., using the Gerchberg-Saxton (GS) algorithm) requires capturing multiple intensity images at different defocus distances (multi-height). This reduces acquisition speed and increases system complexity.
Deep Learning Limitations: Existing deep learning approaches for single-frame phase retrieval often suffer from:
- Poor Generalization: Models trained on specific samples fail on others.
- Training Efficiency: Architectures like U-Net require long training times (e.g., ~18 hours) and often necessitate "patch-and-stitch" procedures for large images due to fixed input size constraints.
- Complex Coding: Some methods require complex output encoding for complex fields.
- Physics Inconsistency: Standard padding methods (zero-padding) used in deep learning can create physical inconsistencies when fed into physics-based reconstruction algorithms like GS.

2. Methodology: The YOSO Framework

The authors propose YOSO (You Only Shot Once), a hybrid framework that combines supervised deep learning with classical physics-based algorithms.

Core Concept: Instead of using a neural network (DNN) to directly output the final phase, YOSO uses a DNN to numerically generate a second hologram ( $\tilde{I}_2$ ) corresponding to a different defocus distance from a single captured hologram ( $I_1$ ).
The Pipeline:
1. Input: A single physically captured in-line hologram ( $I_1$ ).
2. AI Augmentation: A Multi-scale ResNet (Deep Neural Network) estimates the second hologram ( $\tilde{I}_2$ ) at a different propagation distance ( $z_2$ ).
3. Physics-Based Reconstruction: The pair $(I_1, \tilde{I}_2)$ is fed into the standard Gerchberg-Saxton (GS) algorithm. The GS algorithm iteratively propagates the wavefield between the two planes, enforcing intensity constraints, to retrieve the complex object wave.
4. Output: The final complex field (amplitude and phase) at the object plane.
Key Architectural & Training Innovations:
- Multi-scale ResNet: Unlike U-Net, this architecture uses parallel branches at different spatial resolutions. It allows for variable input sizes, enabling training on small images (e.g., $256 \times 256$ ) and direct inference on full-sized holograms (e.g., $2048 \times 2048$ ) without patch-and-stitching.
- Computer-Generated Training Data: The model is trained on synthetic data derived from natural images (flower images from Kaggle). The network learns to perform diffraction propagation over a specific distance ( $z_2 - z_1$ ) rather than memorizing specific object features, ensuring strong generalization across diverse sample types.
- Physics-Consistent Padding: The DNN is trained to generate hologram padding that respects diffraction physics. This ensures that the padded regions of the estimated hologram ( $\tilde{I}_2$ ) are consistent with the input ( $I_1$ ), a critical requirement for the GS algorithm to function correctly.

3. Key Contributions

Hybrid AI-Physics Approach: YOSO shifts the role of AI from "black-box phase retrieval" to "data augmentation." By using AI only to generate the second frame for a robust GS algorithm, the method minimizes "hallucinations" and leverages the physical guarantees of the GS method.
Efficient and Scalable Architecture: The Multi-scale ResNet enables training in under 2 hours (27 mins on high-end, 75 mins on mid-range hardware) compared to ~18 hours for previous U-Net methods. It also eliminates the need for patch-and-stitch processing.
Superior Generalization: Training on diverse natural images allows the model to handle various sample types (phase objects, absorbing objects, thick biological tissues) without retraining.
3D Compatibility: Because the method operates in defocused planes and does not assume a single object plane, it is inherently compatible with 3D objects and enables subsequent numerical refocusing.

4. Experimental Results

The framework was validated through simulations and experiments on diverse systems (lensless and lens-based DIHM) and samples:

Simulation: YOSO effectively suppressed twin-image artifacts, achieving phase reconstruction quality comparable to standard GS using two physically captured frames (RMSE = 0.022 rad, SSIM = 0.529).
Phase Test Target: YOSO successfully recovered quantitative phase delays (0.66 rad) and outperformed standard GS in low-frequency recovery, likely due to the elimination of alignment errors associated with physical multi-height acquisition.
Human Cheek Cells (Lensless):
- Demonstrated scalability: A model trained on $256 \times 256$ patches successfully reconstructed full $2048 \times 2048$ holograms with high fidelity.
- Demonstrated diffraction-aware padding: The AI-generated padding extended Gabor fringes naturally, unlike zero-padding.
Mouse Brain Slice (Thick Sample): Successfully imaged a thick, non-sparse tissue slice at near-UV wavelengths ( $\lambda = 0.405 \mu m$ ). It clearly resolved anatomical structures (hippocampus, cortex, etc.) and separated phase from amplitude variations, proving applicability to complex, thick biological samples.
Human Sperm (Lens-based, Dynamic): Applied to a high-speed (90 fps) lens-based system. YOSO successfully reconstructed 3D suspended sperm cells and enabled numerical refocusing of out-of-focus cells, demonstrating potential for 4D tracking and holographic tomography.

5. Significance and Impact

Speed and Simplicity: YOSO enables high-quality, twin-image-free phase imaging from a single shot, making it suitable for dynamic processes and high-throughput applications where multi-frame acquisition is impossible.
Robustness: By decoupling the AI from the final phase output and relying on the GS algorithm, the method is more robust against artifacts and alignment errors.
Accessibility: The use of computer-generated data and a fast-training architecture lowers the barrier to entry for implementing advanced phase retrieval, removing the need for laborious ground-truth data collection.
Open Source: The authors have made the software, trained models, and data publicly available, fostering community adoption and further development in computational imaging.

In conclusion, YOSO represents a significant advancement in DIHM by effectively merging the generalization power of deep learning with the physical rigor of the Gerchberg-Saxton algorithm, solving the twin-image problem in single-frame acquisition while maintaining compatibility with 3D samples and numerical post-processing.