Res-U2Net: Untrained Deep Learning for Phase Retrieval and Image Reconstruction

TL;DR

This work tackles the data-demand problem in deep-learning image reconstruction by employing untrained networks that invert a known forward model, introducing Res-U2Net for phase retrieval and 3D surface estimation. The method leverages a Fourier-based forward model and minimizes a loss between measured and predicted intensities $I_z$, training networks (UNet, U2Net, Res-U2Net) without prior data. Quantitatively, Res-U2Net delivers superior 2D phase quality (as shown by BRISQUE and NIQE) and improved 3D mesh accuracy (lower MSE and skewness), particularly under Fourier-Born diffraction, with processing times in the 0.5–5 s range. This physics-informed, untrained approach shows strong potential for efficient phase retrieval and 3D reconstruction in imaging domains where labeled data are scarce, and it points to future extensions using GANs and cross-domain applications across spectral bands.

Abstract

Conventional deep learning-based image reconstruction methods require a large amount of training data which can be hard to obtain in practice. Untrained deep learning methods overcome this limitation by training a network to invert a physical model of the image formation process. Here we present a novel untrained Res-U2Net model for phase retrieval. We use the extracted phase information to determine changes in an object's surface and generate a mesh representation of its 3D structure. We compare the performance of Res-U2Net phase retrieval against UNet and U2Net using images from the GDXRAY dataset.

Figures (8)

• Figure 1: Schematic of the phase retrieval process. An intensity image $I_z(x,y)$ is fed into a neural network, returning an estimate of the near-field phase $\tilde{\theta}(x,y)$. Diffraction model $H_z$ converts the estimated near field phase to an estimated far field intensity profile $\tilde{I_z(x,y)}$. The mean square error (MSE) between $I_z(x,y)$ and $I_z(x,y)^{*}$ serves as a loss function for optimizing the parameters of the neural network.
• Figure 2: Res-U2Net architecture: (a) U2Net model of configuration based on sequence multi-scale, that integrates res-model in the network, (b) Res-UNet model, the encoder extracts features using convolutional layers (Conv2D) with batch normalization, ReLU activation (ResBlock), and spatial resolution reduction via max pooling (MaxPooling2D). This is followed by a decoder assigning phases to the features by upsampling using transpose convolutions (Conv2DTranspose) with skip connections. Residual connections link the encoder and decoder layers to improve the training performance. Finally, a $1\times440\times440$ convolutional layer generates the segmentation mask, resulting in the network output.
• Figure 3: 3D Phase Retrieval: (a) 2D Ray-X test image, (b) 2D phase retrieval estimate, and (c) resulting 3D mesh.
• Figure 4: Examples from the GDXRAY dataset of $440 \times 440$ pixel images.
• Figure 5: 2D Fourier phase retrieval using (a) UNet, (b) U2Net, and (c) Res-U2Net.