Self-supervised learning for phase retrieval

TL;DR

Addressing nonlinear phase retrieval under data-scarce conditions, the paper proposes a self-supervised framework that exploits translation invariance to learn from measurements alone, using the model $y = |A x|^2$. It introduces a reconstruction loss that combines amplitude-based measure consistency with an equivariance term, formalized as $L(\theta) = L_A(\theta) + \lambda L_E(\theta)$ and implemented on a U-Net. Experiments on a MNIST-derived synthetic dataset show that the auto-supervised method can achieve performance close to fully supervised approaches when translations are exploited, particularly at moderate sampling ratios; amplitude-based losses can provide advantages over intensity-based losses. This work demonstrates that translation-invariance based self-supervision is a viable route for nonlinear inverse problems where ground-truth data are scarce, potentially extending to other transformation groups and signal classes.

Abstract

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'. However, in medical and scientific imaging, the lack of fully sampled data limits supervised learning. Recent advances have made it possible to reconstruct images from measurement data alone, eliminating the need for references. However, these methods remain limited to linear problems, excluding non-linear problems such as phase retrieval. We propose a self-supervised method that overcomes this limitation in the case of phase retrieval by using the natural invariance of images to translations.

Figures (2)

• Figure 1: Cosinus similarité en fonction du taux d'échantillonnage $\alpha$ pour la méthode supervisée et les méthodes auto-supervisées.
• Figure 2: Images reconstruites pour les méthodes supervisée, auto-supervisée et pour une résolution par descente de gradient.