Physics Augmented U-Net: A High-Frequency Aware Generative Prior for Microscopy

A key challenge in optical microscopy is to image fast at high-resolution. To address this problem, we propose "Physics Augmented U-Net", which combines deep learning and structured illumination microscopy (SIM). In SIM, the structured illumination aliases out-of-band high-frequencies to the passband of the microscope; thus SIM captures some high-frequencies even when the image is sampled at low-resolution. To utilize these features, we propose a three-element method: 1) a modified U-Net model, 2) a physics-based forward model of SIM 3) an inference algorithm combining the two models. The modified U-Net architecture is similar to the seminal work, but the bottleneck is modified by concatenating two latent vectors, one encoding low-frequencies (LFLV), and the other encoding high-frequencies (HFLV). LFLV is learned by U-Net contracting path, and HFLV is learned by a second encoding path. In the inference mode, the high-frequency encoder is removed; HFLV is then optimized to fit the measured microscopy images to the output of the forward model for the generated image by the U-Net. We validated our method on two different datasets under different experimental conditions. Since a latent vector is optimized instead of a 2D image, the inference mode is less computationally complex. The proposed model is also more stable compared to other generative prior-based methods. Finally, as the forward model is independent of the U-Net, Physics Augmented U-Net can enhance resolution on any variation of SIM without further retraining.