FPM2Stain Net: physics-guided super-resolution and multi-modal virtual staining for digital histopathology

We propose FPM2Stain Net, a jointly optimized end-to-end computational pipeline that integrates physics-guided super-resolution with deep learning-based virtual staining to enable high-resolution, multi-modal digital histopathology. The first stage, bidirectional physics-based Fourier ptychographic microscopy (BiP-FPM), reconstructs high-resolution amplitude and phase maps from a multi-LED FPM image stack using a self-supervised ResNet-U-Net guided by a differentiable point spread function (PSF) model with learnable pupil correction and bidirectional physics-consistent constraints. The second stage employs a multi-task conditional generative adversarial network (cGAN) enhanced with wavelet-based spatial-frequency fusion and perceptual supervision to synthesize clinically relevant staining modalities, including H&E, DAPI, LAP2, and panCK. Extensive experiments on both simulated and real tissue datasets demonstrate that FPM2Stain Net outperforms conventional FPM, GAN-based methods, and diffusion-based models in both reconstruction fidelity and staining accuracy. The synthesized virtual stains not only preserve fine structural details but also enable downstream analysis, such as cell segmentation and biomarker quantification, with higher accuracy than using images acquired with a conventional 40× objective microscope. These results confirm that FPM2Stain Net achieves a greater-than-10× pixel-level upsampling factor relative to the low-magnification (4×) input image, and provides a fast, scalable, and cost-effective alternative to chemical staining in digital pathology, multiplex imaging, and point-of-care diagnostics.