Generative Neural Networks for Inverse Problems in Microscopy

This project explores the use of generative models as priors to solve ill-posed inverse problems in imaging, with a focus on microscopy image reconstruction.

We implement and compare:

• A Variational Autoencoder (VAE) baseline using latent space optimization
• A diffusion-based prior (RED-Diff) using a pretrained score-based model

Problem Overview

We consider inverse problems of the form:

$$ y = H(x) + \epsilon $$

where:

• $x$: clean image
• $H$: degradation operator (blur, noise, subsampling)
• $y$: observed corrupted image
• $\epsilon$: observation noise

These problems are typically ill-posed, requiring strong priors to obtain meaningful reconstructions.

Methods

VAE Baseline

• Learns a latent representation of the data
• Reconstruction via optimization in latent space: $$ \hat{z} = \arg\min_z |y - H(G_\theta(z))|^2 + \lambda |z|^2 $$

Diffusion-Based Reconstruction (RED-Diff)

• Uses a pretrained diffusion model as a score-based prior
• Combines data consistency and a learned prior via denoising / score estimation

Dataset

• Microscopy images from PatchCamelyion (PCAM)
• Resolution: 96×96
• Adapted to 128×128 for compatibility with pretrained diffusion models

Setup

Install dependencies:

pip install -r requirements.txt