Theory and Practice of Diffusion Models in Medical Imaging and Inverse Problems

This research project, in collaboration with Dr. Hassan Mohy-ud-Din (Website) and informally with Dr. Muhammad Tahir, investigates both the theoretical and practical dimensions of diffusion models, with a particular emphasis on medical imaging, inverse problems, and signal processing.

• Extensive Survey: We are undertaking a comprehensive survey that compiles recent advancements in diffusion models specifically designed for inverse problems. This includes notable algorithms such as BIRD, DPS, Blind-DPS, and ReSample, each uniquely addressing the challenges posed by inverse problems through diffusion methodologies.

• Addressing Medical Imaging Challenges: The survey highlights critical challenges in medical imaging, such as data reconstruction from (non)linear degradations, including issues of low resolution, deblurring, phase retrieval, artifact removal, and high-dimensionality. We will discuss how diffusion models can effectively address these issues, leveraging techniques like unsupervised (conditional) fine-tuning, plug-and-play methods that utilize pretrained restoration modules or generative priors, cross-modality learning, and latent space optimizations (e.g., ControlNet, StableSR, MedSyn, SDSeg, CoDi, DiffBR, ADD).

• Conditional Medical Image Segmentation: A primary objective of this research is to advance “conditional medical image segmentation,” where conditions may range from text prompts to volume slices. This initiative aims to enable more complex multi-class segmentations, particularly in applications like Cardiac MRI, with the potential to alleviate the computational demands associated with high-dimensional 2D and 3D segmentation tasks.

• Ongoing Work: This project is actively progressing, and a work-in-progress survey is accessible here.