DDPM_MRI

A practical tutorial demonstrating score-based diffusion models (DDPM) for accelerated MRI reconstruction — with k-space data conditioning and optional data consistency (DC) enforcement, applied to mask undersampling on the CMRxRecon dataset.

MRI Reconstruction with Diffusion Models

A hands-on workshop notebook demonstrating accelerated MRI reconstruction using a Denoising Diffusion Probabilistic Model (DDPM). Notebook used in the context of the IDRE-ECR workshop: https://idre.ucla.edu/calendar-event/physic-informed-diffusion-models-for-medical-imaging

Author: Thomas Coudert

Collaborators: Amit Rand, Zhengyang Ming
IDRE Workshop

---

Overview

This notebook shows how a conditioned DDPM trained on the CMRxRecon cardiac MRI dataset can reconstruct high-quality images from undersampled k-space, with optional hard k-space data consistency (DC) enforcement.

The pretrained model can be load directly via the notebook cell.

---

Workflow

Fully-sampled k-space from val set 
       │
       │  ← apply undersampling mask  (Cartesian / Radial / Poisson)
       ▼
Undersampled k-space  →  Zero-filled reconstructed image  (aliased, blurry)
       │
       │  ← reverse DDPM sampling (500 steps) with/w.o Data Consistency
       ▼
DDPM Reconstruction  VS  Ground truth

---

Key Concepts

Concept	Description
Forward diffusion	Adds Gaussian noise to the missing k-space region over T steps
Reverse diffusion	Iteratively denoises from pure Gaussian noise using a UNet that predicts $\hat{\varepsilon}$
Data conditioning	The observed (undersampled) image is concatenated as UNet input channels at every step — the model cannot hallucinate away from acquired data
Hard Data Consistency (DC)	At each reverse step: FFT the current estimate, replace sampled lines with the measured k-space, then IFFT back — enforces strict fidelity to raw measurements
Mask choice	Cartesian, Radial, and Poisson patterns produce different aliasing; incoherent patterns (Poisson, Radial) are generally easier for the model to remove

---

Notebook Contents

Section	Description
0 — Imports & Paths	Setup, paths, model hyper-parameters
1 — Download the Pretrained Model	Auto-download checkpoint from Dropbox (~400 MB)
2 — Load the Example Slice	Load provided cardiac k-space slice + RSS ground truth visualisation
3 — Choose an Undersampling Strategy	Select Cartesian / Radial / Poisson mask and acceleration factor
4 — Load the Pretrained DDPM	Build UNet, load checkpoint weights
5 — Visualise the Noise Schedule	Cosine beta schedule: signal & noise mixing coefficients
6 — Run the Diffusion Reconstruction	Full reverse diffusion chain (dc_mode='none')
6b — Results	Side-by-side comparison: GT / zero-filled / DDPM + error maps + PSNR/NMSE
7 — Hard K-space Data Consistency	Enforce measured k-space at every denoising step (dc_mode='hard')
8 — Visualise the Denoising Trajectory	Watch the image emerge from noise (workshop demo)
9 — Summary	Take-home messages

---

Requirements

• Python 3.8+
• PyTorch
• CMRxRecon validation data correctely preprocessed or slice example (provided here)
• Pretrained DDPM checkpoint (downloaded from dropbox in the notebook)

---

Citation

If you use this work, please acknowledge this workshop material.