CDiffMR: Can We Replace the Gaussian Noise with K-Space Undersampling
  for Fast MRI?
Jiahao Huang Angelica Aviles-Rivero Carola-Bibiane Schönlieb Guang Yang
Deep learning has shown the capability to substantially accelerate MRI
reconstruction while acquiring fewer measurements. Recently, diffusion models
have gained burgeoning interests as a novel group of deep learning-based
generative methods. These methods seek to sample data points that belong to a
target distribution from a Gaussian distribution, which has been successfully
extended to MRI reconstruction. In this work, we proposed a Cold
Diffusion-based MRI reconstruction method called CDiffMR. Different from
conventional diffusion models, the degradation operation of our CDiffMR is
based on \textit{k}-space undersampling instead of adding Gaussian noise, and
the restoration network is trained to harness a de-aliaseing function. We also
design starting point and data consistency conditioning strategies to guide and
accelerate the reverse process. More intriguingly, the pre-trained CDiffMR
model can be reused for reconstruction tasks with different undersampling
rates. We demonstrated, through extensive numerical and visual experiments,
that the proposed CDiffMR can achieve comparable or even superior
reconstruction results than state-of-the-art models. Compared to the diffusion
model-based counterpart, CDiffMR reaches readily competing results using only
$1.6 \sim 3.4\%$ for inference time. The code is publicly available at
https://github.com/ayanglab/CDiffMR.