  We propose a novel and unified method, measurement-conditioned denoising
diffusion probabilistic model (MC-DDPM), for under-sampled medical image
reconstruction based on DDPM. Different from previous works, MC-DDPM is defined
in measurement domain (e.g. k-space in MRI reconstruction) and conditioned on
under-sampling mask. We apply this method to accelerate MRI reconstruction and
the experimental results show excellent performance, outperforming full
supervision baseline and the state-of-the-art score-based reconstruction
method. Due to its generative nature, MC-DDPM can also quantify the uncertainty
of reconstruction. Our code is available on github.
