MRG rekonstrüksiyonu için difüzyon köprüleri

Magnetic Resonance Imaging (MRI) reconstruction typically involves a dealiasing process to transform undersampled data into fully-sampled data. However, conventional diffusion priors perform a denoising transformation, starting from a state of Gaussian noise and ending with fully-sampled data. Since the aliasing artifacts associated with many k-space sampling patterns have spatial structures that differ significantly from white Gaussian noise, this denoising process can lead to reconstruction errors due to suboptimal suppression of artifacts. To overcome this limitation, we introduce the first Fourier-constrained diffusion bridge (FDB) for MRI reconstruction. Unlike task-agnostic diffusion priors, the FDB is specifically designed to perform a dealiasing transformation, starting with undersampled data and ending with fully-sampled data. The starting point is created using a novel stochastic degradation operator that removes a randomly selected, progressively increasing set of spatial frequencies. Unlike diffusion priors that start from a heavily degraded state, the FDB uses a moderately undersampled starting point to enhance the reverse diffusion sampling process. Furthermore, unlike existing diffusion bridges that degrade data based on a weighted average of the start and end points, the FDB uses a binary removal of k-space points, aligning more closely with the nature of accelerated MRI acquisitions. To further enhance image quality, the FDB employs a novel sampling algorithm based on a learned correction term, enabling soft dealiasing by continuously refining estimates of the recovered k-space data during reverse diffusion steps. Tests on brain MRI show that the FDB outperforms competing non-diffusion priors by 4.8 dB PSNR and 11.8% SSIM, and diffusion priors by 4.7 dB PSNR and 6.6% SSIM.