MRI Reconstruction with Regularized 3D Diffusion Model (R3DM)

In order to speed up the acquisition time, MRI instruments acquire sub-sampled k-space data, a technique where only a fraction of the total k-space data points are sampled during the imaging process. Several attempts have been proposed to develop two-dimensional (2D) and three-dimensional (3D) image reconstruction techniques for sub-sampled k-space, as discussed in [11, 13, 31]. Advancements in 3D MR imaging methods can address the challenges posed by complex anatomical structures of human organs and plant growths. Consequently, the demand for developing 3D MR image reconstruction methods has intensified. Currently, most works reconstruct a 3D volumetric image by stacking 2D reconstructions because MR images are acquired slice by slice. This method doesn't consider the inter-dependency between the slices, thus can lead to inconsistencies and artifacts, as discussed in [4, 8, 50]. This particularly affects datasets that have equally distributed information and structures with high continuity on all dimensions, such as roots and vessels [4, 38, 50]. Before the deep learning-based models, which learn the data-driven prior, the model-based iterative reconstruction method proved its effectiveness in the 3D MRI reconstruction problem [15, 54]. The problem is formulated as an optimization problem where a data consistency term is applied to ensure fidelity, and a regularisation term, such as the Total Variation (TV) penalty [24] is utilized to provide general prior knowledge of MRI data.