Diffusion model-based approaches recently achieved re-markable success in MRI reconstruction, but integration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is partic-ularly notable when directly apply conventional diffusion process to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. To tackle these challenges, we introduce subspace diffusion model with orthogonal decomposition, a method (referred to as Sub-DM) that restrict the diffusion process via projections onto subspace as the k-space data distribution evolves toward noise. Particularly, the subspace diffusion model circumvents the inference challenges posed by the com-plex and high-dimensional characteristics of k-space data, so the highly compact subspace ensures that diffusion process requires only a few simple iterations to produce accurate prior information. Furthermore, the orthogonal decomposition strategy based on wavelet transform hin-ders the information loss during the migration of the vanilla diffusion process to the subspace. Considering the strate-gy is approximately reversible, such that the entire pro-cess can be reversed. As a result, it allows the diffusion processes in different spaces to refine models through a mutual feedback mechanism, enabling the learning of ac-curate prior even when dealing with complex k-space data. Comprehensive experiments on different datasets clearly demonstrate that the superiority of Sub-DM against state of-the-art methods in terms of reconstruction speed and quality.

Abstract: This chapter provides an overview of deep learning techniques for improving the spatial resolution of MRI, ranging from convolutional neural networks, generative adversarial networks, to more advanced models including transformers, diffusion models, and implicit neural representations. Our exploration extends beyond the methodologies to scrutinize the impact of super-resolved images on clinical and neuroscientific assessments. We also cover various practical topics such as network architectures, image evaluation metrics, network loss functions, and training data specifics--including downsampling methods for simulating lowresolution images and dataset selection. Finally, we discuss existing challenges and potential future directions regarding the feasibility and reliability of deep learning-based MRI superresolution, with the aim to facilitate its wider adoption to benefit various clinical and neuroscientific applications. Keywords: Single-image super-resolution, deep learning, convolutional neural network, generative adversarial network, transformer, diffusion model, implicit neural representation, loss function, transfer learning, uncertainty estimation. Introduction MRI with higher spatial resolution provides more detailed insights into the structure and function of living human bodies non-invasively, which is highly desirable for accurate clinical diagnosis and image analysis. The spatial resolution of MRI is characterized by in-plane and through-plane resolutions (Figure 1). On the other hand, the through-plane resolution, also referred to as slice thickness, is determined differently for 2D and 3D imaging. In 2D imaging, the slice thickness is defined by the full width at half maximum (FWHM) of the slice-selection radiofrequency (RF) pulse profile. In 3D imaging, the slice-selection direction is encoded by another phase encoding gradient. Consequently, the through-plane resolution is determined similarly to the in-plane resolution by the maximal extent of the k-space along slice-selection direction as in Eq. 1. The in-plane resolution is dictated by the k-space coverage, and a larger k-space coverage brings higher spatial resolution (a). The slice thickness is determined by the slice-selective RF pulse for 2D imaging, and by k-space extent along sliceselection direction for 3D imaging (b).

Dropout is conventionally used during the training phase as regularization method and for quantifying uncertainty in deep learning. We propose to use dropout during training as well as inference steps, and average multiple predictions to improve the accuracy, while reducing and quantifying the uncertainty. The results are evaluated for fractional anisotropy (FA) and mean diffusivity (MD) maps which are obtained from only 3 direction scans. With our method, accuracy can be improved significantly compared to network outputs without dropout, especially when the training dataset is small. Moreover, confidence maps are generated which may aid in diagnosis of unseen pathology or artifacts.