Singular value decomposition based under-sampling pattern optimization for MRI reconstruction

Background: Magnetic resonance imaging (MRI) is a crucial medical imaging technique that can determine the structural and functional status of body tissues and organs. However, the prolonged MRI acquisition time increases the scanning cost and limits its use in less developed areas. Purpose: The objective of this study is to design a lightweight, data-driven under-sampling pattern for fastMRI to achieve a balance between MRI reconstruction quality and sampling time while also being able to be integrated with deep learning to further improve reconstruction quality. Methods: In this study, we attempted to establish a connection between k-space and the corresponding MRI through singular value decomposition(SVD). Specifically, we apply SVD to MRI to decouple it into multiple components, which are sorted by energy contribution. Then, the sampling points that match the energy contribution in the k-space, which correspond to each component are selected sequentially. Finally, the sampling points obtained from all components are merged to obtain a mask. This mask can be used directly as a sampler or integrated into deep learning as an initial or fixed sampling points. Results: The experiments were conducted on two public datasets, and the results demonstrate that when the mask generated based on our method is directly used as the sampler, the MRI reconstruction quality surpasses that of state-of-the-art heuristic samplers. In addition, when integrated into the deep learning models, the models converge faster and the sampler performance is significantly improved. Conclusions: The proposed lightweight data-driven sampling approach avoids time-consuming parameter tuning and the establishment of complex mathematical models, achieving a balance between reconstruction quality and sampling time.