K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets

作者：Frederic Wang, Han Qi, Alfredo De Goyeneche, Reinhard Heckel, Michael Lustig, Efrat Shimron · 发表于：PubMed · 年份：2023 · DOI：10.48550/arxiv.2308.02958 · 被引用次数：1 · 研究领域：Medical Imaging Techniques and Applications、Advanced MRI Techniques and Applications、Sparse and Compressive Sensing Techniques

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI), where acquisition of high-resolution fully sampled k-space data is impractical. We introduce a novel mathematical framework, dubbed k-band, that enables training DL models using only partial, limited-resolution k-space data. Specifically, we introduce training with stochastic gradient descent (SGD) over k-space subsets. In each training iteration, rather than using the fully sampled k-space for computing gradients, we use only a small k-space portion. This concept is compatible with different sampling strategies; here we demonstrate the method for k-space "bands", which have limited resolution in one dimension and can hence be acquired rapidly. We prove analytically that our method stochastically approximates the gradients computed in a fully-supervised setup, when two simple conditions are met: (i) the limited-resolution axis is chosen randomly-uniformly for every new scan, hence k-space is fully covered across the entire training set, and (ii) the loss function is weighed with a mask, derived here analytically, which facilitates accurate reconstruction of high-resolution details. Numerical experiments with raw MRI data indicate that k-band outperforms two other methods trained on limited-resolution data and performs comparably to state-of-t...