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-the-art (SoTA) methods trained on
high-resolution data. k-band hence obtains SoTA performance, with the advantage
of training using only limited-resolution data. This work hence introduces a
practical, easy-to-implement, self-supervised training framework, which
involves fast acquisition and self-supervised reconstruction and offers
theoretical guarantees.

通过在有限分辨率数据上进行自监督训练来提供实验保证，并且在解决磁共振成像问题中达到了现有方法的性能水平。