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Although deep learning (DL) methods are powerful for solving inverseproblems, their reliance on high-quality training data is a major hurdle. Thisis significant in high-dimensional (dynamic/volumetric) magnetic resonanceimaging (MRI), where acquisition of high-resolution fully sampled k-space datais impractical. We introduce a novel mathematical framework, dubbed k-band,that enables training DL models using only partial, limited-resolution k-spacedata. Specifically, we introduce training with stochastic gradient descent(SGD) over k-space subsets. In each training iteration, rather than using thefully sampled k-space for computing gradients, we use only a small k-spaceportion. This concept is compatible with different sampling strategies; here wedemonstrate the method for k-space "bands", which have limited resolution inone dimension and can hence be acquired rapidly. We prove analytically that ourmethod stochastically approximates the gradients computed in a fully-supervisedsetup, when two simple conditions are met: (i) the limited-resolution axis ischosen randomly-uniformly for every new scan, hence k-space is fully coveredacross the entire training set, and (ii) the loss function is weighed with amask, derived here analytically, which facilitates accurate reconstruction ofhigh-resolution details. Numerical experiments with raw MRI data indicate thatk-band outperforms two other methods trained on limited-resolution data andperforms comparably to state-of-the-art (SoTA) methods trained onhigh-resolution data. k-band hence obtains SoTA performance, with the advantageof training using only limited-resolution data. This work hence introduces apractical, easy-to-implement, self-supervised training framework, whichinvolves fast acquisition and self-supervised reconstruction and offerstheoretical guarantees.

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