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

• URL: http://arxiv.org/abs/2308.02958v3
• Date: Thu, 23 May 2024 12:27:41 GMT
• Title: K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets
• Authors: Frederic Wang, Han Qi, Alfredo De Goyeneche, Reinhard Heckel, Michael Lustig, Efrat Shimron,
• Abstract summary: We introduce a novel mathematical framework, dubbed k-band, that enables training DL models using only partial, limited-resolution k-space data. In each training iteration, rather than using the fully sampled k-space for computing gradients, we use only a small k-space portion. Numerical experiments with raw MRI data indicate that k-band outperforms two other methods trained on limited-resolution data.
• Score: 16.785465381844435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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