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

TL;DR

This paper introduces k-band, a self-supervised MRI reconstruction method that trains on limited-resolution k-space data using stochastic gradient descent over k-space subsets, achieving state-of-the-art results without high-resolution training data.

Contribution

The paper presents a novel self-supervised training framework for MRI reconstruction using stochastic gradient descent over k-space subsets, with theoretical guarantees and practical advantages.

Findings

k-band outperforms other limited-resolution training methods

k-band matches state-of-the-art performance with limited data

The method is theoretically justified and practically easy to implement

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.