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Joint Supervised and Self-supervised Learning for MRI Reconstruction

George Yiasemis, Nikita Moriakov, Clara I. Sánchez, Jan-Jakob Sonke, Jonas Teuwen

TL;DR

This work tackles the challenge of high-quality MRI reconstruction when fully-sampled target data are unavailable. It introduces Joint Supervised and Self-supervised Learning (JSSL), which jointly leverages supervised learning on proxy, fully-sampled datasets and self-supervised learning on subsampled target data, integrated within a physics-guided unrolled reconstruction framework. The approach demonstrates substantial improvements over standard SSL methods, provides theoretical motivation for variance reduction via proxy supervision, and offers practical guidelines for training choices. Across multiple datasets and architectures, JSSL proves robust and effective, particularly at high acceleration factors, enabling better reconstructions in clinically challenging settings.

Abstract

Magnetic Resonance Imaging (MRI) represents an important diagnostic modality; however, its inherently slow acquisition process poses challenges in obtaining fully-sampled $k$-space data under motion. In the absence of fully-sampled acquisitions, serving as ground truths, training deep learning algorithms in a supervised manner to predict the underlying ground truth image becomes challenging. To address this limitation, self-supervised methods have emerged as a viable alternative, leveraging available subsampled $k$-space data to train deep neural networks for MRI reconstruction. Nevertheless, these approaches often fall short when compared to supervised methods. We propose Joint Supervised and Self-supervised Learning (JSSL), a novel training approach for deep learning-based MRI reconstruction algorithms aimed at enhancing reconstruction quality in cases where target datasets containing fully-sampled $k$-space measurements are unavailable. JSSL operates by simultaneously training a model in a self-supervised learning setting, using subsampled data from the target dataset(s), and in a supervised learning manner, utilizing datasets with fully-sampled $k$-space data, referred to as proxy datasets. We demonstrate JSSL's efficacy using subsampled prostate or cardiac MRI data as the target datasets, with fully-sampled brain and knee, or brain, knee and prostate $k$-space acquisitions, respectively, as proxy datasets. Our results showcase substantial improvements over conventional self-supervised methods, validated using common image quality metrics. Furthermore, we provide theoretical motivations for JSSL and establish "rule-of-thumb" guidelines for training MRI reconstruction models. JSSL effectively enhances MRI reconstruction quality in scenarios where fully-sampled $k$-space data is not available, leveraging the strengths of supervised learning by incorporating proxy datasets.

Joint Supervised and Self-supervised Learning for MRI Reconstruction

TL;DR

This work tackles the challenge of high-quality MRI reconstruction when fully-sampled target data are unavailable. It introduces Joint Supervised and Self-supervised Learning (JSSL), which jointly leverages supervised learning on proxy, fully-sampled datasets and self-supervised learning on subsampled target data, integrated within a physics-guided unrolled reconstruction framework. The approach demonstrates substantial improvements over standard SSL methods, provides theoretical motivation for variance reduction via proxy supervision, and offers practical guidelines for training choices. Across multiple datasets and architectures, JSSL proves robust and effective, particularly at high acceleration factors, enabling better reconstructions in clinically challenging settings.

Abstract

Magnetic Resonance Imaging (MRI) represents an important diagnostic modality; however, its inherently slow acquisition process poses challenges in obtaining fully-sampled -space data under motion. In the absence of fully-sampled acquisitions, serving as ground truths, training deep learning algorithms in a supervised manner to predict the underlying ground truth image becomes challenging. To address this limitation, self-supervised methods have emerged as a viable alternative, leveraging available subsampled -space data to train deep neural networks for MRI reconstruction. Nevertheless, these approaches often fall short when compared to supervised methods. We propose Joint Supervised and Self-supervised Learning (JSSL), a novel training approach for deep learning-based MRI reconstruction algorithms aimed at enhancing reconstruction quality in cases where target datasets containing fully-sampled -space measurements are unavailable. JSSL operates by simultaneously training a model in a self-supervised learning setting, using subsampled data from the target dataset(s), and in a supervised learning manner, utilizing datasets with fully-sampled -space data, referred to as proxy datasets. We demonstrate JSSL's efficacy using subsampled prostate or cardiac MRI data as the target datasets, with fully-sampled brain and knee, or brain, knee and prostate -space acquisitions, respectively, as proxy datasets. Our results showcase substantial improvements over conventional self-supervised methods, validated using common image quality metrics. Furthermore, we provide theoretical motivations for JSSL and establish "rule-of-thumb" guidelines for training MRI reconstruction models. JSSL effectively enhances MRI reconstruction quality in scenarios where fully-sampled -space data is not available, leveraging the strengths of supervised learning by incorporating proxy datasets.
Paper Structure (44 sections, 4 theorems, 34 equations, 14 figures, 6 tables, 1 algorithm)

This paper contains 44 sections, 4 theorems, 34 equations, 14 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Materials and Methods
  4. MRI Acquisition and Reconstruction
  5. MRI Reconstruction
  6. MRI Reconstruction with Supervised Learning
  7. MRI Reconstruction with Self-supervised Learning
  8. Joint Supervised and Self-supervised Learning
  9. JSSL Training Framework
  10. Supervised Learning Loss
  11. Self-supervised Learning Loss
  12. JSSL Loss:
  13. JSSL at Inference
  14. JSSL: A Theoretical Motivation
  15. Reconstruction Network
  16. ...and 29 more sections

Key Result

Proposition 1

Consider two distributions $p_i, \, i=1,2$ with means and variances ${\mu}_i, {\sigma}_i, \, i=1,2$, with unknown ${\mu}_1$, and ${\mu}_1 \neq {\mu}_2$. Then if $(\mu_1 - \mu_2)^2 < c \frac{{\sigma}_1^2}{N}$ for some $c \in (0, 1)$ and $N \in \mathbb{Z}^{+}$, then $\tilde{{x}} = \frac{1}{N+K} \sum_{

Figures (14)

  • Figure 1: Overview of the JSSL framework for MRI reconstruction. Training uses ground truth data from proxy domain(s) and subsampled data (no ground truth) from a target domain, jointly in supervised and self-supervised manners, respectively.
  • Figure 2: (a) The training process for the proposed JSSL method is divided into two phases: (1) Supervised Learning using fully-sampled $k$-space data from proxy datasets. During this phase, the model is trained to predict fully-sampled data from retrospectively subsampled proxy data. (2) Self-supervised Learning utilizing subsampled $k$-space data from the target dataset, partitioned into two disjoint subsets. The model takes one subset as input and aims to predict the other. Loss functions are defined for both SL and SSL settings in both $k$-space and image domains and the JSSL loss comprises all these components. The model is jointly trained with both supervised and self-supervised loss functions to enhance MRI reconstruction in the target domain. In all phases, sensitivity maps $\mathbf{S}$ are learned using the autocalibration signal (center of $k$-space) from available measurements. A U-Net, functioning as a Sensitivity Map Estimator module (omitted in the diagram)., is trained end-to-end with the reconstruction network. (b) In the inference phase, the trained network predicts the underlying ground truth image from the target dataset based on input subsampled data.
  • Figure 3: Evaluation results for different training setups with the prostate as target dataset, and the brain and knee datasets as proxy datasets
  • Figure 4: Evaluation results for different training setups with the cardiac as target dataset, and the brain, knee and prostate datasets as proxy datasets
  • Figure 5: Example reconstructions of a slice from the prostate dataset subsampled at different acceleration factors from the test set (experiment set A) from each training setup.
  • ...and 9 more figures

Theorems & Definitions (8)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof