A review on deep learning MRI reconstruction without fully sampled k-space

Abstract

Background: Magnetic resonance imaging (MRI) is an effective auxiliary diagnostic method in clinical medicine, but it has always suffered from the problem of long acquisition time. Compressed sensing and parallel imaging are two common techniques to accelerate MRI reconstruction. Recently, deep learning provides a new direction for MRI, while most of them require a large number of data pairs for training. However, there are many scenarios where fully sampled k-space data cannot be obtained, which will seriously hinder the application of supervised learning. Therefore, deep learning without fully sampled data is indispensable.

Main text: In this review, we first introduce the forward model of MRI as a classic inverse problem, and briefly discuss the connection of traditional iterative methods to deep learning. Next, we will explain how to train reconstruction network without fully sampled data from the perspective of obtaining prior information.

Conclusion: Although the reviewed methods are used for MRI reconstruction, they can also be extended to other areas where ground-truth is not available. Furthermore, we may anticipate that the combination of traditional methods and deep learning will produce better reconstruction results.

Fig. 1

Flowchart of deep learning for MRI reconstruction with fully sampled data (a) and without fully sampled data (b). The difference between (a) and (b) is that (a) can train the network in a supervised manner. The network takes undersampled data and other prior as inputs and update parameters by backpropagation algorithms such as SGD and its variation. In reconstructing phase, the trained network can reconstruct high-quality images from the input

Fig. 2

Unrolled network frame for VSQP. Here, each block consists of a regularization R and a data consistency (DC), which correspond to Eq. (3) and Eq. (4) respectively in VSQP

Fig. 3

Image reconstruction with self-partition undersampled k-space data. Acquired undersampled k-space data $\mathrm{\Omega }$ will be divided into two subsets satisfying $\mathrm{\Omega }={\mathrm{\Lambda }}_j\cup {\mathrm{\Theta }}_j$ before training network, where $j=1,\dots ,\text{K}$ denoting the number of partitions for each scan, $\mathrm{\Lambda }$ and $\mathrm{\Theta }$ is used as input for training and to calculate the loss function separately. The network is unrolled based on the VSQP algorithm. This figure is reproduced following Fig. 1 in Ref. [65]

Fig. 4

The structure diagram in [73]. In data preparation, the fully encoded k-space is obtained by k-space integration and averaging of multiple frames in a time-interleaved sampling manner, then which is undersampled with a designed sampling mask and performs some operations including inverse Fourier transform and coil combination to get input and output data pairs separately. The parallel neural network consists of coil reconstruction and coil combination, we can refer to [41] for more details about ADMM-Net-III. This figure is reproduced following Fig. 1 and Fig. 3 in Ref. [73]

Fig. 5

Unsupervised GAN learning system. The input and output of the generator is measurement complex-valued k-space data and two-dimensional image, then the output of generator performs forward measurement operation including a random undersampled mask to get simulation undersampled k-space data, finally, discriminator tries to distinguish between simulation data and measurement data. This figure is reproduced following Fig. 1 in Ref. [83]