Geometric Approaches to Increase the Expressivity of Deep Neural Networks for MR Reconstruction

Abstract

Recently, deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. Although these approaches provide significant performance gain compared to compressed sensing MRI (CS-MRI), it is not clear how to choose a suitable network architecture to balance the trade-off between network complexity and performance. Recently, it was shown that an encoder-decoder convolutional neural network (CNN) can be interpreted as a piecewise linear basis-like representation, whose specific representation is determined by the ReLU activation patterns for a given input image. Thus, the expressivity or the representation power is determined by the number of piecewise linear regions. As an extension of this geometric understanding, this paper proposes a systematic geometric approach using bootstrapping and subnetwork aggregation using an attention module to increase the expressivity of the underlying neural network. Our method can be implemented in both k-space domain and image domain that can be trained in an end-to-end manner. Experimental results show that the proposed schemes significantly improve reconstruction performance with negligible complexity increases.

Unsupervised MR Motion Artifact Deep Learning using Outlier-Rejecting Bootstrap Aggregation

“…If the full k-space data is available, the benefit of bootstrap aggregation may seem unclear. However, in our prior work [22], we demonstrated that instead of using just a single stronger deep learner, bootstrap aggregation can still provide high quality image reconstruction in the compressed sensing MRI.…”

“…Our network architecture is based on U-Net [42] and it consists of convolution layers, instance normalization [43], activation layers and pooling layers. Furthermore, we employ adaptive residual learning [22] to improve reconstruction performance. Specifically, the network's original output and the residual output are combined by the channel concatenation, from which the final output is generated using the last 1 × 1 convolution layer.…”

“…Recently, deep learning approaches for MRI reconstruction have been extensively studied [19]- [22]. Deep learning methods for MRI motion artifact reduction [23]- [27] have also been proposed.…”

“…Rather than relying on the difficult sparse outliers identification as done in [17], the main idea of this work comes from k-space random subsampling, which can eliminate sparse outliers in k-space from motions in a probabilistic sense. In fact, this is ideally fit to the deep learning framework thanks to its close relationship with bootstrap aggregation [34], which has been recently explored in deep learning MR reconstruction [22]. In particular, if a neural network has been trained using motion-free training data as a reconstruction network from undersampled k-space data, the bootstrap subsampling in the k-space domain can eliminate some of the sparse k-space outliers from the motion, so that corresponding neural network creates images with fewer motion artifacts.…”

Two-stage deep learning for accelerated 3D time-of-flight MRA without matched training data

“…Moreover, we utilize nonlinear attention module which is known to enhance the expressivity of the network (Cha et al, 2020). For G Θ in Step I, due to the large discrepancy between the input and the desired distribution, we utilize the same network architecture from Fig.…”