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.