  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.
