  The advanced magnetic resonance (MR) image reconstructions such as the
compressed sensing and subspace-based imaging are considered as large-scale,
iterative, optimization problems. Given the large number of reconstructions
required by the practical clinical usage, the computation time of these
advanced reconstruction methods is often unacceptable. In this work, we propose
using Google's Tensor Processing Units (TPUs) to accelerate the MR image
reconstruction. TPU is an application-specific integrated circuit (ASIC) for
machine learning applications, which has recently been used to solve
large-scale scientific computing problems. As proof-of-concept, we implement
the alternating direction method of multipliers (ADMM) in TensorFlow to
reconstruct images on TPUs. The reconstruction is based on multi-channel,
sparsely sampled, and radial-trajectory $k$-space data with sparsity
constraints. The forward and inverse non-uniform Fourier transform operations
are formulated in terms of matrix multiplications as in the discrete Fourier
transform. The sparsifying transform and its adjoint operations are formulated
as convolutions. The data decomposition is applied to the measured $k$-space
data such that the aforementioned tensor operations are localized within
individual TPU cores. The data decomposition and the inter-core communication
strategy are designed in accordance with the TPU interconnect network topology
in order to minimize the communication time. The accuracy and the high parallel
efficiency of the proposed TPU-based image reconstruction method are
demonstrated through numerical examples.
