  Inverse problems spanning four or more dimensions such as space, time and
other independent parameters have become increasingly important.
State-of-the-art 4D reconstruction methods use model based iterative
reconstruction (MBIR), but depend critically on the quality of the prior
modeling. Recently, plug-and-play (PnP) methods have been shown to be an
effective way to incorporate advanced prior models using state-of-the-art
denoising algorithms. However, state-of-the-art denoisers such as BM4D and deep
convolutional neural networks (CNNs) are primarily available for 2D or 3D
images and extending them to higher dimensions is difficult due to algorithmic
complexity and the increased difficulty of effective training.
  In this paper, we present multi-slice fusion, a novel algorithm for 4D
reconstruction, based on the fusion of multiple low-dimensional denoisers. Our
approach uses multi-agent consensus equilibrium (MACE), an extension of
plug-and-play, as a framework for integrating the multiple lower-dimensional
models. We apply our method to 4D cone-beam X-ray CT reconstruction for non
destructive evaluation (NDE) of samples that are dynamically moving during
acquisition. We implement multi-slice fusion on distributed, heterogeneous
clusters in order to reconstruct large 4D volumes in reasonable time and
demonstrate the inherent parallelizable nature of the algorithm. We present
simulated and real experimental results on sparse-view and limited-angle CT
data to demonstrate that multi-slice fusion can substantially improve the
quality of reconstructions relative to traditional methods, while also being
practical to implement and train.
