  In this work, we evaluate how neural networks with periodic activation
functions can be leveraged to reliably compress large multidimensional medical
image datasets, with proof-of-concept application to 4D diffusion-weighted MRI
(dMRI). In the medical imaging landscape, multidimensional MRI is a key area of
research for developing biomarkers that are both sensitive and specific to the
underlying tissue microstructure. However, the high-dimensional nature of these
data poses a challenge in terms of both storage and sharing capabilities and
associated costs, requiring appropriate algorithms able to represent the
information in a low-dimensional space. Recent theoretical developments in deep
learning have shown how periodic activation functions are a powerful tool for
implicit neural representation of images and can be used for compression of 2D
images. Here we extend this approach to 4D images and show how any given 4D
dMRI dataset can be accurately represented through the parameters of a
sinusoidal activation network, achieving a data compression rate about 10 times
higher than the standard DEFLATE algorithm. Our results show that the proposed
approach outperforms benchmark ReLU and Tanh activation perceptron
architectures in terms of mean squared error, peak signal-to-noise ratio and
structural similarity index. Subsequent analyses using the tensor and spherical
harmonics representations demonstrate that the proposed lossy compression
reproduces accurately the characteristics of the original data, leading to
relative errors about 5 to 10 times lower than the benchmark JPEG2000 lossy
compression and similar to standard pre-processing steps such as MP-PCA
denosing, suggesting a loss of information within the currently accepted levels
for clinical application.
