  This paper introduces a novel computationally efficient method of solving the
3D single image super-resolution (SR) problem, i.e., reconstruction of a
high-resolution volume from its low-resolution counterpart. The main
contribution lies in the original way of handling simultaneously the associated
decimation and blurring operators, based on their underlying properties in the
frequency domain. In particular, the proposed decomposition technique of the 3D
decimation operator allows a straightforward implementation for Tikhonov
regularization, and can be further used to take into consideration other
regularization functions such as the total variation, enabling the
computational cost of state-of-the-art algorithms to be considerably decreased.
Numerical experiments carried out showed that the proposed approach outperforms
existing 3D SR methods.
