  Tomographic image sizes keep increasing over time and while the GPUs that
compute the tomographic reconstruction are also increasing in memory size, they
are not doing so fast enough to reconstruct the largest datasets. This problem
is often solved by reconstructing data in large clusters of GPUs with enough
devices to fit the measured X-ray projections and reconstructed volume. Often
this requires tens of GPUs, which is a very economically expensive solution.
Access to single-node machines designed to reconstruct using just one or a few
GPUs is more common in the field, but current software does not allow iterative
reconstruction of volumes that do not fit in those GPUs. In this work, we
propose a strategy to execute efficiently the required operations for iterative
reconstruction for arbitrarily large images with any number of GPUs with
arbitrarily small memories in a single node. Strategies for both the forward
and backprojection operators are presented, along with two regularization
approaches that are easily generalized to other projection types or
regularizers. The proposed improvement also accelerates reconstruction of
smaller images on single or multiple GPUs, providing faster code for
time-critical medical applications. The resulting algorithm has been added to
the TIGRE toolbox, a repository for iterative reconstruction algorithms for
general CT, but this memory-saving and problem-splitting strategy can be easily
adapted for any other GPU-based CT code.
