  Multimode optical fibres are hair-thin strands of glass that efficiently
transport light. They promise next-generation medical endoscopes that provide
unprecedented sub-cellular image resolution deep inside the body. However,
confining light to such fibres means that images are inherently scrambled in
transit. Conventionally, this scrambling has been compensated by
pre-calibrating how a specific fibre scrambles light and solving a stationary
linear matrix equation that represents a physical model of the fibre. However,
as the technology develops towards real-world deployment, the unscrambling
process must account for dynamic changes in the matrix representing the fibre's
effect on light, due to factors such as movement and temperature shifts, and
non-linearities resulting from the inaccessibility of the fibre tip when inside
the body. Such complex, dynamic and nonlinear behaviour is well-suited to
approximation by neural networks, but most leading image reconstruction
networks rely on convolutional layers, which assume strong correlations between
adjacent pixels, a strong inductive bias that is inappropriate for fibre
matrices which may be expressed in a range of arbitrary coordinate
representations with long-range correlations. We introduce a new concept that
uses self-attention layers to dynamically transform the coordinate
representations of varying fibre matrices to a basis that admits compact,
low-dimensional representations suitable for further processing. We demonstrate
the effectiveness of this approach on diverse fibre matrix datasets. We show
our models significantly improve the sparsity of fibre bases in their
transformed bases with a participation ratio, p, as a measure of sparsity, of
between 0.01 and 0.11. Further, we show that these transformed representations
admit reconstruction of the original matrices with < 10% reconstruction error,
demonstrating the invertibility.
