  The row-column addressed array is an emerging probe for ultrafast 3-D
ultrasound imaging. It achieves this with far fewer independent electronic
channels and a wider field of view than traditional 2-D matrix arrays, of the
same channel count, making it a good candidate for clinical translation.
However, the image quality of row-column arrays is generally poor, particularly
when investigating tissue. Ultrasound localisation microscopy allows for the
production of super-resolution images even when the initial image resolution is
not high. Unfortunately, the row-column probe can suffer from imaging artefacts
that can degrade the quality of super-resolution images as `secondary' lobes
from bright microbubbles can be mistaken as microbubble events, particularly
when operated using plane wave imaging. These false events move through the
image in a physiologically realistic way so can be challenging to remove via
tracking, leading to the production of 'false vessels'. Here, a new type of
rolling window image reconstruction procedure was developed, which integrated a
row-column array-specific coherence-based beamforming technique with acoustic
sub-aperture processing for the purposes of reducing `secondary' lobe
artefacts, noise and increasing the effective frame rate. Using an {\it{in
vitro}} cross tube, it was found that the procedure reduced the percentage of
`false' locations from $\sim$26\% to $\sim$15\% compared to traditional
orthogonal plane wave compounding. Additionally, it was found that the noise
could be reduced by $\sim$7 dB and that the effective frame rate could be
increased to over 4000 fps. Subsequently, {\it{in vivo}} ultrasound
localisation microscopy was used to produce images non-invasively of a rabbit
kidney and a human thyroid.
