  We demonstrate that a joint analysis of LSST-like ground-based imaging with
Euclid-like space-based imaging leads to increased precision and accuracy in
galaxy shape measurements. At galaxy magnitudes of $i \sim 24.5$, a combined
survey analysis increases the effective galaxy number density for cosmic shear
studies by $\sim 50$ percent in comparison to an analysis of each survey alone.
Using a realistic distribution of galaxy sizes, ellipticities and magnitudes
down to $i = 25.2$, we simulate LSST-like and Euclid-like images of over one
million isolated galaxies. We compare the precision and accuracy of the
recovered galaxy ellipticities for four different analyses: LSST-only,
Euclid-only, a simultaneous joint-pixel analysis of the two surveys, and a
simple catalogue-level survey combination. In the faint and small-galaxy
regime, where neither survey excels alone, we find a $\sim 20$ percent increase
in the precision of galaxy shape measurement when we adopt a joint-pixel
analysis, compared to a catalogue-level combination. As the statistical power
of cosmic shear is dominated by intrinsic ellipticity noise, however, this
improvement in shape measurement noise only leads to a $\sim 5$ percent
improvement in the effective number density of galaxies for lensing studies. We
view this as the minimum improvement that should be expected from a joint-pixel
analysis over a less accurate catalogue-level combination, as the former will
also improve the capability of LSST to de-blend close objects.
