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

Galaxy shape measurement synergies between LSST and Euclid