  Reconstruction of gravitational lensing effects in the CMB from current and
upcoming surveys is still dominated by temperature anisotropies. Extragalactic
foregrounds in temperature maps can induce significant biases in the lensing
power spectrum obtained with the standard quadratic estimators. Techniques such
as masking cannot remove these foregrounds fully, and the residuals can still
lead to large biases if unaccounted for. In this paper, we study the
"shear-only" estimator, an example of a class of geometric methods that
suppress extragalactic foreground contamination while making only minimal
assumptions about foreground properties. The shear-only estimator has only been
formulated in the flat-sky limit and so is not easily applied to wide surveys.
Here, we derive the full-sky version of the shear-only estimator and its
generalisation to an $m=2$ multipole estimator that has improved performance
for lensing reconstruction on smaller scales. The multipole estimator is
generally not separable, and so is expensive to compute. We explore separable
approximations based on a singular-value decomposition, which allow efficient
evaluation of the estimator with real-space methods. Finally, we apply these
estimators to simulations that include extragalactic foregrounds and verify
their efficacy in suppressing foreground biases.
