  When analyzing the galaxy bispectrum measured from spectroscopic surveys, it
is imperative to account for the effects of non-uniform survey geometry.
Conventionally, this is done by convolving the theory model with the the window
function; however, the computational expense of this prohibits full exploration
of the bispectrum likelihood. In this work, we provide a new class of
estimators for the unwindowed bispectrum; a quantity that can be
straightforwardly compared to theory. This builds upon the work of Philcox
(2021) for the power spectrum, and comprises two parts (both obtained from an
Edgeworth expansion): a cubic estimator applied to the data, and a Fisher
matrix, which deconvolves the bispectrum components. In the limit of weak
non-Gaussianity, the estimator is minimum-variance; furthermore, we give an
alternate form based on FKP weights that is close-to-optimal and easy to
compute. As a demonstration, we measure the binned bispectrum monopole of a
suite of simulations both using conventional estimators and our unwindowed
equivalents. Computation times are comparable, except that the unwindowed
approach requires a Fisher matrix, computable in an additional
$\mathcal{O}(100)$ CPU-hours. Our estimator may be straightforwardly extended
to measure redshift-space distortions and the components of the bispectrum in
arbitrary separable bases. The techniques of this work will allow the
bispectrum to straightforwardly be included in the cosmological analysis of
current and upcoming survey data.
