  We present a new estimation method for mapping the gravitational lensing
potential from observed CMB intensity and polarization fields. Our method uses
Bayesian techniques to estimate the average curvature of the potential over
small local regions. These local curvatures are then used to construct an
estimate of a low pass filter of the gravitational potential. By utilizing
Bayesian/likelihood methods one can easily overcome problems with missing
and/or non-uniform pixels and problems with partial sky observations (E and B
mode mixing, for example). Moreover, our methods are local in nature which
allow us to easily model spatially varying beams and are highly parallelizable.
We note that our estimates do not rely on the typical Taylor approximation
which is used to construct estimates of the gravitational potential by Fourier
coupling. We present our methodology with a flat sky simulation under nearly
ideal experimental conditions with a noise level of 1 $\mu K$-arcmin for the
temperature field, $\sqrt{2}$ $\mu K$-arcmin for the polarization fields, with
an instrumental beam full width at half maximum (FWHM) of 0.25 arcmin.
