  We describe a new method for analyzing gravitational lens images, for the
case where the source light distribution is pixelized. The method is suitable
for high resolution, high S/N data of a multiply-imaged extended source. For a
given mass distribution, we show that the step of inverting the image to obtain
the deconvolved pixelized source light distribution, and the uncertainties, is
a linear one. This means that the only parameters of the non-linear problem are
those required to model the mass distribution. This greatly simplifies the
search for a min.-chi^2 fit to the data and speeds up the inversion. The method
is extended in a straightforward way to include linear regularization. We apply
the method to simulated Einstein ring images and demonstrate the effectiveness
of the inversion for both the unregularized and regularized cases.
