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.
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