Strong Lensing Reconstruction.
We present a general linear algorithm for measuring the surface mass density 1-kappa from the observable reduced shear g=gamma&solm0;&parl0;1-kappa&parr0; in the strong lensing regime. We show that in general, the observed polarization field can be decomposed into "electric" and "magnetic" components, which have independent and redundant solutions, but orthogonal noise properties. By combining these solutions, one can increase the signal-to-noise ratio by 2. The solutions allow dynamic optimization of signal and noise, both in real and Fourier space (using arbitrary smoothing windows). Boundary conditions have no effect on the reconstructions, apart from its effect on the signal-to-noise ratio. Many existing reconstruction techniques are recovered as special cases of this framework. The magnetic solution has the added benefit of yielding the global and local parity of the reconstruction in a single step.