  I propose a new approach to free-form cluster lens modeling that is inspired
by the JPEG image compression method. This approach is motivated specifically
by the need for accurate modeling of high-magnification regions in galaxy
clusters. Existing modeling methods may struggle in these regions due to their
limited flexibility in the parametrization of the lens, even for a wide variety
of free-form methods. This limitation especially hinders the characterization
of faint galaxies at high redshifts, which have important implications for the
formation of the first galaxies and even for the nature of dark matter. JPEG
images are extremely accurate representations of their original, uncompressed
counterparts but use only a fraction of number of parameters to represent that
information. Its relevance is immediately obvious to cluster lens modeling.
Using this technique, it is possible to construct flexible models that are
capable of accurately reproducing the true mass distribution using only a small
number of free parameters. Transferring this well-proven technology to cluster
lens modeling, I demonstrate that this `JPEG parametrization' is indeed
flexible enough to accurately approximate an N-body simulated cluster.
