MARS: A New Maximum Entropy-Regularized Strong Lensing Mass
  Reconstruction Method
  Free-form strong-lensing (SL) mass reconstructions typically suffer from
overfitting, which manifest itself as false-positive small-scale fluctuations.
We present a new free-form MAximum-entropy ReconStruction (${\tt MARS}$) method
without the assumption that light traces mass (LTM). The ${\tt MARS}$ algorithm
enables us to achieve excellent convergence in source positions ~0.001$"$,
minimize spurious small-scale fluctuations, and provide a quasi-unique solution
independently of initial conditions. Our method is tested with the publicly
available synthetic SL data ${\tt FF-SIMS}$ and the comparison with the truth
shows that the reconstruction quality is on a par with those of the
best-performing LTM methods published in the literature, which have been
demonstrated to outperform the existing free-form methods. In terms of the
radial mass profile reconstruction, we achieve $<1$% agreements with the truth
for the regions constrained by the multiple images. Finally, we apply ${\tt
MARS}$ to A1689 and find that the cluster mass in the SL regime is dominated by
the primary halo centered on the brightest cluster galaxy and the weaker
secondary halo also coincident with the bright cluster member ~160 kpc
northeast. Within the SL field, the A1689 radial profile is well-described by a
Navarro-Frenk-White (NFW) profile with $c_{200}=5.53\pm0.77$ and
$r_s=538^{+90}_{-100}$ kpc and we find no evidence that A1689 is
over-concentrated.
