  Estimating parameters of Partial Differential Equations (PDEs) from noisy and
indirect measurements often requires solving ill-posed inverse problems. These
so called parameter estimation or inverse medium problems arise in a variety of
applications such as geophysical, medical imaging, and nondestructive testing.
Their solution is computationally intense since the underlying PDEs need to be
solved numerous times until the reconstruction of the parameters is
sufficiently accurate. Typically, the computational demand grows significantly
when more measurements are available, which poses severe challenges to
inversion algorithms as measurement devices become more powerful.
  In this paper we present jInv, a flexible framework and open source software
that provides parallel algorithms for solving parameter estimation problems
with many measurements. Being written in the expressive programming language
Julia, jInv is portable, easy to understand and extend, cross-platform tested,
and well-documented. It provides novel parallelization schemes that exploit the
inherent structure of many parameter estimation problems and can be used to
solve multiphysics inversion problems as is demonstrated using numerical
experiments motivated by geophysical imaging.
