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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 and 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 …