  We consider the inverse problem of finding unknown elastic parameters from
internal measurements of displacement fields for tissues. In the sequel to
Ammari, Waters, Zhang (2015), we use pseudodifferential methods for the problem
of recovering the shear modulus for Stokes systems from internal data. We prove
stability estimates in $d=2,3$ with reduced regularity on the estimates and
show that the presence of a finite dimensional kernel can be removed. This
implies the convergence of the Landweber numerical iteration scheme. We also
show that these hypotheses are natural for experimental use in constructing
shear modulus distributions.
