We discuss the inverse problem associated with the propagation of the field autocorrelation of light through a highly scattering object like tissue. In the first part of the work, we reconstruct the optical absorption coefficient ${\mu }_a$ and particle diffusion coefficient $D_B$ from simulated measurements which are integrals of a quantity computed from the measured intensity and intensity autocorrelation $g_2\left(\tau \right)$ at the boundary. In the second part we recover the mean square displacement (MSD) distribution of particles in an inhomogeneous object from the sampled $g_2\left(\tau \right)$ measured on the boundary. From the MSD, we compute the storage and loss moduli distributions in the object. We have devised computationally easy methods to construct the sensitivity matrices which are used in the iterative reconstruction algorithms for recovering these parameters from the measurements. The results of the reconstruction of ${\mu }_a$ , $D_B$ , MSD and the viscoelastic parameters, which are presented, show reasonably good position and quantitative accuracy.