  We propose a correction to the conventional Rytov approximation (RA) and
investigate its performance for predicting wave scattering under strong
scattering conditions. An important motivation for the correction and
investigation is to help in the development of better models for inverse
scattering. The correction is based upon incorporating the high frequency
theory of inhomogeneous wave propagation for lossy media into the RA
formulation. We denote the technique as the extended Rytov approximation for
lossy media (xRA-LM). xRA-LM significantly improves upon existing non-iterative
linear scattering approximations such as RA and the Born approximation (BA) by
providing a validity range for the permittivity of the objects of up to 50
times greater than RA. We demonstrate the technique by providing results for
predicting wave scattering from piece-wise homogeneous scatterers in a
two-dimensional (2D) region. Numerical investigation of the performance of
xRA-LM for solving direct problem show that xRA-LM can accurately predict wave
scattering by electrically large, low-loss scatterers with high complex
permittivity ($\epsilon_r> 50+5j$). To the best of our knowledge, this is the
first non-iterative, linear approximate wave scattering model which has a large
validity range in terms of both permittivity and electrical size.
