  The Rytov approximation is known in near-infrared spectroscopy including
diffuse optical tomography. In diffuse optical tomography, the Rytov
approximation often gives better reconstructed images than the Born
approximation. Although related inverse problems are nonlinear, the Rytov
approximation is almost always accompanied by the linearization of nonlinear
inverse problems. In this paper, we will develop nonlinear reconstruction with
the inverse Rytov series. By this, linearization is not necessary and higher
order terms in the Rytov series can be used for reconstruction. The convergence
and stability are discussed. We find that the inverse Rytov series has a
recursive structure similar to the inverse Born series.
