The inverse Rytov series for diffuse optical tomography

TL;DR

This paper develops a nonlinear reconstruction method for diffuse optical tomography using the inverse Rytov series, avoiding linearization and potentially improving image quality.

Contribution

It introduces a novel nonlinear reconstruction approach based on the inverse Rytov series, extending beyond traditional linearized methods.

Findings

Inverse Rytov series has a recursive structure similar to the inverse Born series.

The method allows higher order terms to improve reconstruction accuracy.

Convergence and stability of the series are discussed.

Abstract

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.