  In this paper, we develop a new regularized version of the Factorization
Method for positive operators mapping a complex Hilbert Space into it's dual
space. The Factorization Method uses Picard's Criteria to define an indicator
function to image an unknown region. In most applications, the data operator is
compact which gives that the singular values can tend to zero rapidly which can
cause numerical instabilities. The regularization of the Factorization Method
presented here seeks to avoid the numerical instabilities in applying Picard's
Criteria. This method allows one to image the interior structure of an object
with little a priori information in a computationally simple and analytically
rigorous way. Here we will focus on an application of this method to diffuse
optical tomography where will prove that this method can be used to recover an
unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples
will be presented in two dimensions.
