  In this paper, we consider a regularization strategy for the factorization
method when there is noise added to the data operator. The factorization method
is a qualitative method used in shape reconstruction problems. These methods
are advantageous to use due to the fact that they are computationally simple
and require little a priori knowledge of the object one wishes to reconstruct.
The main focus of this paper is to prove that the regularization strategy
presented here produces stable reconstructions. We will show this is the case
analytically and numerically for the inverse shape problem of recovering an
isotropic scatterer with a conductive boundary condition. We also provide a
strategy for picking the regularization parameter with respect to the noise
level. Numerical examples are given for a scatterer in 2 dimensions.
