ABSTRACT
The field of inverse problem is a fairly mature area of research and was initially motivated by industrial problems This chapter describes Electrical Impedance Tomography as an example of an ill-posed inverse problem involving partial differential equation. It also describes Diffuse Optical Tomography as another example of an ill-posed inverse problem. The inverse problem instead uses knowledge of the source and boundary data and finds the conductivity interior to the object. The goal is to estimate the conductivity distribution q from all pairs of current and voltage measurements. The variational type methods uses an iterative type method of a linearized model or fully nonlinear model such as sparisty cosnstraints, iteratively regularized Gauss–Newton method. These analytical methods can be effective in determining specific conductivity, but statistical inversion methods] can offer an alternative approach.
