Fluorescence optical tomography with a priori information

In this work, we discuss the incorporation of a priori information into the inverse problem formulation for fluorescence optical tomography. In this respect, we first formulate the inverse problem in the optimization framework which allows the incorporation of a priori information about the solution and its gradient. Then, we consider the variational problem, which is equivalent to the optimization problem and prove the existence and uniqueness of the solution. Finally, we discuss the design of the functions that incorporate the a priori information into the inverse problem formulation and present a model problem to illustrate the design procedure.