On fluorescence imaging: model and algorithm

Fluorescence imaging is a type of wave spectroscopy that extracts the quantitative property of fluorescence from some measurable data of the sample. By introducing the average of angularly reserved wave energy density, we derive an imaging model by a coupled diffusion system for the average fields. This nonlinear inverse problem is linearized with an error estimate on the excitation field indicating the model approximation. Then we give the explicit expression for emission fields, which provide the fundamentals for the efficient realizations for fluorescence imaging by the iterative schemes. Finally, in terms of the representations of the solution to the diffusion equation, the imaging of fluorophore is implemented by solving a linear integral equation of the first kind. The uniqueness and non-uniqueness of this inverse problem are rigorously analyzed for boundary measurement data. Numerical implementations are also presented.