Fourth-order oriented partial-differential equations for noise removal of two-photon fluorescence images

We derive the fourth-order oriented partial-differential equations (PDEs) for noise removal of two-photon fluorescence images. We consider it from two aspects: one is based on a variational method; the other is based on controlling the diffusion direction. Our filtering model makes the diffusion along only the special orientation--decided via all the information in the established filtering window, so the edges are protected during filtering. Compared with related PDEs models, our model shows superior performance in terms of both objective criteria and subjective human vision via processing simulated and experimental noisy images.