APPLICATION OF THE SCHRODINGER EQUATIONS IN DENOISING BY COMPLEX DIFFUSION PROCESSES

Generalization of the linear and nonlinear scale spaces to the complex domain, bycombining the diffusion and the free Schrodinger equations, further enhances the the-oretical framework of the diffusion-type PDE approach to image processing. Analysisof its behavior shows that the generalized diffusion process combines properties ofboth forward and inverse diffusion. We prove that the imaginary part is a smoothedsecond derivative, scaled by time, when the complex diffusion coefficient approachesthe real axis. Based on this observation, In this paper we develop two examples ofnonlinear complex processes, useful in image processing: a regularized shock lter forimage enhancement and a ramp preserving denoising process.

Keywords:

Scale-space , image ltering , image denoising , image enhancement , nonlinear diffusion , complex diffusion , edge detection , shock lters