title: Image enhancement and denoising by complex diffusion processes.
abstract: The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.
authors.affiliation: Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel. gilboa@tx.technion.ac.il
authors.forename: Guy
authors.initials: G
authors.lastname: Gilboa
authors.forename: Nir
authors.initials: N
authors.lastname: Sochen
authors.forename: Yehoshua Y
authors.initials: YY
authors.lastname: Zeevi
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D004058:Diffusion; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes; D013382:Subtraction Technique