Wavelet-based Image Enhancement using Nonlinear Anisotropic Diffusion

Many sensing techniques and image processing applications are characterized by random noisy, or corrupted, image data. Nonlinear Anisotropic diffusion is a popular, and theoretically well understood, technique for enhancing such images.Diffusion approaches however require the selection of an “edge stopping” function, the definition of which is typically adhoc. Many recent techniques for digital image enhancement and multi scale image representations are based on nonlinear partial differential equations (PDEs).This paper describes in a systematic way their theoretical foundations, numerical aspects, and applications. A large number of references enable the reader to acquire an up-to-date overview of the original literature. The central emphasis is on anisotropic nonlinear diffusion filters. Their flexibility allows combine smoothing properties with image enhancement qualities. A general framework is explored covering well-posedness and scale-space results not only for the continuous, but also for the algorithmically important semi discrete and fully discrete settings. The presented examples range from applications in medical image analysis to problems in computer aided quality control. This connection leads to a new “edge-stopping” function estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion, detecting the boundaries between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Keywords-wavelet, wavelet transform,diffusion, enhancement,Nonlinear anisotropic diffusion.