Adaptive Non-linear Diffusion in Wavelet Domain

Abstract

Traditional diffusivity based denoising models detect edges by the gradients of intensities, and thus are easily affected by noise. In this paper, we develop a nonlinear diffusion denoising method which adapts to the local context and thus preserves edges and diffuses more in the smooth regions. In the proposed diffusion model, the modulus of gradient in a diffusivity function is substituted by the modulus of a wavelet detail coefficient and the diffusion of wavelet coefficients is performed based on the local context. The local context is derived directly by analyzing the energy of transform across the scales and thus it performs efficiently in the real-time. The redundant representation of the stationary wavelet transform (SWT) and its shift-invariance lend themselves to edge detection and denoising applications. The proposed stationary wavelet context-based diffusivity (SWCD) model produces a better quality image compared to that attained by two high performance diffusion models, i.e. higher Peak Signal-to-Noise Ratio on average and lesser artifacts and blur are observed in a number of images representing texture, strong edges and smooth backgrounds.