Image denoising via fundamental anisotropic diffusion and wavelet shrinkage: A comparative study

摘要

Noise removal faces a challenge: Keeping the image details. Resolving the dilemma of two purposes (smoothing and keeping image features in tact) working inadvertently of each other was an almost impossible task until anisotropic diffusion (AD) was formally introduced by Perona and Malik (PM). AD favors intra-region smoothing over inter-region in piecewise smooth images. Many authors regularized the original PM algorithm to overcome its drawbacks. We compared the denoising performances of such 'fundamental' AD algorithms and one of the most powerful multiresolution tools available today, namely, wavelet shrinkage. The AD algorithms here are called 'fundamental' in the sense that the regularized versions center around the original PM algorithm with minor changes to the logic. The algorithms are tested with different noise types and levels. On top of the visual inspection, two mathematical metrics are used for performance comparison: Signal-to-noise ratio (SNR) and universal image quality index (UIQI). We conclude that some of the regularized versions of PM algorithm (AD) perform comparably with wavelet shrinkage. This saves a lot of computational power. With this conclusion, we applied the better-performing fundamental AD algorithms to a new imaging modality: Optical Coherence Tomography (OCT).