A New Feature-preserving Nonlinear Anisotropic Diffusion Method for Image Denoising

Abstract

We present a new diffusion method for noise reduction and feature preservation. Presently, denoising methods commonly use a first-order derivative to detect edges in order to achieve a good balance between noise removal and feature preserving. However, if edges are partly lost to a certain extent or contaminated severely by noise, these methods may not be able to detect them and thus fail to preserve various features in images. To overcome this problem, we propose a new and more sophisticated feature detector by combining first-and second-order derivatives for a nonlinear anisotropic diffusion model. Numerical experiments show that the new diffusion filter outperforms many popular filters for denoising images containing edges, blobs and ridges and textures made of these features.

Translation Microscopy (TRAM) for super-resolution imaging

“…Since edges embedded in small and complex structures are prone to noise contamination, the gradient-based operators may not be able to robustly detect edges under noise contamination and therefore can fail to characterize and preserve complex structures. In a recent study 20 , we developed an anisotropic diffusion model by employing first- and second-order nonlocal differences (NLD) as feature detectors and demonstrated a superior performance of image restoration compared to many state-of-the-art denoising algorithms, particularly in high noise levels. This idea is based on our observations that diverse biological structures such as vesicles, filaments, microtubules are made primarily of two basic features, blob and ridge 21 22 , which are better characterized by a combination of these two NLDs.…”

Signal Smoothing with Time-Space Fractional Order Model

“…It is a challenge to smooth a noisy signal for preserving features such as peak or discontinuity. Therefore, some research has been focused on features preservation [4], [8], [11], [20], [21]. For instance, nonlinear diffusion filtering was designed to smooth spectrum data while preserving peaks [4].…”

“…In image processing, nonlinear diffusion filtering, total variation model, etc. were widely used for featurespreserving filtering [8], [11], [20], [21]. Among these methods, the features of a signal can be preserved having the feedback in the iterative process.…”