Boost image denoising via noise level estimation in quaternion wavelet domain

Wavelet thresholding is an important branch of the image denoising field. A key parameter in the algorithms is noise level. As a novel tool of image analysis, quaternion wavelet owns some superior properties compared to discrete wavelets, such as nearly shift-invariant wavelet coefficients and phase based texture presentation. We aim to propose an easy and efficient method to estimate the noise level accurately via quaternion wavelet and further improve the denoising performance. We find that the variance sum of high frequency coefficients of quaternion wavelet is approximately equal to the noise level. However, with the advent of strong edges and/or less smooth regions, this metric would overestimate the noise level. Phases in the quaternion wavelet domain can represent the image texture information. On the premise of detecting smooth regions via phases operation, i.e. without many textures, the proposed noise level estimation method is also suitable to images with complex scenes. The performance of the proposed noise level estimation algorithm is demonstrated superior to classical algorithms. Also, the proposed algorithm can enhance those noise level dependent techniques to improve the denoising performances which are competitive to the state-of-art denoising algorithms.