Nonlocal Mean Image Denoising Using Anisotropic Structure Tensor

We present a novel nonlocal mean (NLM) algorithm using an anisotropic structure tensor to achieve higher accuracy of imaging denoising and better preservation of fine image details. Instead of using the intensity to identify the pixel, the proposed algorithm uses the structure tensor to characterize the boundary information around the pixel more comprehensively. Meanwhile, similarity of the structure tensor is computed in a Riemannian space for more rigorous comparison, and the similarity weight of the pixel (or patch) is determined by the intensity and structure tensor simultaneously. The proposed algorithm is compared with the original NLM algorithm and a modified NLM algorithm that is based on the principle component analysis. Quantitative and qualitative comparisons of the three NLM algorithms are presented as well. 1. Introduction Image denoising is a key preprocessing step for higher level of processes such as image segmentation and pattern recognition. The most straightforward denoising approach is the direct application of spatial coherence which assumes noisy samples in a local area of a given pixel follow the same distribution of that pixel [1]. Although many efforts have been done dedicatedly to overcome it such as anisotropic filtering [2] and total variation minimization [3], this kind of algorithms comes with a common drawback of image blurring due to smoothing effect in both homogeneous regions and at object boundaries. Besides denoising methods in spatial domain, removing noise in transformation domain is also well developed, such as DCT transform [4] and wavelet [5]. In contrast to spatial coherence based image smoothing, nonlocal means (NLM) denoising algorithms have been recently proposed, which average pixel intensities weighted by the similarity of pixel gray level in a certain neighborhood [6]. This kind of pixel selection scheme makes NLM significantly outperform traditional denoising methods such as anisotropic filtering [2], total variation [3], and bilateral filtering [7], which has enabled it to be used in various applications such as computer vision and statistical nonparametric regression [8, 9]. Extension of the original approach including scale and rotation invariance for the data patches used to define the weights is well studied [10–13]. However, as proposed in local denoising methods before [14], the pixel intensity itself cannot fully characterize the information contained in the image. Besides this, this kind of pointwise mean will cause large flat zones and spurious contours which are called “staircasing” effects. To