Detail-preserving Image Denoising Via Adaptive Clustering And Progressive PCA Approximation

Digital cameras and other imaging modalities such as Magnetic Resonance Imaging(MRI),Nuclear Medicine Imaging,Fluorescence Microscopy,are always susceptible to various kinds of noise.Computer vision and biomedical imaging applications have increasingly called for detail-preserving image denoising.However,many state-of-the-art denoising algorithms fail to preserve important image detail(edges and textures)and often over-smooth the image.To solve this problem,we exploit the relationship between additive Gaussian noise and the noise in digital camera,MRI,Nuclear Medicine Imaging,and Fluorescence Microscopy,and transform the problem of image denoising in these imaging modalities into that of Gaussian denoising.When considering the Gaussian denoising,we apply the Marchenko-Pastur(MP)law in random matrix theory to obtain a robust and accurate noise level estimation.Then,a texture-preserving noise reduction algorithm based on adaptive clustering and progressive PCA-transform-domain approximation has also been proposed.Specifically,for the noise level estimation,we use the MP law in the matrix theory to interpret eigenvalues of the covariance matrix of the noise-disturbed data matrix,and a robust noise-estimation performance is achieved.When the noise level estimation value is estimated,we perform the detail-preserving noise reduction.First of all,we propose a two-step clustering algorithm in an overclustering-anditerative-merging approach to adaptively divide the image into distinct clusters.This clustering algorithm first uses the ”divide and conquer” technique to obtain excess clusters.Then an iterative cluster merging is performed based on a custom threshold related to the noise level and cluster size.When the total cluster number is no longer reduced,the algorithm converges.After the adaptive clustering is completed,we use a progressive PCA-transform-domain approximation for detail-preserving noise reduction for the cluster matrix.PCA is first used to decorrelate the various dimensions of the patch vector.Then according to the noise level and the MP law,the dimensions containing the main signal are selected by a hard threshold,while the dimensions mainly composed of noise are discarded.For each of the remaining signal-dominated dimensions,we use the suboptimal Wiener filter for detail-preserving noise reduction.Taking into account the varieties of the coefficients of each dimension,we obtain the optimal window length for the Wiener filter parameter estimation using the local polynomial approximationintersection of confidence interval algorithm(LPA-ICI).The final denoising result is obtained after the patches in all the clusters are aggregated and averaged.Experiments show that the proposed denoising algorithm has favorable visual and quantitative performances when dealing with stochastic texture images,surpassing many state-of-the-art noise reduction algorithms,including the deep-learning based noise reduction algorithm proposed in recent years.In experiments for the real noisy images from MRI,nuclear medicine imaging,and fluorescence microscopy,the proposed algorithm also shows satisfactory detailpreserving denoising performance.