Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means

International audienceWe first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. Based on the convergence theorems, we propose a patch-based weighted means filter for removing an impulse noise and its mixture with a Gaussian noise by combining the essential idea of the trilateral filter and that of the non-local means filter. Experiments show that our filter is competitive compared to recently proposed methods. We also introduce the notion of degree of similarity to measure the impact of the similarity among patches on the non-local means filter for removing a Gaussian noise, as well as on our new filter for removing an impulse noise or a mixed noise. Using again the convergence theorem in distribution , together with the notion of degree of similarity, we obtain an estimation for the PSNR value of the denoised image by the non-local means filter or by the new proposed filter, which is close to the real PSNR value

Color image restoration with Fuzzy Gaussian mixture model driven nonlocal filter

© Springer International Publishing Switzerland 2015. Color image denoising is one of the classical image processing problem and various techniques have been explored over the years. Recently, nonlocal means (NLM) filter is proven to obtain good results for denoising Gaussian noise corrupted digital images using weighted mean among similar patches. In this paper, we consider fuzzy Gaussian mixture model (GMM) based NLM method for removing mixed Gaussian and impulse noise. By computing an automatic homogeneity map we identify impulse noise locations and utilize an adaptive patch size. Experimental results on mixed noise affected color images show that our scheme performs better than NLM, anisotropic diffusion and GMM-NLM over different noise levels. Comparison with respect to structural similarity, color image difference, and peak signal to noise ratio error metrics are undertaken and our scheme performs well overall without generating color artifacts

Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell_1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure

Mixed-Model Noise Removal in 3D MRI via Rotation-and-Scale Invariant Non-Local Means

Mixed noise is a major issue influencing quantitative analysis in different forms of magnetic resonance image (MRI), such as T1 and diffusion image like DWI and DTI. Using different filters sequentially to remove mixed noise will severely deteriorate such medical images. We present a novel algorithm called rotation-and-scale invariant nonlocal means filter (RSNLM) to simultaneously remove mixed noise from different kinds of three-dimensional (3D) MRI images. First, we design a new similarity weights, including rank-ordered absolute difference (ROAD), coming from a trilateral filter (TriF) that is obtained to detect the mixed and high-level noise. Then, we present a shape view to consider the MRI data as a 3D operator, with which the similarity between the patches is calculated with the rigid transformation. The translation, rotation and scale have no influence on the similarity. Finally, the adaptive parameter estimation method of ROAD is illustrated, and the effective proof that validates the proposed algorithm is presented. Experiments using synthetic data with impulse noise, Rician noise, and the real MRI data confirm that the proposed method yields superior performance compared with current state-of-the-art methods

NON-LOCAL FILTER FOR REMOVING A MIXTURE OF GAUSSIAN AND IMPULSE NOISES

International audienceIn this paper we first present two convergence theorems which give a theoretical justification of the Non-Local Means Filter. Based on these theorems, we propose a new filter, called Non-Local Mixed Filter, to remove a mixture of Gaussian and random impulse noises. This filter combines the essential ideas of the Trilateral Filter and the Non-Local Means Filter. It improves the Trilateral Filter and extends the Non-Local Means Filter. Our experiments show that the new filter generally outperforms two other recent proposed methods. A careful discussion and simple formulas are given for the choice of parameters for the proposed filter

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure