Adaptive Non-Local Means using Weight Thresholding

Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses a patch-based approach to find similar regions within a search neighborhood and estimate the denoised pixel based on the weighted average of all the pixels in the neighborhood. All the pixels are considered for averaging, irrespective of the value of their weights. This thesis proposes an improved variant of the original NLM scheme, called Weight Thresholded Non-Local Means (WTNLM), by thresholding the weights of the pixels within the search neighborhood, where the thresholded weights are used in the averaging step. The key parameters of the WTNLM are defined using learning-based models. In addition, the proposed method is used as a two-step approach for image denoising. At the first step, WTNLM is applied to generate a basic estimate of the denoised image. The second step applies WTNLM once more but with different smoothing strength. Experiments show that the denoising performance of the proposed method is better than that of the original NLM scheme, and its variants. It also outperforms the state-of-the-art image denoising scheme, BM3D, but only at low noise levels (σ ≤ 80)

A new ADMM algorithm for the Euclidean median and its application to robust patch regression

The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel algorithm for computing the EM (and its box-constrained counterpart) using variable splitting and the method of augmented Lagrangian. The attractive feature of this approach is that the subproblems involved in the ADMM-based optimization of the augmented Lagrangian can be resolved using simple closed-form projections. The proposed ADMM solver is used for robust patch-based image denoising and is shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201

Artifact reduction for separable non-local means

It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can perform fast non-local means (NLM) denoising of one-dimensional signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for non-local means denoising of images. To bypass this, the authors proposed a separable approximation in which the image rows and columns are filtered using lifting. The overall algorithm is significantly faster than NLM, and the results are comparable in terms of PSNR. However, the separable processing often produces vertical and horizontal stripes in the image. This problem was previously addressed by using a bilateral filter-based post-smoothing, which was effective in removing some of the stripes. In this letter, we demonstrate that stripes can be mitigated in the first place simply by involving the neighboring rows (or columns) in the filtering. In other words, we use a two-dimensional search (similar to NLM), while still using one-dimensional patches (as in the previous proposal). The novelty is in the observation that one can use lifting for performing two-dimensional searches. The proposed approach produces artifact-free images, whose quality and PSNR are comparable to NLM, while being significantly faster.Comment: To appear in Journal of Electronic Imagin

DERMATOLOGICAL IMAGE DENOISING USING ADAPTIVE HENLM METHOD

In this paper we propose automatic image denoising method based on Hermite functions (HeNLM). It is an extension of non-local means (NLM) algorithm. Differences between small image blocks (patches) are replaced by differences between feature vectors thus reducing computational complexity. The features are calculated in coordinate system connected with image gradient and are invariant to patch rotation. HeNLM method depends on the parameter that controls filtering strength. To chose automatically this parameter we use a no-reference denoising quality assessment method. It is based on Hessian matrix analysis. We compare the proposed method with full-reference methods using PSNR metrics, SSIM metrics, and its modifications MSSIM and CMSC. Image databases TID, DRIVE, BSD, and a set of dermatological immunofluorescence microscopy images were used for the tests. It was found that more perceptual CMSC and MSSIM metrics give worse correspondence than SSIM and PSNR to the results of information preservation by the non-reference image denoising

Total Variation as a local filter

International audienceIn the Rudin-Osher-Fatemi (ROF) image denoising model, Total Variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by Total Variation do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose to build a purely local filter by considering the ROF model in a given neighborhood of each pixel. We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter, and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction a ROF drawback called "staircasing effect". We finally present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the non-local means patch-based method

Adaptive non-local means for multiview image denoising: Searching for the right patches via a statistical approach

ABSTRACT We present an adaptive non-local means (NLM) denoising method for a sequence of images captured by a multiview imaging system, where direct extensions of existing single image NLM methods are incapable of producing good results. Our proposed method consists of three major components: (1) a robust joint-view distance metric to measure the similarity of patches; (2) an adaptive procedure derived from statistical properties of the estimates to determine the optimal number of patches to be used; (3) a new NLM algorithm to denoise using only a set of similar patches. Experimental results show that the proposed method is robust to disparity estimation error, out-performs existing algorithms in multiview settings, and performs competitively in video settings. Index Terms-Non-local means, adaptive filtering, multiview denoising, patch-based denoisin

Adaptive Image Denoising by Targeted Databases

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images and face images. Experimental results show the superiority of the new algorithm over existing methods.Comment: 15 pages, 13 figures, 2 tables, journa