Adaptive Regularization of the NL-Means: Application to Image and Video Denoising

Sutour, Camille; Deledalle, Charles-Alban; Aujol, Jean-François

doi:10.1109/tip.2014.2329448

Cited by 136 publications

(77 citation statements)

References 58 publications

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“…As one can see, we keep the same regularization term as in the ROF model, but we adapt the data fidelity term to the Cauchy noise, introducing one that is suitable for such a type of noise. We emphasize that TV regularization is a very useful tool for preserving edges but is not so good for texture recovery; thus, clearly, the proposed model can be extended to other modern regularization terms such as nonlocal TV [26,58,63], high order TV [61], dictionary learning [22,33], or a tight-frame approach [8,38]. Unfortunately, since the data fidelity term is not convex, the restored results depend on the initialization and the numerical scheme.…”

mentioning

confidence: 99%

Variational Approach for Restoring Blurred Images with Cauchy Noise

Sciacchitano

Dong

Zeng

2015

SIAM J. Imaging Sci.

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Abstract. The restoration of images degraded by blurring and noise is one of the most important tasks in image processing. In this paper, based on the total variation (TV) we propose a new variational method for recovering images degraded by Cauchy noise and blurring. In order to obtain a strictly convex model, we add a quadratic penalty term, which guarantees the uniqueness of the solution. Due to the convexity of our model, the primal dual algorithm is employed to solve the minimization problem. Experimental results show the effectiveness of the proposed method for simultaneously deblurring and denoising images corrupted by Cauchy noise. Comparison with other existing and well-known methods is provided as well.

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mentioning

confidence: 99%

Variational Approach for Restoring Blurred Images with Cauchy Noise

Sciacchitano

Dong

Zeng

2015

SIAM J. Imaging Sci.

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“…In contrast, in an isolated structure, very few similar neighbors are identified and most weights ω i,j are (close to) zero, leading to a very noisy estimate Σ (WML) i . To account for this disparity between estimates, we follow the idea of [27] and set the sum of weights τ i at pixel i (see Eq. (8)) to be inversely proportional to the standard deviation of the estimator:…”

Section: A Posteriori Energy Ementioning

confidence: 99%

“…These regularization models applied alone suffer some limits like staircasing effects affecting low slope areas and leading to piecewise constant reconstruction [26]. Following the approach proposed in [27] for image and video, we investigate the combination of both a patch-based approach and TV regularization for elevation estimation in a multi-baseline interferometric framework, exploiting the whole statistical distribution of the interferometric data.…”

Section: Introductionmentioning

confidence: 99%

Parisar: Patch-Based Estimation and Regularized Inversion for Multibaseline SAR Interferometry

Ferraioli

Deledalle

Denis

et al. 2018

IEEE Trans. Geosci. Remote Sensing

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Abstract-Reconstruction of elevation maps from a collection of SAR images obtained in interferometric configuration is a challenging task. Reconstruction methods must overcome two difficulties: the strong interferometric noise that contaminates the data, and the 2π phase ambiguities. Interferometric noise requires some form of smoothing among pixels of identical height. Phase ambiguities can be solved, up to a point, by combining linkage to the neighbors and a global optimization strategy to prevent from being trapped in local minima. This paper introduces a reconstruction method, PARISAR, that achieves both a resolution-preserving denoising and a robust phase unwrapping by combining non-local denoising methods based on patch similarities and total-variation regularization. The optimization algorithm, based on graph-cuts, identifies the global optimum. Combining patch-based speckle reduction methods and regularization-based phase unwrapping requires solving several issues: (i) computational complexity, the inclusion of non-local neighborhoods strongly increasing the number of terms involved during the regularization, and (ii) adaptation to varying neighborhoods, patch comparison leading to large neighborhoods in homogeneous regions and much sparser neighborhoods in some geometrical structures. PARISAR solves both issues. We compare PARISAR with other reconstruction methods both on numerical simulations and satellite images and show a qualitative and quantitative improvement over state-of-the-art reconstruction methods for multi-baseline SAR interferometry.

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“…The authors compare the performance obtained with 2D and 3D patches. Sutour et al [56] proposed to add an adaptive spatial regularization to non-local means, and to apply it to images and videos, also with 3D patches. In [49,50] the authors extend the K-SVD [20] image denoising method to video by learning a dictionary of spatio-temporal rectangular 3D patches.…”

Section: Introductionmentioning

confidence: 99%

Video Denoising via Empirical Bayesian Estimation of Space-Time Patches

Arias

Morel

2017

J Math Imaging Vis

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In this paper we present a new patch-based empirical Bayesian video denoising algorithm. The method builds a Bayesian model for each group of similar space-time patches. These patches are not motion compensated, and therefore avoid the risk of inaccuracies caused by motion estimation errors. The high dimensionality of spatio-temporal patches together with a limited number of available samples, poses challenges when estimating the statistics needed for an empirical Bayesian method. We therefore assume that groups of similar patches have a low intrinsic dimensionality, leading to a spiked covariance model. Based on theoretical results about the estimation of spiked covariance matrices, we propose estimators of the eigenvalues of the a priori covariance in high dimensional spaces as simple corrections of the eigenvalues of the sample covariance matrix. We demonstrate empirically that these estimators lead to better empirical Wiener filters. A comparison on classic benchmark videos demonstrates improved visual quality and an increased PSNR with respect to state-of-the-art video denoising methods.

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Adaptive Regularization of the NL-Means: Application to Image and Video Denoising

Cited by 136 publications

References 58 publications

Variational Approach for Restoring Blurred Images with Cauchy Noise

Variational Approach for Restoring Blurred Images with Cauchy Noise

Parisar: Patch-Based Estimation and Regularized Inversion for Multibaseline SAR Interferometry

Video Denoising via Empirical Bayesian Estimation of Space-Time Patches

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