A general framework for kernel similarity-based image denoising

Kheradmand, Amin; Milanfar, Peyman

doi:10.1109/globalsip.2013.6736903

Cited by 22 publications

(20 citation statements)

References 17 publications

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“…Proposed image priors in the literature include total variation (TV) [1], sparsity prior [2] and autoregressive prior [3]. Leveraging on the recent advances in graph signal processing (GSP) [4], [5], a relatively new prior is the graph Laplacian regularizer, which has been shown empirically to perform well, despite its simplicity, in a wide range of inverse problems, such as denoising [6]- [8], super-resolution [9], [10], deblurring [11], de-quantization of JPEG images [12]- [14] and bit-depth enhancement [15], [16]. We study the mechanisms and implications of graph Laplacian regularization for inverse imaging problems in this paper.…”

Section: A Motivationmentioning

confidence: 99%

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Pang

Cheung

2017

IEEE Trans. on Image Process.

226

228

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Abstract-Inverse imaging problems are inherently underdetermined, and hence it is important to employ appropriate image priors for regularization. One recent popular priorthe graph Laplacian regularizer-assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming nonlocal self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

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Section: A Motivationmentioning

confidence: 99%

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Pang

Cheung

2017

IEEE Trans. on Image Process.

226

228

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“…With the recent advances in GSP, newly developed GSP tools such as graph Fourier transforms (GFT) [4] are now being used for traditional image processing tasks such as image compression [10,11], denoising [12,13,14] and interpolation [15,16] with demonstrable gains. The key to much of these previous work is that with appropriate edge weights, a target graph-signal contains mostly low graph frequencies and thus can be compactly represented.…”

Section: Related Workmentioning

confidence: 99%

“…We discuss the design of H next. In GSP for image processing [11,12,13,16,17], a graph G is used to model inter-pixel correlation or similarities for a target pixel patch. Typically, a four-connected graph is employed to connect each pixel (represented as nodes in G) to its immediately neighbors vertically and horizontally.…”

Section: Problem Formulationmentioning

confidence: 99%

Joint denoising and contrast enhancement of images using graph laplacian operator

Liu

Cheung

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Images and videos are often captured in poor light conditions, resulting in low-contrast images that are corrupted by acquisition noise. To recreate a high-quality image for visual observation, the captured image must be denoised and contrastenhanced. Conventional methods perform these two tasks in two separate stages: an image is first denoised, followed by an enhancement procedure. In this paper, we propose to jointly denoise and enhance an image in one unified optimization framework. The crux of the optimization rests on the definition of the enhancement operator, described by a graph Laplacian matrix H. The operator must enhance the high frequency details of the original image without amplifying additive noise. We propose a graph-based low-pass filtering approach to denoise edge weights in the graph, resulting in a more robust estimate of H. Experimental results show that our proposed joint approach can outperform the separate approach in demonstrable image quality.

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“…Spatial domain methods that focus on the noise suppression approach estimate each pixel value as a weighted average of other pixels, then the weighted average of the high weights is considered to be similar pixels. 11. For the bilateral filter (BF), similarity is determined by both geometric and photometric distances between pixels, as shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Synthetic aperture radar image despeckling based on adaptive iterative risk estimator

Chu

Zhang

et al. 2015

J. Electron. Imaging

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Some classical filters, such as bilateral filter, nonlocal means (NLM) filter, and locally adaptive regression kernel, have proven to have a good performance in image denoising. However, there is one shortcoming, i.e., they cannot control the denoising strength very well. As for synthetic aperture radar (SAR) images, due to the special multiplicative noise, the denoising process becomes more complicated. A diffusion iterative filter can enhance the performance of a kernel in the denoising process but will lose some latent details and important targets from the underlying SAR image. In contrast, an iterative boosting filter can preserve these latent details of the SAR image well, although the improvement of the kernel performance is not very desired. By adopting the advantages of diffusion and boosting of the two iterative methods, an adaptive iterative risk estimator minimum mean square error (Min-MSE) method is proposed, which is mainly based on the Min-MSE to adaptively get the optimal iterative method and the corresponding optimal iterative number. The analysis of the experimental results and the comparison with some other state of the art methods demonstrate that our proposed method can improve the performance of an NLM filter and effectively suppress the SAR image speckle. Ji et al.: Synthetic aperture radar image despeckling based on adaptive iterative risk estimator Downloaded From: http://electronicimaging.spiedigitallibrary.org/ on 07/26/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Then we can get the MSE by summing the values of Eqs. (19) and (20): Journal of Electronic Imaging 043001-3 Jul∕Aug 2015 • Vol. 24(4) Ji et al.: Synthetic aperture radar image despeckling based on adaptive iterative risk estimator Downloaded From: http://electronicimaging.spiedigitallibrary.org/ on 07/26/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspxFig. 4 Comparison of denoising performance on SAR1: (a) SAR1 image; (b) PDE filtering result; (c) MAP filtering result; (d) NLM filtering result; (e) Lee filtering result; and (f) proposed method result. Ji et al.: Synthetic aperture radar image despeckling based on adaptive iterative risk estimator Downloaded From: http://electronicimaging.spiedigitallibrary.org/ on 07/26/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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A general framework for kernel similarity-based image denoising

Cited by 22 publications

References 17 publications

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Joint denoising and contrast enhancement of images using graph laplacian operator

Synthetic aperture radar image despeckling based on adaptive iterative risk estimator

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