Graph Signal Recovery via Primal-Dual Algorithms for Total Variation Minimization

Berger, Peter M.; Hannák, Gábor; Matz, Gerald

doi:10.1109/jstsp.2017.2726978

Cited by 56 publications

(28 citation statements)

References 45 publications

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“…By applying stronger smoothing, the convergence speed can be improved but the reconstruction performance deteriorates in general, which is in agreement with [18], [20]. We highlight that Nestereov's smoothing strategy seems to be very effective for graphs with vastly varying node degrees, even though the additional smoothing step typically slows down the convergence on different graph models [16], [19]. For graphs with a = 1.5 and thus larger degree variations (stronger hubs), the convergence of FISTA is further slowed down so that the advantage of ACD becomes even more pronounced as can be seen in Fig.…”

Section: Algorithm 1 Acd Graph Signal Recoverysupporting

confidence: 76%

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Coordinate descent accelerations for signal recovery on scale-free graphs based on total variation minimization

Berger

Hannah

Matz

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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We extend our previous work on learning smooth graph signals from a small number of noisy signal samples. Minimizing the signal's total variation amounts to a non-smooth convex optimization problem. We propose to solve this problem using a combination of Nesterov's smoothing technique and accelerated coordinate descent. The resulting algorithm converges substantially faster, specifically for graphs with vastly varying node degrees (e.g., scale-free graphs).

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Section: Algorithm 1 Acd Graph Signal Recoverysupporting

confidence: 76%

“…Building on TV, we formulate graph signal recovery as a non-smooth convex optimization problem. In our previous work, we solved this problem using a combination of ADMM with denoising [15], a primal-dual algorithm [16], and Nesterov's method [17] (cf. [18]).…”

Section: Introductionmentioning

confidence: 99%

Coordinate descent accelerations for signal recovery on scale-free graphs based on total variation minimization

Berger

Hannah

Matz

2017

2017 25th European Signal Processing Conference (EUSIPCO)

Self Cite

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“…By modeling pixels as nodes with weighted edges that reflect inter-pixel similarities, images (or image patches) can be interpreted as graph signals. For image restoration, graph based image priors, such as graph Laplacian regularizer [9] and GTV [12]- [15], have been designed for different inverse problems.…”

Section: B Graph Based Image Priormentioning

confidence: 99%

Graph-Based Blind Image Deblurring From a Single Photograph

Bai

Cheung

Liu

et al. 2019

IEEE Trans. on Image Process.

156

124

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Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, deconvolve blurry input to restore the target image. In this paper, we propose a graph-based blind image deblurring algorithm by interpreting an image patch as a signal on a weighted graph. Specifically, we first argue that a skeleton image-a proxy that retains the strong gradients of the target but smooths out the details-can be used to accurately estimate the blur kernel and has a unique bi-modal edge weight distribution. Then, we design a reweighted graph total variation (RGTV) prior that can efficiently promote a bi-modal edge weight distribution given a blurry patch. Further, to analyze RGTV in the graph frequency domain, we introduce a new weight function to represent RGTV as a graph l1-Laplacian regularizer. This leads to a graph spectral filtering interpretation of the prior with desirable properties, including robustness to noise and blur, strong piecewise smooth (PWS) filtering and sharpness promotion. Minimizing a blind image deblurring objective with RGTV results in a non-convex non-differentiable optimization problem. We leverage the new graph spectral interpretation for RGTV to design an efficient algorithm that solves for the skeleton image and the blur kernel alternately. Specifically for Gaussian blur, we propose a further speedup strategy for blind Gaussian deblurring using accelerated graph spectral filtering. Finally, with the computed blur kernel, recent non-blind image deblurring algorithms can be applied to restore the target image. Experimental results demonstrate that our algorithm successfully restores latent sharp images and outperforms state-of-the-art methods quantitatively and qualitatively.

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“…The p value in (7) can take 1, 2 and ∞. When p = 1, S 1 ( f ) is the total variation of the signal on a graph [20]: …”

Section: A Non-local Patch Graph Total Variationmentioning

confidence: 99%

Image denoising via a non-local patch graph total variation

Zhang

Kong

et al. 2019

PLoS ONE

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Total variation (TV) based models are very popular in image denoising but suffer from some drawbacks. For example, local TV methods often cannot preserve edges and textures well when they face excessive smoothing. Non-local TV methods constitute an alternative, but their computational cost is huge. To overcome these issues, we propose an image denoising method named non-local patch graph total variation (NPGTV). Its main originality stands for the graph total variation method, which combines the total variation with graph signal processing. Schematically, we first construct a K-nearest graph from the original image using a non-local patch-based method. Then the model is solved with the Douglas-Rachford Splitting algorithm. By doing so, the image details can be well preserved while being denoised. Experiments conducted on several standard natural images illustrate the effectiveness of our method when compared to some other state-of-the-art denoising methods like classical total variation, non-local means filter (NLM), non-local graph based transform (NLGBT), adaptive graph-based total variation (AGTV).

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Graph Signal Recovery via Primal-Dual Algorithms for Total Variation Minimization

Cited by 56 publications

References 45 publications

Coordinate descent accelerations for signal recovery on scale-free graphs based on total variation minimization

Coordinate descent accelerations for signal recovery on scale-free graphs based on total variation minimization

Graph-Based Blind Image Deblurring From a Single Photograph

Image denoising via a non-local patch graph total variation

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