Total Variation Denoising With Non-Convex Regularizers

Zou, Jian; Shen, Marui; Zhang, Ya; Li, Haifeng; Liu, Guoqi; Ding, Shuxue

doi:10.1109/access.2018.2888944

Cited by 27 publications

(12 citation statements)

References 46 publications

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“…Therefore, denoising is a crucial step to facilitate subsequent image processing such as segmentation, registration and visualization. For several decades, various denoising techniques have been presented for noise removal such as wavelet based methods [1], partial differential equations (PDE) based methods [2], total variation based methods [3], [4], nonlocal means (NLM) methods [5] and deep learning based methods [6]. Among these methods, the NLM method has attracted much attention in the field of image denoising.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Means Image Denoising With Minimum MSE-Based Decay Parameter Adaptation

Zhan

Ding

et al. 2019

IEEE Access

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Nonlocal means (NLM), a patch-based nonlocal recovery paradigm, has attracted much attention in recent decades. The decay parameter will greatly affect restoration performance of the NLM method. However, the existing NLM methods with decay parameter adaptation cannot determine this parameter effectively. To address this problem, we have proposed the minimum mean square error (MSE) based decay parameter adaptation method for the NLM denoising. In the proposed method, the globally optimal decay parameter is determined to produce the pre-denoised image based on the derived relation between the global minimum MSE and the decay parameter. Then, the pixel-wise MSE is estimated based on the pre-denoised result and the corresponding method noise. Finally, the optimal pixel-wise decay parameter is obtained by minimizing the pixel-wise MSE to produce the estimated restored image and the boosting strategy is implemented on this image to generate the final denoised result. Extensive simulations on the standard test images and real images corrupted with Gaussian noise and speckle noise demonstrate that the proposed method significantly outperforms some compared NLM methods in noise reduction and detail preservation and can provide better restoration performance than other state-of-the-art denoising methods in most cases in terms of objective metrics and human vision. INDEX TERMS Nonlocal means, decay parameter, mean square error, Gaussian noise, speckle noise. u(x, y) = NL[I ](x, y) = (p,q)∈ I (p, q)ω(x, y, p, q) (p,q)∈ ω(x, y, p, q) , (1) where NL denotes the nonlocal means, and is a search window. The weight ω(x, y, p, q) denoting the similarity between two pixels at (p, q) and (x, y) is calculated as: ω(x, y, p, q) = exp − ||I (P(p, q)) − I (P(x, y))|| 2 2,a h 2 , (2) where h denotes the decay parameter controlling the filtering degree, P(p, q) and P(x, y) are the two similarity windows (image patches) centered at (x, y) and (p, q), respectively; ||I (P(p, q)) − I (P(x, y))|| 2 2,a means the weighted Euclidean distance between two image patches P(p, q) and P(x, y) of

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Section: Introductionmentioning

confidence: 99%

Nonlocal Means Image Denoising With Minimum MSE-Based Decay Parameter Adaptation

Zhan

Ding

et al. 2019

IEEE Access

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“…For instance, Mila Nikolova used a non-convex penalty to denoise binary images in a convex optimization problem [32]. This idea, later called the Convex Non-Convex strategy, has been further developed to sparse-regularized optimization problems [3,25,43], including 1D and 2D total variation denoising [20,28,30,54], transform-based denoising [18,36], low-rank matrix estimation [37], and segmentation of images and scalar fields over surfaces [12,24]. This CNC approach to sparse regularization has been used in machine fault detection [7,52].…”

Section: Related Workmentioning

confidence: 99%

Non-convex Total Variation Regularization for Convex Denoising of Signals

et al. 2020

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Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a 'convex non-convex' strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising. 1 Introduction Piecewise constant signals arise in numerous fields such as physics, biology, and medicine [29]. These signals are often corrupted by additive noise which should be suppressed. Conventional linear time-invariant (LTI) filters

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“…is the non-convex TV regularization based on the Moreau envelop and minimax-concave penalty [28], [29].…”

Section: ) Model Constructionmentioning

confidence: 99%

Fusing Multilevel Deep Features for Fabric Defect Detection Based NTV-RPCA

Dong

Wang

et al. 2020

IEEE Access

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Fabric defect detection plays an important role in automated inspection and quality control in textile manufacturing. As the fabric images have complex and diverse textures and defects, traditional detection methods show a poor adaptability and low detection accuracy. Robust principal component analysis (RPCA) model that can be used to separate the image into object and background have proven applicable in fabric defect detection. However, how to represent texture feature of the fabric image more effectively is still problematic in this kind of method. In addition, the use of the traditional RPCA may result in low accuracy and more noises in sparse part. In this paper, a novel fabric defect detection method based on multilevel deep features fusion and non-convex total variation regularized RPCA (NTV-RPCA) is proposed. Firstly, the image representation ability is well enhanced through multilevel deep features extracted by a convolutional neural network. Then, the non-convex total variation regularized RPCA is proposed in which total variation constraint significantly reduces the noises in sparse part and non-convex solution is more approximate to the authentic one. Next, multilevel saliency maps generated by the sparse matrixes are fused via RPCA to produce a more reliable detection result. Finally, the defect region is located by segmenting the fused saliency map via a threshold segmentation algorithm. Qualitative and quantitative experiments conducted on two public fabric image databases demonstrate that the proposed method improves the adaptability and detection accuracy comparing to the state-of-the-arts.

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Total Variation Denoising With Non-Convex Regularizers

Cited by 27 publications

References 46 publications

Nonlocal Means Image Denoising With Minimum MSE-Based Decay Parameter Adaptation

Nonlocal Means Image Denoising With Minimum MSE-Based Decay Parameter Adaptation

Non-convex Total Variation Regularization for Convex Denoising of Signals

Fusing Multilevel Deep Features for Fabric Defect Detection Based NTV-RPCA

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