Nonlocal Total Variation Model Research Articles

Spatial-Frequency domain nonlocal total variation for image denoising

<p style='text-indent:20px;'>Following the pioneering works of Rudin, Osher and Fatemi on total variation (TV) and of Buades, Coll and Morel on non-local means (NL-means), the last decade has seen a large number of denoising methods mixing these two approaches, starting with the nonlocal total variation (NLTV) model. The present article proposes an analysis of the NLTV model for image denoising as well as a number of improvements, the most important of which being to apply the denoising both in the space domain and in the Fourier domain, in order to exploit the complementarity of the representation of image data. A local version obtained by a regionwise implementation followed by an aggregation process, called Local Spatial-Frequency NLTV (L-SFNLTV) model, is finally proposed as a new reference algorithm for image denoising among the family of approaches mixing TV and NL operators. The experiments show the great performance of L-SFNLTV in terms of image quality and of computational speed, comparing with other recently proposed NLTV-related methods.

An image denoising approach based on adaptive nonlocal total variation

In the nonlocal total variation (NLTV) model the constant regularization parameter λ cannot adaptively control the balance between the regularization term and the fidelity term, which may results in over-smoothing and the more losing image details in non-flat areas when λ is small, or insufficient noise removal in flat areas when λ is large. It is better that λ has different values according to the characteristics of image areas. In this paper, we introduce an adaptive regularization parameter λ(x) which can recognize flat areas and non-flat areas of an image and propose an improved NLTV model by replacing regularization parameter λ in NLTV model with the function λ(x). In addition, we calculate the similarity weight function of our model from the pre-filtered image to reduce the influence of noise on it. Experimental results demonstrate our approach outperforms some existing methods in terms of objective criteria and subjective visual perception.

Enhanced Non-Local Total Variation Model and Multi-Directional Feature Prediction Prior for Single Image Super Resolution.

It is widely acknowledged that single image super-resolution (SISR) methods play a critical role in recovering the missing high-frequencies in an input low-resolution image. As SISR is severely ill-conditioned, image priors are necessary to regularize the solution spaces and generate the corresponding high-resolution image. In this paper, we propose an effective SISR framework based on the enhanced non-local similarity modeling and learning-based multi-directional feature prediction (ENLTV-MDFP). Since both the modeled and learned priors are exploited, the proposed ENLTV-MDFP method benefits from the complementary properties of the reconstruction-based and learning-based SISR approaches. Specifically, for the non-local similarity-based modeled prior [enhanced non-local total variation, (ENLTV)], it is characterized via the decaying kernel and stable group similarity reliability schemes. For the learned prior [multi-directional feature prediction prior, (MDFP)], it is learned via the deep convolutional neural network. The modeled prior performs well in enhancing edges and suppressing visual artifacts, while the learned prior is effective in hallucinating details from external images. Combining these two complementary priors in the MAP framework, a combined SR cost function is proposed. Finally, the combined SR problem is solved via the split Bregman iteration algorithm. Based on the extensive experiments, the proposed ENLTV-MDFP method outperforms many state-of-the-art algorithms visually and quantitatively.

Image denoising via an improved non‐local total variation model

This study presents an improved non-local total variation (NLTV) model by using the block-matching and three-dimensional filtering (BM3D) algorithm for image denoising. First, the preprocessed image is obtained with the BM3D algorithm. Then, taking the place of the noisy image, the preprocessed image is used to construct the fidelity term of the energy functional and calculate the weight function in NLTV regularisation term. Finally, the energy functional is solved by the split Bregman algorithm. Experimental results demonstrate that the proposed model achieves better denoising performance than the original NLTV model in the visual appearance and objective indices, especially for the highly degenerated images. In addition, the proposed model can effectively suppress the appearance of the false information in the flat region, which overcomes the problem faced by the BM3D algorithm.

A tensor-based nonlocal total variation model for multi-channel image recovery

Abstract In this paper, a new nonlocal total variation (NLTV) regularizer is proposed for solving the inverse problems in multi-channel image processing. Different from the existing nonlocal total variation regularizers that rely on the graph gradient, the proposed nonlocal total variation involves the standard image gradient and simultaneously exploits three important properties inherent in multi-channel images through a tensor nuclear norm, hence we call this proposed functional as tensor-based nonlocal total variation (TenNLTV). In specific, these three properties are the local structural image regularity, the nonlocal image self-similarity, and the image channel correlation, respectively. By fully utilizing these three properties, TenNLTV can provide a more robust measure of image variation. Then, based on the proposed regularizer TenNLTV, a novel regularization model for inverse imaging problems is presented. Moreover, an effective algorithm is designed for the proposed model, and a closed-form solution is derived for a two-order complex eigen system in our algorithm. Extensive experimental results on several inverse imaging problems demonstrate that the proposed regularizer is systematically superior over other competing local and nonlocal regularization approaches, both quantitatively and visually.

Nonlocal Similarity Modeling and Deep CNN Gradient Prior for Super Resolution

This letter presents a novel super-resolution (SR) method via nonlocal similarity modeling and deep convolutional neural network (CNN) gradient prior (GP). Specifically, on the one hand, the group similarity reliability (GSR) strategy is proposed for improving the adaptive high-dimensional nonlocal total variation (AHNLTV) model [statistical prior, GSR-based AHNLTV (GA)], which captures the structures of the underlying high-resolution (HR) image via the image itself. On the other hand, the GP is learned by using the deep CNN (learned prior), which predicts the gradients from external images. Finally, the GA–GP approach is proposed by incorporating the two complementary priors. The results show that GA–GP achieves better performance than other state-of-the-art SR methods.

Image Block Compressive Sensing Reconstruction via Group-Based Sparse Representation and Nonlocal Total Variation

Compressive sensing (CS) has recently drawn considerable attentions in signal and image processing communities as a joint sampling and compression approach. Generally, the image CS reconstruction can be formulated as an optimization problem with a properly chosen regularization function based on image priors. In this paper, we propose an efficient image block compressive sensing (BCS) reconstruction method, which combine the best of group-based sparse representation (GSR) model and nonlocal total variation (NLTV) model to regularize the solution space of the image CS recovery optimization problem. Specifically, the GSR model is utilized to simultaneously enforce the intrinsic local sparsity and the nonlocal self-similarity of natural images, while the NLTV model is explored to characterize the smoothness of natural images on a larger scale than the classical total variation (TV) model. To efficiently solve the proposed joint regularized optimization problem, an algorithm based on the split Bregman iteration is developed. The experimental results demonstrate that the proposed method outperforms current state-of-the-art image BCS reconstruction methods in both objective quality and visual perception.

Efficient L1-based nonlocal total variational model of Retinex for image restoration

Characteristics of an image, such as smoothness, edge, and texture, can be better preserved using the nonlocal differential operator in image processing. We establish an L1-based nonlocal total variational (NLTVL1) model based on Retinex theory that can be solved by a fast computational algorithm via the alternating direction method of multipliers. Experiential results demonstrate that our NLTVL1 method has a good performance on enhancing contrast, eliminating the influence of nonuniform illumination, and suppressing noise. Furthermore, compared with previous works, including traditional Retinex methods and variational Retinex methods, our proposed approach achieves superior performance on edge and texture preservation and needs fewer iterations on recovering the reflectance image, which is illustrated by examples and statistics.

A new local and nonlocal total variation regularization model for image denoising

The total variation (TV) method for image deblurring is effective for sharpening image details in noisy images although this method tends to over-smooth the image details and inevitably results in staircase effects in smooth areas of the image. The nonlocal total variation (NLTV) method overcomes these drawbacks and retains fine details. However, it is not suitable for detecting similar patches and usually blurs edges in the image. Considering that the TV and NLTV are complementary, we propose a new local and nonlocal total variation (LNLTV) model. In this model, we first decompose the original image into a cartoon component and a detail component, then respectively apply the TV and NLTV to both components. To optimize the hybrid model, the Bregman iteration-based multivariable minimization (BIMM) method and the fast iteration-based multivariable minimization (FIMM) method are respectively employed to minimize the LNLTV energy function. The experimental results clearly demonstrate that the LNLTV model has better performance than some other state-of-the-art models with regard to evaluation indices and visual quality, and the FIMM method has a faster convergence rate and requires less time than the BIMM method.

Saliency driven vasculature segmentation with infinite perimeter active contour model

Automated detection of retinal blood vessels plays an important role in advancing the understanding of the mechanism, diagnosis and treatment of cardiovascular disease and many systemic diseases, such as diabetic retinopathy and age-related macular degeneration. Here, we propose a new framework for precisely segmenting retinal vasculatures. The proposed framework consists of three steps. A non-local total variation model is adapted to the Retinex theory, which aims to address challenges presented by intensity inhomogeneities, and the relatively low contrast of thin vessels compared to the background. The image is then divided into superpixels, and a compactness-based saliency detection method is proposed to locate the object of interest. For better general segmentation performance, we then make use of a new infinite active contour model to segment the vessels in each superpixel. The proposed framework has wide applications, and the results show that our model outperforms its competitors.

Video restoration based on a novel second order nonlocal total variation model

Total variation and its variants have been widely used in the video/image restoration area in the past decades. Among them, the nonlocal total variation model introduces penalization on nonlocal gradients and demonstrates remarkable performance gain in many applications. However, this approach tends to suppress intensity-changes of visual contents, and hence cannot restore complicated visual contents well enough. To address this issue, this paper proposes a novel second order nonlocal total variation model for video restoration problems. Firstly, the directed space-time nonlocal gradients are defined in our model to formulate the spatio-temporal intensity-changes of video contents. Secondly, mean-value approximations of these nonlocal gradients are introduced into the model. Based on them, we build up a new model that consists of both first order and second order nonlocal regularization terms. Furthermore, for the purpose of adapting to specific visual contents, it is also augmented with a content-adaptive modification. These features make the proposed second order nonlocal total variation model a high order generalization of the original one. Experimental results on various video restoration problems show that the proposed model significantly improves the restoration qualities, compared with other state-of-the-art approaches.

Enhanced Image Inpainting in Remotely Sensed Images by Optimizing NLTV model by Ant Colony Optimization

Filling dead pixels or eliminating unwanted things is typically preferred within the applications of remotely sensed images. In proposed article, a competent image imprinting technique is demonstrated to resolve this drawback, relied nonlocal total variation. Initially remotely sensed images are effected by ill posed inverse problems i.e. image destripping, image de-noising etc. So it is required to use regularization technique to makes these problems well posed i.e. NLTV method, which is the combination of nonlocal operators and total variation model. Actually this method can make use of the good features of non-local operators for textured images and total variation method in edge preserving for color images. To optimize the proposed variation model, an Ant Colony Optimization algorithm is used in order to get similarity with the original image. And evaluate the outcomes of proposed technique with the existing technique i.e. MNLTV optimized by Bregmanized-operator-splitting algorithm which is a prediction based method. The investigation of all outcomes confirms the efficacy of this rule.

Fast algorithm for color texture image inpainting using the non-local CTV model

The classical non-local Total Variation model has been extensively used for gray texture image inpainting previously, but such model can not be directly applied to color texture image inpainting du...

基于非局部全变差模型和全局非零局部秩惩罚的图像去模糊

图像成像及分析模块是未来汽车应用系统中的重要组成部分，清晰的图像为后续的智能控制提供可靠保证。然而，由于成像设备自身硬件的问题，使得图像出现模糊等问题。因此，为了能够从降质图像中复原出高质量的清晰图像，并为后续的处理带来便利，本文提出一种基于非局部全变差模型和全局非零局部秩惩罚的图像去模糊方法。非局部全变差模型主要用于恢复图像中的纹理细节，而非零局部秩惩罚则主要用于约束图像的边缘，达到锐化边缘的目的。本文所提出的方法在模拟图像和真实模糊图像的去模糊上都取得了很好的效果。 The imaging and analysis module is an important part of automobile application system in the fu-ture, and clear images provide a reliable guarantee for the intelligent control system. However, due to the existing problems of imaging equipment hardware, the obtained images appear blurring. Therefore, in order to restore the clean images from the blur ones and bring convenience to the subsequent processing, this paper proposes an image deblurring method based on non-local total variation and global non-zero local rank penalty. The non-local total variation model is mainly used to restore the texture details of image, and the non-zero local rank penalty is mainly used to sharp the edge of the image. The proposed deblurring method in this paper has achieved better results on simulated images and real blurred image than other methods.

Hyperspectral image recovery employing a multidimensional nonlocal total variation model

Hyperspectral images (HSIs) have a high spectral resolution and ground-object recognition ability, but inevitably suffer from various factors in the imaging procedure, such as atmospheric effects, secondary illumination, and the physical limitations, which have a direct bearing on the visual quality of the images and the accuracy of the subsequent processing. HSI restoration is therefore a crucial task for improving the precision of the subsequent products. Currently, patch-based schemes have offered promising results for the preservation of detailed information and the removal of additive noise. In HSIs, the information in the spectral dimension is more redundant than the information in the spatial dimension. We therefore propose a multidimensional hyperspectral nonlocal model, in which both the correlation of the spectral bands and the similarity of the spatial structure are considered. In the model, a multidimensional nonlocal total variation constraint is applied to preserve edge sharpness. Experiments with both synthetic and real hyperspectral data illustrate that the proposed method can obtain promising results in HSI restoration.

Content-based adaptive image denoising using spatial information

The maximum a posteriori (MAP) model is widely used in image processing fields, such as denoising, deblurring, segmentation, reconstruction, and others. However, the existing methods usually employ a fixed prior item and regularization parameter for the whole image and ignore the local spatial adaptive properties. Though the non-local total variation model has shown great promise because of exploiting the correlation in the image, the computation cost and memory load are the issues. In this paper, a content-based local spatial adaptive denoising algorithm is proposed. To realize the local spatial adaptive process of the prior model and regularization parameter, first the degraded image is divided into several same-sized blocks and the Tchebichef moment is used to analyze the local spatial properties of each block. Different property prior items and regularization parameters are then applied adaptively to different properties’ blocks. To reduce the computational load in denoising process, the split Bregman iteration algorithm is employed to optimize the non-local total variation model and accelerate the speed of the image denoising. Finally, a set of experiments and performance evaluation using recent image quality assessment index are provided to assess the effectiveness of the proposed method.

A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.

Inpainting for Remotely Sensed Images With a Multichannel Nonlocal Total Variation Model

Filling dead pixels or removing uninteresting objects is often desired in the applications of remotely sensed images. In this paper, an effective image inpainting technology is presented to solve this task, based on multichannel nonlocal total variation. The proposed approach takes advantage of a nonlocal method, which has a superior performance in dealing with textured images and reconstructing large-scale areas. Furthermore, it makes use of the multichannel data of remotely sensed images to achieve spectral coherence for the reconstruction result. To optimize the proposed variation model, a Bregmanized-operator-splitting algorithm is employed. The proposed inpainting algorithm was tested on simulated and real images. The experimental results verify the efficacy of this algorithm.

Non-blind image deblurring method by local and nonlocal total variation models

Although the total variation (TV) model can preserve the salient edges of the image, it smoothes out the image details. To preserve the salient edges while restoring the image details effectively, in this paper, we propose a new non-blind image deblurring (NBID) method, which combines the TV and the nonlocal total variation (NLTV) models. First, the original image is decomposed into three components: salient edges, details, and constant regions by a global gradient extraction scheme (GGES). Second, the TV model is applied on the salient edges and constant regions, and the NLTV model is applied on the details. At last, a split Bregman based multi-variable minimization (SBMM) iterative scheme is employed to optimize the proposed NBID inverse problem. Experiments demonstrate the viability and efficiency of the proposed method in terms of subjective vision, peak signal-to-noise ratio (PSNR), and self-similarity measure (SSIM).

非局部变分修复法去除高密度椒盐噪声

The reasons of ineffectiveness of median filtering and its improved algorithm for eliminating the high-density salt-and-pepper noise are analyzed. A variational inpainting method is adopted to remove the high-density salt-and-pepper noise,and a inpainting model of Non-local Total Variation( NL-TV) based on the existing model of Total Variation( TV) is proposed in this article. In the NL-TV model based on the characteristics of salt-and-pepper noise( uniform distribution and the gray value of 0 or 255),we view the noise points as the lost or damaged points of an image to find the districts similar to the neighborhoods of noise points in an image,and then interpolate the noise points by taking the central pixel in a similar district as a new neighborhood of noise points. By this method,we transform the problem of image denoising into a problem of image restoration to remove the high-density noise. The experimental results show that the Peak Signal to Noise Ratios( PSNRs) are 22. 85 and 28. 77 after removing the noise for a color and gray-scale image with 90% of noise density,which is better than the results obtained by median filter and its improved algorithm in terms of the objective evaluation criteria. Using this model,we can effectively remove the high-density salt-and-pepper noise and restore the image details better,which provides a new approach to remove the high-density noise.