Nonlocal Regularization Research Articles

Analytical Low-Dose CBCT Reconstruction Using Non-local Total Variation Regularization for Image Guided Radiation Therapy.

Purpose: Conventional iterative low-dose CBCT reconstruction techniques are slow and tend to over-smooth edges through uniform weighting of the image penalty gradient. In this study, we present a non-iterative analytical low-dose CBCT reconstruction technique by restoring the noisy low-dose CBCT projection with the non-local total variation (NLTV) method.Methods: We modeled the low-dose CBCT reconstruction as recovering high quality, high-dose CBCT x-ray projections (100 kVp, 1.6 mAs) from low-dose, noisy CBCT x-ray projections (100 kVp, 0.1 mAs). The restoration of CBCT projections was performed using the NLTV regularization method. In NLTV, the x-ray image is optimized by minimizing an energy function that penalizes gray-level difference between pair of pixels between noisy x-ray projection and denoising x-ray projection. After the noisy projection is restored by NLTV regularization, the standard FDK method was applied to generate the final reconstruction output.Results: Significant noise reduction was achieved comparing to original, noisy inputs while maintaining the image quality comparable to the high-dose CBCT projections. The experimental validations show the proposed NLTV algorithm can robustly restore the noise level of x-ray projection images while significantly improving the overall image quality. The improvement in normalized mean square error (NMSE) and peak signal-to-noise ratio (PSNR) measured from the non-local total variation-gradient projection (NLTV-GPSR) algorithm is noticeable compared to that of uncorrected low-dose CBCT images. Moreover, the difference of CNRs from the gains from the proposed algorithm is noticeable and comparable to high-dose CBCT.Conclusion: The proposed method successfully restores noise degraded, low-dose CBCT projections to high-dose projection quality. Such an outcome is a considerable improvement to the reconstruction result compared to the FDK-based method. In addition, a significant reduction in reconstruction time makes the proposed algorithm more attractive. This demonstrates the potential use of the proposed algorithm for clinical practice in radiotherapy.

SAR Image Despeckling Based on Combination of Fractional-Order Total Variation and Nonlocal Low Rank Regularization

Regularization method is an effective tool for synthetic aperture radar (SAR) image despeckling. Design of the effective regularization terms describing the image priors plays a vital role in this kind of method. In this article, a new combinational regularization model for speckle reduction (CRM-SR) is proposed, in which a regularization term is elaborately designed to contain both a fractional-order total variation (FrTV) regularization and a nonlocal low rank (NLR) regularization. The new regularization model inherits both the advantages of FrTV and NLR and improves the performance of SAR despeckling and, therefore, better preserves the edges and geometrical features of the images during the despeckling process. An efficient algorithm based on alternating direction optimization is derived to solve the proposed combinational regularization model. Experimental results show that the proposed model can effectively remove SAR image speckle and preserve the geometrical features of images according to both subjective visual assessment of image quality and objective evaluation.

Adaptively weighted nonlocal means and TV minimization for speckle reduction in SAR images

Speckle noise reduction is an important issue in synthetic aperture radar (SAR) imaging. Because SAR images are distinct in being complex valued and susceptible to corruption owing to multiplicative fluctuations, specialized methods for speckle reduction are needed. Techniques based on nonlocal means perform denoising by exploiting the natural redundancy of patterns within an image. They calculate a weighted average of pixels whose neighborhoods are close to one another, where this significantly reduces noise while preserving most image content. While this method performs well on flat areas and textures, its results are excessively smooth in low-contrast areas, and leave residual noise around edges and singular structures. Another variational denoising method uses total variation (TV) minimization to restore regular images but is prone to excessively smooth textures, the staircasing effect, and contrast losses. Our proposed model is intended for the logarithmic domain of SAR data, and combines the above two methods by minimizing an adaptive TV using a nonlocal data fidelity term. In the variational functionals developed here, weighted parameters of nonlocal regularization are adaptively tuned based on local heterogeneity information and noise in the images. A fast iterative shrinkage/thresholding algorithm (FISTA) is then used to solve the optimization problem. The results of experiments on real SAR images verify the effectiveness of the proposed method in terms of speckle reduction.

Cyber Intrusion Prevention for Large-Scale Semi-Supervised Deep Learning Based on Local and Non-Local Regularization

The cyber intrusion prevention model represents a new means of cyber protection with intelligent defense capability. It can not only detect intrusion behavior but also respond to such behavior in a timely manner. This study applies deep learning theory and semi-supervised clustering to cyber intrusion prevention technology. Deep learning based on deep structures represents the current development trend of neural networks. Semi-supervised learning uses a large amount of unlabeled cyber traffic data and a small amount of labeled cyber traffic data to achieve cyber intrusion prevention with a low recognition error rate. Discriminative deep belief network (DDBN)-based cyber defense technology has emerged as a research hotspot in the field of cyber intrusion prevention owing to its low error rate. This paper proposes a cyber intrusion prevention technology using DDBN for large-scale semi-supervised deep learning based on local and non-local regularization to overcome the problem of high classification error rates of the cyber intrusion prevention model. Through comparisons with the cyber intrusion prevention results of the Hopfield, support vector machine (SVM), generative adversarial network (GAN), and deep belief network-random forest (DBN-RFS) classifiers, the proposed DDBN model is shown to have the lowest error rate. Thus, the proposed approach can improve the performance of the cyber intrusion prevention system. The training and testing error rates of the exponent loss function with local and non-local regularization (exponent with LNR) are lower than those of the exponent, square, and hinge loss functions. The experimental results show that the running time decreases as the number of hidden layers increases, especially with 6144 and 4096 hidden layer nodes.

Weighted Nonlocal Low-Rank Tensor Decomposition Method for Sparse Unmixing of Hyperspectral Images

The low spatial resolution of hyperspectral images leads to the coexistence of multiple ground objects in a single pixel (called mixed pixels). A large number of mixed pixels in a hyperspectral image hinders the subsequent analysis and application of the image. In order to solve this problem, a novel sparse unmixing method, which considers highly similar patches in nonlocal regions of a hyperspectral image, is proposed in this article. This method exploits spectral correlation by using collaborative sparsity regularization and spatial information by employing total variation and weighted nonlocal low-rank tensor regularization. To effectively utilize the tensor decomposition, nonlocal similar patches are first grouped together. Then, these nonlocal patches are stacked to form a patch group tensor. Finally, weighted low-rank tensor regularization is enforced to constrain the patch group to obtain an estimated low-rank abundance image. Experiments on simulated and real hyperspectral datasets validated the superiority of the proposed method in better maintaining fine details and obtaining better unmixing results.

A Variational Image Segmentation Model Based on Normalized Cut with Adaptive Similarity and Spatial Regularization

Image segmentation is a fundamental research topic in image processing and computer vision. In recent decades, researchers developed a large number of segmentation algorithms for various applications. Among these algorithms, the normalized cut (Ncut) segmentation method is widely applied due to its good performance. The Ncut segmentation model is an optimization problem whose energy is defined on a specifically designed graph. Thus, the segmentation results of the existing Ncut method are largely dependent on a preconstructed similarity measure on the graph since this measure is usually given empirically by users. This flaw will lead to some undesirable segmentation results. In this paper, we propose an Ncut-based segmentation algorithm by integrating an adaptive similarity measure and spatial regularization. The proposed model combines the Parzen--Rosenblatt window method, nonlocal weights entropy, Ncut energy, and regularizer of phase field in a variational framework. Our method can adaptively update the similarity measure function by estimating some parameters. This adaptive procedure enables the proposed algorithm to find a better similarity measure for classification than the Ncut method. We provide some mathematical interpretation of the proposed adaptive similarity from multiple viewpoints, such as statistics and convex optimization. In addition, the regularizer of phase field can guarantee that the proposed algorithm has a robust performance in the presence of noise, and it can also rectify the similarity measure with a spatial priori. The well-posed theory such as the existence of the minimizer for the proposed model is given in the paper. Compared with some existing segmentation methods such as the traditional Ncut-based model and the classical Chan--Vese model, the numerical experiments show that our method can provide promising segmentation results.

Hyperspectral Image Compressive Sensing Reconstruction Using Subspace-Based Nonlocal Tensor Ring Decomposition

Hyperspectral image compressive sensing reconstruction (HSI-CSR) can largely reduce the high expense and low efficiency of transmitting HSI to ground stations by storing a few compressive measurements, but how to precisely reconstruct the HSI from a few compressive measurements is a challenging issue. It has been proven that considering the global spectral correlation, spatial structure, and nonlocal self-similarity priors of HSI can achieve satisfactory reconstruction performances. However, most of the existing methods cannot simultaneously capture the mentioned priors and directly design the regularization term to the HSI. In this article, we propose a novel subspace-based nonlocal tensor ring decomposition method (SNLTR) for HSI-CSR. Instead of designing the regularization of the low-rank approximation to the HSI, we assume that the HSI lies in a low-dimensional subspace. Moreover, to explore the nonlocal self-similarity and preserve the spatial structure of HSI, we introduce a nonlocal tensor ring decomposition strategy to constrain the related coefficient image, which can decrease the computational cost compared to the methods that directly employ the nonlocal regularization to HSI. Finally, a well-known alternating minimization method is designed to efficiently solve the proposed SNLTR. Extensive experimental results demonstrate that our SNLTR method can significantly outperform existing approaches for HSI-CSR.

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

Hyperspectral image (HSI) super-resolution is a technique to improve the spatial resolution of a HSI for better visual perception and down stream applications. This is a very ill-posed inverse problem and is often solved by fusing the low-resolution (LR) HSI with a high-resolution (HR) multispectral image (MSI). It is more challenging for blind HSI super-resolution, i.e., when the spatial degradation operators are completely unknown. In this paper, we propose a novel sparse tensor factorization model for the task of blind HSI super-resolution using the spatial non-local self-similarity and spectral global correlation of HSIs. Image clustering method is employed to collect some similar 3D cubes of HSIs which can be formed as some 4D image clusters with high correlation. We conduct cluster wise computation to not only save computation time but also to introduce a non-local regularity originated from the redundancy of cubes. By using the sparsity of tensor decomposition and the low-rank in non-local self-similarity direction underlying 4D similar clusters, we design a sparse tensor regularization term, which preserves the spatial-spectral structural correlation of HSIs. In addition, we present a proximal alternating direction method of multipliers (ADMM) based algorithm to efficiently solve the proposed model. Numerical experiments demonstrate that the proposed model outperforms many state-of-the-art HSI super-resolution methods.

Robust Image Compressive Sensing Based on Truncated Cauchy Loss and Nonlocal Low-Rank Regularization

This work presents a novel robust image compressive sensing reconstruction approach. In contrast to the existing work, we employ the truncated Cauchy loss function to measure the errors induced during the measurement, showing strong robustness to impulsive noise and outliers. To ensure high quality reconstructed images, we utilize a non-local low rank regularizer - with truncated Schatten-p norm being the surrogate function of rank - to capture the self-similar property inherent in most natural images. Considering the fact that the whole optimization model is neither convex nor smooth, to solve it effectively, we firstly use the half-quadratic strategy to transform the loss function into a quadratic objective by introducing some auxiliary variables, and then iteratively and alternatively optimize different groups of variables. Extensive experimental results demonstrate its effectiveness in terms of both quantitative indexes of Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM), and visual quality under impulsive noise.

On the Fusion of Energy Resolved Scatter and Attenuation Data for Limited-View X-Ray Materials Characterization With Application to Security Screening

Motivated by the use of X-rays for security screening, we demonstrate the utility of fusing energy-resolved observations of scattered photons with traditional attenuation data for the joint recovery of electron density and photoelectric coefficient in the context of limited-view tomographic imaging scenarios. We begin by developing a physical and associated numerical model for the scatter physics used within our processing. With this model, in this paper, we propose a variational approach for recovering the two material properties. In addition to the typical data-fidelity terms, the optimization functional includes regularization for both the electron density and photoelectric coefficients. We consider an edge-preserving method in the case of electron density. We employ a nonlocal regularization scheme that improves the stability with which we can recover the photoelectric coefficient. Imaging results using Monte-Carlo simulations demonstrate both qualitative and quantitative advantages associated with supplementing traditional attenuation data with scatter observations for mapping the two material properties. The work in this paper has focused on providing an initial proof-of-concept concerning the potential utility in fusing observations of scattered and attenuated photons. Furthermore, enhancements are required to adapt this method for use in deployed security screening systems.

Nonlocal TV-Gaussian prior for Bayesian inverse problems with applications to limited CT reconstruction

Bayesian inference methods have been widely applied in inverse problems due to the ability of uncertainty characterization of the estimation. The prior distribution of the unknown plays an essential role in the Bayesian inference, and a good prior distribution can significantly improve the inference results. In this paper, we propose a hybrid prior distribution on combining the nonlocal total variation regularization (NLTV) and the Gaussian distribution, namely NLTG prior. The advantage of this hybrid prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the hybrid prior. We apply the proposed prior to limited tomography reconstruction problem that is difficult due to severe data missing. Both maximum a posteriori and conditional mean estimates are computed through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior.

Coupled damage variable based on fracture locus: Modelling and calibration

A continuum ductile damage and failure model coupled with metal plasticity is presented, with the focus on capturing different failure mechanisms and prediction of the strain localisation. The onset of diffuse necking and local thinning is observed in the early stage of experiment and it is caused by the very low strain hardening capability of the material under study. Uniaxial tensile tests have been performed on notched and shear samples, specifically designed to cover different stress states by varying both the notch radius and orientation with respect to the sample axis. The experiments have revealed strain localisation caused by material softening. The latter is modelled by a coupled damage accumulation rule whose magnitude is dictated by the actual stress state and strain to fracture. Since the numerical model relies on the fracture strain determined by digital image correlation (DIC), which is dependent on the length scale imposed by the resolution of the DIC grid, an experimentally resolved length scale parameter l is introduced by nonlocal regularization of the material flow, based on large-deformation gradient theory. Apart from its common role of ensuring mesh independency, the length scale parameter obtains a new additional role: it makes the fracture locus calibration procedure robust under changes induced by different spatial averaging of the experimental fracture strain. The measured width of the strain localisation equals to the regularization length scale parameter l used in finite element (FE) simulations, thereby ensuring tight correspondence of physical reality and numerical model on the basis of a measurable quantity. As a result, the nonlocal regularization term prevents the strain in the numerical model to localise to a higher extent than experimentally observed. Eventually, the fracture locus has been constructed as a function of stress triaxiality ratio and Lode angle parameter. The FE-modelling methodology is calibrated by force-displacement curves and surface strain profiles prior to failure, obtained by DIC for a subset of sample geometries. The predictive capability of the proposed methodology is demonstrated by computing and comparing FE results to another experimentally characterized sample, not used in calibration procedure, i.e. dog-bone specimen. It undergoes a complicated loading path different from the paths used in the calibration procedure. It has been shown that regularization of strains and metal plasticity model supplemented by a damage variable are indispensable for an overall agreement of experimental and numerical results. The unique numerical model formulation has proven capable of capturing strongly different ductile failure modes, which are experimentally observed and further discussed.

Hyperspectral Image Denoising With Total Variation Regularization and Nonlocal Low-Rank Tensor Decomposition

Hyperspectral images (HSIs) are normally corrupted by a mixture of various noise types, which degrades the quality of the acquired image and limits the subsequent application. In this article, we propose a novel denoising method for the HSI restoration task by combining nonlocal low-rank tensor decomposition and total variation regularization, which we refer to as TV-NLRTD. To simultaneously capture the nonlocal similarity and high spectral correlation, the HSI is first segmented into overlapping 3-D cubes that are grouped into several clusters by the $k$ -means++ algorithm and exploited by low-rank tensor approximation. Spatial–spectral total variation (SSTV) regularization is then investigated to restore the clean HSI from the denoised overlapping cubes. Meanwhile, the $\ell _{1} $ -norm facilitates the separation of the clean nonlocal low-rank tensor groups and the sparse noise. The proposed TV-NLRTD method is optimized by employing the efficient alternating direction method of multipliers (ADMM) algorithm. The experimental results obtained with both simulated and real hyperspectral data sets confirm the validity and superiority of the proposed method compared with the current state-of-the-art HSI denoising algorithms.

Video deraining via nonlocal low-rank regularization

Outdoor videos captured in rainy weather may be significantly corrupted by the undesired rain streaks, which severely affect the video processing tasks in outdoor computer vision systems. In this paper, we propose a tensor-based video rain streaks removal method using the nonlocal low-rank regularization. Specifically, we first divide videos into overlapped spatial–temporal patches. Then for each patch, we group its nonlocal similar spatial–temporal patches to form a third-order tensor. To model the clean videos, we characterize the wealth redundancy by adopting the tensor nuclear norm to regularize the low-rankness of the third-order tensors formed by similar spatial–temporal patches of clean videos. We also consider the piecewise smoothness and the temporal continuity of clean videos and utilize the unidirectional total variation to enhance the smoothness and continuity. Moreover, as rain streaks are sparse and smooth along the rain direction, we model the rain streaks by employing an ℓ1 norm and the unidirectional total variation penalty to boost the sparsity and directional smoothness, respectively. We develop an efficient alternating direction method of multipliers to solve the proposed model. Experimental results on both synthetic and real rainy videos show that our method outperforms the state-of-the-art methods quantitatively and qualitatively.

Accurate Transmission Estimation for Removing Haze and Noise from a Single Image.

Image noise usually causes depth-dependent visual artifacts in single image dehazing. Most existing dehazing methods exploit a two-step strategy in the restoration, which inevitably leads to inaccurate transmission maps and low-quality scene radiance for noisy and hazy inputs. To address these problems, we present a novel variational model for joint recovery of the transmission map and the scene radiance from a single image. In the model, we propose a transmission-aware non-local regularization to avoid noise amplification by adaptively suppressing noise and preserving fine details in the recovered image. Meanwhile, to improve the accuracy of transmission estimation, we introduce a semantic-guided regularization to smooth out the transmission map while keeping depth inconsistency at the boundaries of different objects. Furthermore, we design an alternating scheme to jointly optimize the transmission map and the scene radiance as well as the segmentation map. Extensive experiments on synthetic and real-world data demonstrate that the proposed algorithm performs favorably against state-of-the-art dehazing methods on noisy and hazy images.

Self-Similarity Sparse Representation for Image Restoration

Image restoration aims to restore an image from a degraded image. The degradation may occur during image acquisition or image transmission. Image degradation lowers the quality of the image. In this paper additive Gaussian noise is considered for degrading the original image. For restoring the image from degraded image the proposed method used both local and non-local similarity patterns. The restoration problem is modeled with regression model. Two regularization terms are considered for representing prior image information. One regularization term is for local patterns and other is for non-local similarity patterns. The additive local regularization term is used to restore the edges. The non-local regularization term works best for local smoothness and edge information will be lost. The proposed algorithm took a clean image of size 256x256 and added with Gaussian noise with different levels of noise levels. A self-adaptive dictionary is trained for a particular window of image with local and non-local patterns and stacked to three dimensional matrix. The patch size considered for training the dictionary is 10x10. For restoring each patch it searches best atoms form the trained dictionary. The efficiency of the algorithm is estimated by parameters mean square error, root mean square error, PSNR and FSIM. The algorithm is also tested for different images like cameraman, house, Barbara, Lena and parrot. The proposed algorithm is tested with conventional algorithms. .

Integral-type regularization of non associated softening plasticity for quasi brittle materials

Within the framework of infinitesimal elasto-plasticity for describing concrete behaviour, this paper proposes a new non-local constitutive model. Particularly, a non-local integral-type regularization technique is applied to the three-invariant Menétrey-Willam model, here modified by the inclusion of a non-associated flow rule. The resulting model allows for taking into account the role of the intermediate principal stress and the Lode parameter, as well as to control inelastic dilatancy. A regularization scheme is hence introduced to circumvent strain localization and resolve the incapability of objectively describing localized material failure. One- and three-dimensional Finite Element analyses are developed to prove the soundness of the novel implemented regularized scheme and the upgraded response with respect to a local approach.

A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

SummaryA mixed membrane eight‐node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history‐dependent 2D stress‐strain constitutive law is used to model masonry material, the element derivation is based on a Hu‐Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral‐type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement‐based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.

Motion-Compensated Spatio-Temporal Filtering for Multi-Image and Multimodal Super-Resolution

The classical multi-image super-resolution model assumes that the super-resolved image is related to the low-resolution frames by warping, convolution and downsampling. State-of-the-art algorithms either use explicit registration to fuse the information for each pixel in its trajectory or exploit spatial and temporal similarities. We propose to combine both ideas, making use of inter-frame motion and exploiting spatio-temporal redundancy with patch-based techniques. We introduce a non-linear filtering approach that combines patches from several frames not necessarily belonging to the same pixel trajectory. The selection of candidate patches depends on a motion-compensated 3D distance, which is robust to noise and aliasing. The selected 3D volumes are then sliced per frame, providing a collection of 2D patches which are finally averaged depending on their similarity to the reference one. This makes the upsampling strategy robust to flow inaccuracies and occlusions. Total variation and nonlocal regularization are used in the deconvolution stage. The experimental results demonstrate the state-of-the-art performance of the proposed method for the super-resolution of videos and light-field images. We also adapt our approach to multimodal sequences when some additional data at the desired resolution is available.

An orthotropic non-local approach to modeling intra-laminar damage progression in laminated composites

A non-local macroscopic constitutive model is presented to simulate the progression of intra-laminar damage in laminated composite structures. A novel feature of the model is an orthotropic, non-local averaging scheme that is specially designed to capture the preferred path of damage / fracture propagation in laminated structures consisting of strongly orthotropic layers. In addition to maintaining the objectivity of the numerical results, through rendering them mesh size and mesh orientation invariant, the orthotropic nonlocal regularization results in a more realistic prediction of damage pattern and damage growth trajectory in orthotropic laminates. The new model, CODAM2, has been implemented in the open source finite element (FE) code, OOFEM, as well as the commercial explicit FE code, LS-DYNA. Numerical examples are presented to demonstrate the capabilities of CODAM2 in predicting the overall response and extent of damage in quasi-statically loaded, notched laminated specimens with various root notch radii ranging from sharp to blunt geometries. The developed methodology serves as a useful tool for robust and efficient inelastic analysis of large-scale composite structures leading to their damage tolerant design.