Academic literature on the topic 'Nonlocal regularization approach'

Abstract In the inverse problem of image processing, we have witnessed that the non-convex and non-smooth regularizers can produce clearer image edges than convex ones such as total variation (TV). This fact can be explained by the uniform lower bound theory of the local gradient in non-convex and non-smooth regularization. In recent years, although it has been numerically shown that the nonlocal regularizers of various image patches based nonlocal methods can recover image textures well, we still desire a theoretical interpretation. To this end, we propose a non-convex non-smooth and block nonlocal regularization model based on image patches. By integrating the advantages of the non-convex and non-smooth potential function in the regularization term, the uniform lower bound theory of the image patches based nonlocal gradient is given. This approach partially explains why the proposed method can produce clearer image textures and edges. Compared to some classical regularization methods, such as TV, non-convex and non-smooth regularization, nonlocal total variation and block nonlocal total variation, our experimental results show that the proposed method improves restoration quality.

We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total variation (TV) method. The high frequency gradients are reweighted in iterations adaptively when we decompose the image into high and low frequency components using the pre-processing technique. The nonlocal regularization is introduced into our method based on nonlocal means (NLM) filtering, which contains prior image structural information to suppress staircase artifacts. An alternating direction multiplier method (ADMM) is used to solve the problem combining reweighted FrTV and nonlocal regularization. Experimental results show that both the peak signal-to-noise ratios (PSNR) and structural similarity index (SSIM) of reconstructed images are higher than those achieved by the other four methods at various sampling ratios less than 25%. At 5% sampling ratios, the gains of PSNR and SSIM are up to 1.63 dB and 0.0114 from ten images compared with reweighted total variation with nuclear norm regularization (RTV-NNR). The improved approach preserves more texture details and has better visual effects, especially at low sampling ratios, at the cost of taking more time.

Purpose This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented. Design/methodology/approach In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented. Findings The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables. Research limitations/implications The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work. Practical implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Social implications The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately. Originality/value The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

Sparse-projection image reconstruction is a useful approach to lower the radiation dose; however, the incompleteness of projection data will cause degeneration of imaging quality. As a typical compressive sensing method, total variation has obtained great attention on this problem. Suffering from the theoretical imperfection, total variation will produce blocky effect on smooth regions and blur edges. To overcome this problem, in this paper, we introduce the nonlocal total variation into sparse-projection image reconstruction and formulate the minimization problem with new nonlocal total variation norm. The qualitative and quantitative analyses of numerical as well as clinical results demonstrate the validity of the proposed method. Comparing to other existing methods, our method more efficiently suppresses artifacts caused by low-rank reconstruction and reserves structure information better.

Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider the sparsity prior in spatial and spectral vector domains via vectorizing hyperspectral cubes along a certain dimension. Besides, in most previous works, little attention has been paid to exploiting the underlying nonlocal structure in spatial domain of the HSI. In this paper, we propose a nonlocal tensor sparse and low-rank regularization (NTSRLR) approach, which can encode essential structured sparsity of an HSI and explore its advantages for HSI-CSR task. Specifically, we study how to utilize reasonably the l 1 -based sparsity of core tensor and tensor nuclear norm function as tensor sparse and low-rank regularization, respectively, to describe the nonlocal spatial-spectral correlation hidden in an HSI. To study the minimization problem of the proposed algorithm, we design a fast implementation strategy based on the alternative direction multiplier method (ADMM) technique. Experimental results on various HSI datasets verify that the proposed HSI-CSR algorithm can significantly outperform existing state-of-the-art CSR techniques for HSI recovery.

In bosonic formulation of the negative energy sea, so-called Dirac sea presented in the preceding paper [arXiv:hep-th/0603242], one of the crucial points is how to construct a positive definite inner product in the negative energy states, since naive attempts would lead to nonpositive definite ones. In the preceding paper, the nonlocal method is used to define the positive definite inner product. In the present paper we, make use of a kind of ∊-regularization and renormalization method which may clarify transparently the analytical properties of our formulation.

We reformulate the zero-dimensional Hermitian one-matrix model as a (nonlocal) collective field theory, for finite N. The Jacobian arising as a result of changing variables from matrix eigenvalues to their density distribution is treated exactly. The semiclassical loop expansion turns out not to coincide with the (topological) [Formula: see text] expansion, because the classical background has a nontrivial N dependence. We derive a simple integral equation for the classical eigenvalue density, which displays strong nonperturbative behavior around N=∞. This leads to IR singularities in the large-N expansion, but UV divergencies appear as well, despite remarkable cancelations among the Feynman diagrams. We evaluate the free energy at the two-loop level and discuss its regularization. A simple example serves to illustrate the problems and admits explicit comparison with orthogonal-polynomial results.

Hyperspectral image (HSI) acquisitions are degraded by various noises, among which additive Gaussian noise may be the worst-case, as suggested by information theory. In this paper, we present a novel tensor-based HSI denoising approach by fully identifying the intrinsic structures of the clean HSI and the noise. Specifically, the HSI is first divided into local overlapping full-band patches (FBPs), then the nonlocal similar patches in each group are unfolded and stacked into a new third order tensor. As this tensor shows a stronger low-rank property than the original degraded HSI, the tensor weighted nuclear norm minimization (TWNNM) on the constructed tensor can effectively separate the low-rank clean HSI patches. In addition, a regularization strategy with spatial–spectral total variation (SSTV) is utilized to ensure the global spatial–spectral smoothness in both spatial and spectral domains. Our method is designed to model the spatial–spectral non-local self-similarity and global spatial–spectral smoothness simultaneously. Experiments conducted on simulated and real datasets show the superiority of the proposed method.

A novel mixed higher order regularizer involving the first and second degree image derivatives is proposed in this paper. Using spectral decomposition, we reformulate the new regularizer as a weightedL1-L2mixed norm of image derivatives. Due to the equivalent formulation of the proposed regularizer, an efficient fast projected gradient algorithm combined with monotone fast iterative shrinkage thresholding, called, FPG-MFISTA, is designed to solve the resulting variational image recovery problems under majorization-minimization framework. Finally, we demonstrate the effectiveness of the proposed regularization scheme by the experimental comparisons with total variation (TV) scheme, nonlocal TV scheme, and current second degree methods. Specifically, the proposed approach achieves better results than related state-of-the-art methods in terms of peak signal to ratio (PSNR) and restoration quality.

A rigorous structural analysis is fundamental in the safety assessment of the built heritage and in its efficient conservation and rehabilitation. In line with the necessity of refined techniques, the objective of the present thesis is to develop and validate, in a displacement-based finite element framework, a nonlinear model apt for the study of masonry and concrete structures under monotonic and cyclic loading. The proposed constitutive law adopts two independent scalar damage variables, d+ and d−, in combination with the spectral decomposition of the elastic strain tensor, to simulate the pronounced dissimilar response under tension and compression, typical of these materials. The assumption of energy-equivalence between the damaged solid and the effective (undamaged) one is considered for representing the orthotropy induced in the material by the degradation process, with the consequence that a thermodynamically consistent constitutive operator, positive definite, symmetric and strain-driven, is derived. The formulation is integrated with a multidirectional damage procedure, addressed to extend the microcrack closure-reopening (MCR) capabilities to generic cyclic conditions, especially shear cyclic conditions, making the model suitable for dealing with seismic actions. Maintaining unaltered the dependence of the constitutive law from d+ and d−, this approach activates or deactivates a tensile (compressive) damage value on the base of the current maximum (minimum) principal strain direction. In correspondence with damage activation (crack opening) or deactivation (crack closure), a smooth transition is introduced, in order to avoid abrupt changes in stiffness and enhance the numerical performance and robustness of the multidirectional procedure. Moreover, the mesh-objectivity of the numerical solutions is ensured by resorting to a nonlocal regularization technique, based on the adoption of damage variables driven by an averaged elastic strain tensor. To perform the averaging of the strain tensor, an internal length lRG is considered in the continuum. The strategy chosen to define the parameters affecting the softening behaviour consists in the modification of the local softening law on the base of the internal length, with the intent of ensuring the proper evaluation of the correct fracture energy Gf. The adequacy of the proposed constitutive model in reproducing experimental results is proven for both monotonic and cyclic loading conditions. Under monotonic loads, unreinforced concrete notched elements subjected to pure tension, pure bending and mixed-mode bending are studied. The two examples of application involving cyclic loads, a masonry and a reinforced concrete wall under in-plane cyclic shear, constitute a validation of the multidirectional damage approach, showing how the suitable representation of unilateral effects and permanent deformations is essential to model the observed structural response in terms of maximum resistance and dissipation capacity. The effectiveness of the regularized damage formulation is proven by successfully studying a masonry arch and reinforced and unreinforced concrete elements. Besides the validation of the numerical results with experimental or analytical data, each application is exploited to highlight one or more features of the formulation: the mesh-size and mesh-bias independence of the results, the effect of the choice of the variable to be averaged, the possibility to reproduce structural size effects, the influence of the internal length lRG. On this latter aspect, the almost null dependence of the regularized solutions on the internal length in terms of force-displacement curves, achieved thanks to the calibration strategy adopted to define the energy dissipation, suggests the interpretation of the internal length as a regularization parameter. On the one hand, this implies an analogy between the role played by the nonlocal internal length in a nonlocal model and the one’s of the mesh size in the crack band approach (Bažant and Oh, 1983). On the other hand, this translates in the versatility of the regularized damage model, which requires only the identification of the standard material properties (elastic constants, fracture energies and strengths). Finally, the d+/d− damage model is successfully applied to the study of a three-span masonry arch bridge subjected to a concentrated vertical load, in order to evaluate its carrying capacity and its failure mechanism. Numerical issues, usually neglected in large-scale applications, are also addressed proving the reliability of the regularized approach to provide mesh-independent results and its applicability.

Cette étude a pour objectif principal d’établir une stratégie de modélisation robuste, fiable et performante pour décrire des propagations de fissures d’échelle centimétrique en régime ductile dans des composants industriels. Le modèle d’endommagement de GTN écrit en grandes déformations est utilisé pour modéliser l’endommagement ductile. Ce modèle conduit généralement à une localisation de la déformation, conformément à l’expérience. L’échelle caractéristique de ce phénomène est introduite dans les équations de comportement via l’adoption d’une formulation non locale.Sur le plan numérique, ce modèle non local rend bien compte de la localisation dans une bande d’épaisseur donnée lorsqu’on raffine suffisamment le maillage. Par ailleurs, le problème de verrouillage numérique associé au caractère initialement isochore de la déformation plastique est limité en utilisant une formulation à base d’éléments finis mixtes. Enfin, la distorsion des éléments totalement cassés (i.e. sans rigidité apparente), qui pourrait nuire à la bonne convergence des simulations numériques, est traitée par une régularisation viscoélastique.L’ensemble de ces ingrédients sont appliqués pour simuler la propagation de fissure dans un milieu infini plasticité confinée), de sorte à établir un lien avec les approches globales en J-Δa. L’émoussement, l’amorçage et la (grande) propagation de fissure sont bien prédits. Le modèle est également appliqué à une tuyauterie métallique testée en grandeur réelle dans le cadre du projet européen Atlas+. Après une phase d’identification des paramètres sur éprouvette, les réponses globales et locales d’autres éprouvettes et du tube sont confrontés aux résultats expérimentaux. Ces résultats illustrent le degré de robustesse, de fiabilité et de performance qu’on peut attendre du modèle
The major goal of this work is to establish a robust, reliable and efficient modeling technique so as to describe ductile tearing over a distance of several centimeters in industrial cases. The GTN damage model expressed in the context of finite strains is chosen to model ductile damage. Generally, the model leads to strain localization in agreement with experimental observations. The characteristic length scale of this phenomenon is introduced into the constitutive equations through the use of a nonlocal formulation.On a numerical ground, the nonlocal model controls the width of the localization band as soon as the mesh is sufficiently refined. Besides, the issue of volumetric-locking associated with plastic incompressibility is handled using a mixed finite element formulation. Finally, the distortion of broken elements (i.e. without any stiffness), which may affect the computational convergence of numerical simulations, is treated using a viscoelastic regularization.The improved GTN model is applied to simulate crack propagation under small-scale yielding conditions, so as to establish a relation with the global (J-Δa) approach. Crack tip blunting, crack initiation and (large) crack propagation are well captured. The model is also applied to a full-scale metallic pipe in the framework of the UE project Atlas+. After a phase of parameter calibration based on the experimental results on some small specimens, the global and local responses of other small specimens and of the full-scale pre-cracked pipe are compared with the experimental results. The results illustrates the robustness, the reliability and the efficiency of the current model