Additional Regularity Research Articles

A Third Order based Additional Regularization in Intrinsic Space of the Manifold

A Third Order based Additional Regularization in Intrinsic Space of the Manifold

Identification of a temporal load in a cantilever beam from measured boundary bending moment

This paper provides a theoretical foundation and numerical method for an inverse source problem of identifying a temporal load in a cantilever beam, with Neumann measured boundary output (i.e. bending moment) , governed by the Euler–Bernoulli equation , , subject to the initial u(x, 0) = ut(x, 0) = 0, , and the boundary conditions u(0, t) = ux(0, t) = 0, , . The spatial load is assumed to be known. The inverse problem is reformulated as an operator equation , , by introducing the input–output operator . Our approach is based on detailed analysis of this operator by developing the regular weak solution theory for the direct problem. We show how to choose the temporal load and the Neumann measured output in order to guarantee solvability of the inverse problem. We introduce a weaker solution to the adjoint problem corresponding to the inverse problem and prove Fréchet differentiability of the Tikhonov functional . An explicit gradient formula for the Tikhonov functional is derived by making use of the unique weaker solution of the adjoint problem. Furthermore, under additional regularity and consistency conditions, the Lipschitz continuity of the Fréchet gradient is proved. This property allows use of the conjugate gradient algorithm (CGA) which is the main computational tool in solving inverse problems. A numerical method based on the finite-element discretization and the CGA is developed for the solution of the inverse source problem. Numerical examples with random noisy measured output are presented to illustrate the validity and effectiveness of the proposed approach.

High accuracy error estimates of a Galerkin finite element method for nonlinear time fractional diffusion equation

AbstractIn this work, an effective and fast finite element numerical method with high‐order accuracy is discussed for solving a nonlinear time fractional diffusion equation. A two‐level linearized finite element scheme is constructed and a temporal–spatial error splitting argument is established to split the error into two parts, that is, the temporal error and the spatial error. Based on the regularity of the time discrete system, the temporal error estimate is derived. Using the property of the Ritz projection operator, the spatial error is deduced. Unconditional superclose result in H1‐norm is obtained, with no additional regularity assumption about the exact solution of the problem considered. Then the global superconvergence error estimate is obtained through the interpolated postprocessing technique. In order to reduce storage and computation time, a fast finite element method evaluation scheme for solving the nonlinear time fractional diffusion equation is developed. To confirm the theoretical error analysis, some numerical results are provided.

Four-Dimensional Tomographic Reconstruction by Time Domain Decomposition

For classical tomography, it is essential that the sample does not change during the acquisition of one tomographic rotation. We derived and successfully implemented a tomographic reconstruction method, which relaxes this requirement of quasi-static samples. In the present paper, dynamic tomographic data sets are decomposed in the temporal domain by projecting to a lower dimensional subspace of basis functions and deploying an additional L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We adopted the primal-dual algorithm of Chambolle and Pock for solving the projected regularization problem and tested it on synthetic data containing different motion types. The proposed implementation on modern GPU systems demonstrates the applicability of the method for processing real data sets.

Adversarially Approximated Autoencoder for Image Generation and Manipulation

Regularized autoencoders learn the latent codes, a structure with the regularization under the distribution, which enables them the capability to infer the latent codes given observations and generate new samples given the codes. However, they are sometimes ambiguous as they tend to produce reconstructions that are not necessarily a faithful reproduction of the inputs. The main reason is to enforce the learned latent code distribution to match a prior distribution while the true distribution remains unknown. To improve the reconstruction quality and learn the latent space a manifold structure, this paper presents a novel approach using the adversarially approximated autoencoder (AAAE) to investigate the latent codes with adversarial approximation. Instead of regularizing the latent codes by penalizing on the distance between the distributions of the model and the target, AAAE learns the autoencoder flexibly and approximates the latent space with a simpler generator. The ratio is estimated using a generative adversarial network to enforce the similarity of the distributions. In addition, the image space is regularized with an additional adversarial regularizer. The proposed approach unifies two deep generative models for both latent space inference and diverse generation. The learning scheme is realized without regularization on the latent codes, which also encourages faithful reconstruction. Extensive validation experiments on four real-world datasets demonstrate the superior performance of AAAE. In comparison to the state-of-the-art approaches, AAAE generates samples with better quality and shares the properties of a regularized autoencoder with a nice latent manifold structure.

Estimation of Crystal Timing Properties and Efficiencies for the Improvement of (Joint) Maximum-Likelihood Reconstructions in TOF-PET.

With increasing improvements in the time of flight (TOF) resolution of positron emission tomography (PET) scanners, an accurate model of the TOF measurements is becoming increasingly important. This work considers two parameters of the TOF kernel; the relative positioning of the timing data-bins and the timing resolution along each line of response (LOR). Similar to an existing data-driven method, we assume that any shifts of data-bins along lines of response can be modelled as differences between crystal timing offsets. Inspired by this, timing resolutions of all LORs are modelled as the hypotenuse of timing resolutions of the crystal-pairs in coincidence. Furthermore, in order to mitigate the influence of potential inaccuracies of detector-pair sensitivities on crystal timing resolutions, relative LOR sensitivities are modelled as the product of efficiency factors for the two crystals in coincidence. We validate estimating maps of crystal timing offsets, timing resolutions and efficiencies from the emission data using noisy simulations of a brain phantom. Results are shown for phantom and patient data scanned on clinically available TOF-PET scanners. We find that the estimation of crystal timing resolutions is more sensitive to the data statistics than the estimation of crystal timing offsets. As a result, estimation of crystal timing properties could either be limited to high count emission data, or be obtained utilizing additional regularizations on the estimates. Using a more accurate model of the TOF acquisition, improvements are observed in standard activity reconstructions as well as joint reconstructions of activity and attenuation.

Homogenization and correctors for linear stochastic equations via the periodic unfolding methods

In this paper, we use the periodic unfolding method and Prokhorov’s and Skorokhod’s probabilistic compactness results to obtain homogenization and corrector results for stochastic partial differential equations (PDEs) with periodically oscillating coefficients. We show the convergence of the solutions of the original problems to the solutions of the homogenized problems. In contrast to the two-scale convergence method, the corrector results obtained in this paper are without any additional regularity assumptions on the solutions of the original problems

SMS MUSSELS: A navigator-free reconstruction for simultaneous multi-slice-accelerated multi-shot diffusion weighted imaging.

To introduce a novel reconstruction method for simultaneous multi-slice (SMS)-accelerated multi-shot diffusion weighted imaging (ms-DWI). SMS acceleration using blipped-CAIPI schemes have been proposed to speed up the acquisition of ms-DWIs. The reconstruction of the data requires (a) phase compensation to combine data from different shots and (b) slice unfolding to separate the data of different slices. The traditional approaches first estimate the phase maps corresponding to each shot and slice which are then employed to iteratively recover the slice unfolded DWIs without phase artifacts. In contrast, the proposed reconstruction directly recovers the slice-unfolded k-space data of the multiple shots for each slice in a single-step recovery scheme. The proposed method is enabled by the low-rank property inherent in the k-space samples of ms-DW acquisition. This enabled to formulate a joint recovery scheme that simultaneously (a) unfolds the k-space data of each slice using a SENSE-based scheme and (b) recover the missing k-space samples in each slice of the multi-shot acquisition employing a structured low-rank matrix completion. Additional smoothness regularization is also utilized for higher acceleration factors. The proposed joint recovery is tested on simulated and in vivo data and compared to similar un-navigated methods. Our experiments show effective slice unfolding and successful recovery of DWIs with minimal phase artifacts using the proposed method. The performance is comparable to existing methods at low acceleration factors and better than existing methods for higher acceleration factors. For the slice accelerations considered in this study, the proposed method can successfully recover DWIs from SMS-accelerated ms-DWI acquisitions.

Structured sequential Gaussian graphical models for monitoring time-varying process

This article introduces a structured and sequential Gaussian graphical approach for monitoring time-varying industrial systems. To address the presence of time-varying trends, the article utilizes a sequential update procedure for Gaussian graphical models that is based on a moving window approach. The implementation of this approach requires that the Gaussian graph models are constructed based on two additional regularization terms. For a time-varying graphical structure, the overall trend can be isolated by the first additional regularization term; while abnormal events can be timely captured using the second regularization term. Unlike conventional graphical networks that rely on other methods for fault detection, this article proposes a unified graphical framework for fault detection and isolation. In addition, the optimization problem of the Gaussian graphical model can be solved using the Alternative Direction Method of Multiplier (ADMM) algorithm, which has a linear convergence rate, making it easily applicable to large-scale systems. The performance of this graph-based technique is demonstrated by a simulation example and the application study to an industrial distillation process.

A priori estimates for the free-boundary Euler equations with surface tension in three dimensions

We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial velocity, which is rotational, belongs to H3, with some additional regularity on the normal component of the initial velocity. This lowers the requirement on the regularity of initial data in the Lagrangian setting. Our methods are direct and involve three key elements: estimates for the pressure, the boundary regularity provided by the mean curvature, and the Cauchy invariance.

Image De-Raining Using a Conditional Generative Adversarial Network

Severe weather conditions, such as rain and snow, adversely affect the visual quality of images captured under such conditions, thus rendering them useless for further usage and sharing. In addition, such degraded images drastically affect the performance of vision systems. Hence, it is important to address the problem of single image de-raining. However, the inherent ill-posed nature of the problem presents several challenges. We attempt to leverage powerful generative modeling capabilities of the recently introduced conditional generative adversarial networks (CGAN) by enforcing an additional constraint that the de-rained image must be indistinguishable from its corresponding ground truth clean image. The adversarial loss from GAN provides additional regularization and helps to achieve superior results. In addition to presenting a new approach to de-rain images, we introduce a new refined loss function and architectural novelties in the generator-discriminator pair for achieving improved results. The loss function is aimed at reducing artifacts introduced by GANs and ensure better visual quality. The generator sub-network is constructed using the recently introduced densely connected networks, whereas the discriminator is designed to leverage global and local information to decide if an image is real/fake. Based on this, we propose a novel single image de-raining method called image de-raining conditional generative adversarial network (ID-CGAN) that considers quantitative, visual, and also discriminative performance into the objective function. The experiments evaluated on synthetic and real images show that the proposed method outperforms many recent state-of-the-art single image de-raining methods in terms of quantitative and visual performances. Furthermore, the experimental results evaluated on object detection datasets using the Faster-RCNN also demonstrate the effectiveness of proposed method in improving the detection performance on images degraded by rain.

Entropic Regularization of Markov Decision Processes.

An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an optimal controller via direct interaction with the environment. Such interactive data gathering commonly leads to divergence towards dangerous or uninformative regions of the state space unless additional regularization measures are taken. Prior works proposed bounding the information loss measured by the Kullback–Leibler (KL) divergence at every policy improvement step to eliminate instability in the learning dynamics. In this paper, we consider a broader family of f-divergences, and more concretely -divergences, which inherit the beneficial property of providing the policy improvement step in closed form at the same time yielding a corresponding dual objective for policy evaluation. Such entropic proximal policy optimization view gives a unified perspective on compatible actor-critic architectures. In particular, common least-squares value function estimation coupled with advantage-weighted maximum likelihood policy improvement is shown to correspond to the Pearson -divergence penalty. Other actor-critic pairs arise for various choices of the penalty-generating function f. On a concrete instantiation of our framework with the -divergence, we carry out asymptotic analysis of the solutions for different values of and demonstrate the effects of the divergence function choice on common standard reinforcement learning problems.

Approximation and Optimal Control of Dissipative Solutions to the Ericksen–Leslie System

We analyze the Ericksen–Leslie system equipped with the Oseen–Frank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the earlier introduced measure-valued solutions. In this article, we argue that dissipative solutions can be numerically approximated by a relatively simple scheme, which fulfills the norm-restriction on the director in every step. We introduce a semi-discrete scheme and derive an approximated version of the relative-energy inequality for solutions of this scheme. Passing to the limit in the semi-discretization, we attain dissipative solutions. Additionally, we introduce an optimal control scheme, showing the existence of an optimal control and a possible approximation strategy. We prove that the cost functional is lower semi-continuous with respect to the convergence of this approximation and argue that an optimal control is attained in the case that there exists a solution admitting additional regularity.

Existence, stability and numerical results for a Timoshenko beam with thermodiffusion effects

In this paper, we consider a new Timoshenko beam model with thermal and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam. Firstly, by the $${C}_{0}$$ -semigroup theory, we prove the well posedness of the considered problem with Dirichlet or Neumann boundary conditions. Then we show, without assuming the well-known equal wave speeds condition, the lack of exponential stability for the Neumann problem, meanwhile one linear frictional damping is strong enough to guarantee the exponential stability for the Dirichlet problem. Then, we introduce a finite element approximation and we prove that the associated discrete energy decays. Finally, we obtain some a priori error estimates assuming additional regularity on the solution and we present some numerical results which demonstrate the accuracy of the approximation and the behaviour of the solution.

Hierarchical spherical deformation for cortical surface registration.

We present hierarchical spherical deformation for a group-wise shape correspondence to address template selection bias and to minimize registration distortion. In this work, we aim at a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, a global rigid alignment and local deformation are independently performed. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To this end, we indirectly encode local displacements by such local composite rotations as functions of spherical locations. Furthermore, we introduce an additional regularization term to the spherical deformation, which maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second order approximation of the energy function that enables fast convergence of the optimization. In the experiments, we validate our method on healthy normal subjects with manual cortical surface parcellation in registration accuracy and distortion. We show an improved shape correspondence with high accuracy in cortical surface parcellation and significantly low registration distortion in surface area and edge length. In addition to validation, we discuss parameter tuning, optimization, and implementation design with potential acceleration.

An improved quantum principal component analysis algorithm based on the quantum singular threshold method

Quantum principal component analysis (qPCA) is a dimensionality reduction algorithm for getting the eigenvectors corresponding to top several eigenvalues of the data matrix and then reconstructing. However, qPCA can only construct the quantum state contains all the eigenvectors and eigenvalues. In this paper, we present an improved quantum principal component analysis (Improved qPCA) algorithm with a fixed threshold. We can reduce the singular value less than the threshold to 0 and obtain a target quantum state which can be used to get an output similar to qPCA after phase estimation. Compared with qPCA, our algorithm has only the target eigenvalues and the probability that we get each target eigenvalue is greater. Furthermore, our algorithm can serve as an additional regularization method and a subroutine for subsequent data processing.

Semi-supervised multi-view clustering based on constrained nonnegative matrix factorization

Most existing clustering approaches address multi-view clustering problems by graph regularized nonnegative matrix factorization to obtain the new representation of each view separately. And then, the additional regularization term is introduced to fuse these representations. However, the graph regularization is no guarantee that the representation obtained by mapping data points has the consistent label information with the original data. In addition, we may have a number of labeled samples in practice. This paper proposes a new semi-supervised multi-view clustering method based on Constrained Nonnegative Matrix Factorization with sparseness constraint, which is called MVCNMF. Our method first learns the representation by introducing an auxiliary matrix for each view and constructs the label constraint matrix shared among all views, where the label constraint matrix can guarantee that the label information is fused into the new representation of each view. Then, by applying the co-regularization and the sparseness constraint in auxiliary matrices, the complementary information from different views is integrated, and the robust feature of each view is extracted. Further, we also present the convergence proof and the computational complexity analysis of our method. Finally, extensive experiments on real datasets have demonstrated that our proposed approach can achieve a better clustering quality as compared to state-of-the-art multi-view clustering methods.

Robust Face Image Super-Resolution via Joint Learning of Subdivided Contextual Model.

In this paper, we focus on restoring high-resolution facial images under noisy low-resolution scenarios. This problem is a challenging problem as the most important structures and details of captured facial images are missing. To address this problem, we propose a novel local patch-based face super-resolution (FSR) method via the joint learning of the contextual model. The contextual model is based on the topology consisting of contextual sub-patches, which provide more useful structural information than the commonly used local contextual structures due to the finer patch size. In this way, the contextual models are able to recover the missing local structures in target patches. In order to further strengthen the structural compensation function of contextual topology, we introduce the recognition feature as additional regularity. Based on the contextual model, we formulate the super-resolved procedure as a contextual joint representation with respect to the target patch and its adjacent patches. The high-resolution image is obtained by weighting contextual estimations. Both quantitative and qualitative validations show that the proposed method performs favorably against state-of-the-art algorithms.

A multiplicative regularized Gauss-Newton method with trust region Sequential Quadratic Programming for structural model updating

Abstract The paper focuses on the development of an iterative minimization algorithm for structural identification. The algorithm consists of a Gauss-Newton method in which the ill-conditioning caused by noise pollution is mitigated by means of a multiplicative regularization technique used in conjunction with a bound constrained trust region method. Unlike the classic additive regularization technique, the amount of regularization is not determined a priori, but computed in an automatic fashion at each step of the iterative procedure. Specifically, the strength of the regularization is controlled by the norm of the model parameters weighted by a factor proportional to the current values of the least-square cost functional and the size of the trust region. The iterative procedure consists in solving a sequence of regularized local quadratic subproblems in a Sequential Quadratic Programming framework, for which a local convexity condition is given. The proposed method is finally tested in the retrieval of the equivalent stiffness of the soil and bearings of a real, in-service bridge pier that was tested using experimental modal analysis.

Comparative Analysis of Scientific Journals Collections

The authors developed an approach to comparative analysis of scientific journals collections based on the analysis of co-authors graph and the text model. The use of time series of co-authorship graphs metrics allowed the authors to analyze trends in the development of journal authors. The text model was built using machine learning techniques. The journals content was classified to determine the authenticity degree of various journals and different issues of a single journal via a text model. The authors developed a metric of Content Authenticity Ratio, which allows quantifying the authenticity of journal collections in comparison. Comparative thematic analysis of journals collections was carried out using the thematic model with additive regularization. Based on the created thematic model, the authors constructed thematic profiles of the journals archives in a single thematic basis. The approach developed by the authors was applied to archives of two journals on the Rheumatology for the period 2000–2018. As a benchmark for comparing the co-author’s metrics, public data sets from the SNAP research laboratory at Stanford University were used. As a result, the authors adapted the existing examples of the effective functioning of the authors collaborations in order to improve the work of journals editorial staff. Quantitative comparison of large volumes of texts and metadata of scientific articles was carried out. As a result of the experiment conducted using the developed methods, it was shown that the content authenticity of the selected journals is 89%, co-authorships in one of the journals have a pronounced centrality, which is a distinctive feature of the policy editor. The clarity and consistency of the results confirm the effectiveness of the approach proposed by the authors. The code developed in the course of the experiment in the Python programming language can be used for comparative analysis of other collections of journals in the Russian language.