Second-order Gradient Research Articles

Blind deblurring with patch-wise second-order gradient prior

The patch-based image priors have been successfully applied to blind image deblurring algorithms. But those priors are time-consuming since too many non-linear operators are involved. However, the solving of these prior needs to use nonlinear operators that greatly decrease the computational efficiency. Proposed in this study is a simply patch-wise image prior that uses non-overlapped local patches to compute the local maximal second-order gradient of an image. We find that the values of the patch-wise second-order gradient (PSG) of an image decrease with the motion blur process. A new optimization algorithm is proposed by combining L1 regularized PSG with the maximum posterior probability. Besides, kernel similarity constraint is employed to control the iteration times to reduce the computational costs. Comparative experiments on mainstream datasets show that the results of the presented algorithm are generally better than those of other algorithms on both quantitative contrast and visual contrast.

SFOC: A NOVEL MULTI-DIRECTIONAL AND MULTI-SCALE STRUCTURAL DESCRIPTOR FOR MULTIMODAL REMOTE SENSING IMAGE MATCHING

Abstract. Accurate matching of multimodal remote sensing (RS) images (e.g., optical, infrared, LiDAR, SAR, and rasterized maps) is still an ongoing challenge because of nonlinear radiometric differences (NRD) between these images. Considering that structural properties are preserved between multimodal images, this paper proposes a robust matching method based on multi-directional and multi-scale structural features, which consist of two critical steps. Firstly, a novel structural descriptor named the Steerable Filters of first- and second-Order Channels (SFOC) is constructed to address severe NRD, which combines the first- and second-order gradient information by using the steerable filters to depict multi-directional and multi-scale structural features of images. Meanwhile, SFOC is further enhanced by performing the dilated Gaussian convolutions with different dilated rates on it, which can capture multi-level context structural features and improve the ability to resist noise. Then, a fast similarity measure, called Fast Normalized Cross-Correlation (Fast-NCCSFOC), is established to detect correspondences by a template matching scheme, which employs the Fast Fourier Transform (FFT) technique and the integral image to improve the matching efficiency. The performance of the proposed SFOC has been evaluated with many different kinds of multimodal RS images, and experimental results show its superior matching performance compared with the state-of-the-art methods.

Effect of gradient concentration pre‐osmotic dehydration on keeping air‐dried apricot antioxidant activity and bioactive compounds

Apricot was treated by osmotic dehydration (OD) before air drying to protect its antioxidant activity and bioactive compound. The experiment set up three groups to pretreat apricot by OD in sucrose solution of different concentrations for 12 h in total, among which, OD-1 was permeated in 60% solution for 12 h; OD-2 was permeated in 45% and 60% solution for 6 h. OD-3 was pretreated in 30%, 45%, and 60% solutions for 4 h. After pretreatment, apricots were dried at 60°C until the water loss rate reaching 75%. Results showed water loss rate and solids gained rate in the OD-2 group were the highest and drying time was shortened effectively. Compared with control, all OD samples could maintain higher content of bioactive compounds and antioxidant capacity, and reduce browning. The OD-2 pretreatment dried apricot could retain the edible quality, bioactive substances, and antioxidant capacity to the maximum extent. Novelty impact statement This research was improved according to the traditional processing technology of preserved fruit. In this study, it was found that under the same pretreatment time, the osmotic dehydration pretreatment with second-order gradient concentration could effectively keep apricots' bioactive compounds and antioxidant activity during the drying process.

A robust multimodal remote sensing image registration method and system using steerable filters with first- and second-order gradients

Co-registration of multimodal remote sensing (RS) images (e.g., optical, infrared, LiDAR, and SAR) is still an ongoing challenge because of nonlinear radiometric differences (NRD) and significant geometric distortions (e.g., scale and rotation changes) between these images. In this paper, a robust matching method based on the Steerable filters is proposed consisting of two critical steps. First, to address severe NRD, a novel structural descriptor named the Steerable Filters of first- and second-Order Channels (SFOC) is constructed, which combines the first- and second-order gradient information by using the steerable filters with a multi-scale strategy to depict more discriminative structure features of images. Then, a fast similarity measure is established called Fast Normalized Cross-Correlation (Fast-NCCSFOC), which employs the Fast Fourier Transform (FFT) technique and the integral image to improve the matching efficiency. Furthermore, to achieve reliable registration performance, a coarse-to-fine multimodal registration system is designed consisting of two pivotal modules. The local coarse registration is first conducted by involving both detection of interest points (IPs) and local geometric correction, which effectively utilizes the prior georeferencing information of RS images to address global geometric distortions. In the fine registration stage, the proposed SFOC is used to resist significant NRD, and to detect control points (CPs) between multimodal images by a template matching scheme. The performance of the proposed matching method has been evaluated with many different kinds of multimodal RS images. The results show its superior matching performance compared with the state-of-the-art methods. Moreover, the designed registration system also outperforms the popular commercial software (e.g., ENVI, ERDAS, and PCI) in both registration accuracy and computational efficiency. Our system is available at https://github.com/yeyuanxin110/SFOC-Multimodal_Remote_Sensing_Image_Registration_System.

Automated Detection of Alzheimer’s via Hybrid Classical Quantum Neural Networks

Deep Neural Networks have offered numerous innovative solutions to brain-related diseases including Alzheimer’s. However, there are still a few standpoints in terms of diagnosis and planning that can be transformed via quantum Machine Learning (QML). In this study, we present a hybrid classical–quantum machine learning model for the detection of Alzheimer’s using 6400 labeled MRI scans with two classes. Hybrid classical–quantum transfer learning is used, which makes it possible to optimally pre-process complex and high-dimensional data. Classical neural networks extract high-dimensional features and embed informative feature vectors into a quantum processor. We use resnet34 to extract features from the image and feed a 512-feature vector to our quantum variational circuit (QVC) to generate a four-feature vector for precise decision boundaries. Adam optimizer is used to exploit the adaptive learning rate corresponding to each parameter based on first- and second-order gradients. Furthermore, to validate the model, different quantum simulators (PennyLane, qiskit.aer and qiskit.basicaer) are used for the detection of the demented and non-demented images. The learning rate is set to 10−4 for and optimized quantum depth of six layers, resulting in a training accuracy of 99.1% and a classification accuracy of 97.2% for 20 epochs. The hybrid classical–quantum network significantly outperformed the classical network, as the classification accuracy achieved by the classical transfer learning model was 92%. Thus, a hybrid transfer-learning model is used for binary detection, in which a quantum circuit improves the performance of a pre-trained ResNet34 architecture. Therefore, this work offers a method for selecting an optimal approach for detecting Alzheimer’s disease. The proposed model not only allows for the automated detection of Alzheimer’s but would also speed up the process significantly in clinical settings.

Gradient Expansions for the Large-Coupling Strength Limit of the Møller-Plesset Adiabatic Connection.

The adiabatic connection that has, as weak-interaction expansion, the Møller–Plesset perturbation series has been recently shown to have a large coupling-strength expansion, in terms of functionals of the Hartree–Fock density with a clear physical meaning. In this work, we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have already been shown to reduce dramatically MP2 errors for large noncovalent complexes. As a byproduct, our investigation of neutral atoms with large number of electrons N indicates that the second-order gradient expansion for exchange grows as N log(N) rather than as N, as often reported in the literature.

Second-order hyperparameter tuning of model-based and adaptive observers for time-varying and unknown chaotic systems

In this paper, a second-order hyperparameter tuning method is proposed to improve the performance of online gradient-descent optimization. Second-order gradient information of a cost function obtained from extremum seeking optimization is embedded into the adaptation of states and parameters. Thus, a faster adaptation capability is provided without computing the inverse Hessian matrix. The convergence property of the adaptation dynamics via proposed hyperparameter is shown using Lyapunov approach. The proposed hyperparameters and conventional learning rates are compared in numerical applications of model-based estimation and adaptive estimation as follows: i) model-based synchronization of chaotic Lü-systems with time-varying parameters is performed by using an efficient nonlinear observer, ii) an adaptive fuzzy neural-network observer based state estimation is conducted for unknown Duffing oscillator. In both cases, online gradient-descent adaptations are boosted using the proposed hyperparameter and conventional learning rates and their capabilities are measured in terms of root-mean squared-error performance. As a result, the proposed hyperparameter tuning method presented more accurate performances where application results are illustrated in figures and in a table.

Robust face recognition for occluded real‐world images using constrained probabilistic sparse network

Aiming at the occluded real-world face images across illumination, pose, expression, and resolution variations, a robust face recognition for occluded real-world images using constrained probabilistic sparse network is presented. A constrained probabilistic sparse representation network is constructed to obtain the features of all the training images from a global perspective, and the new network nodes are generated through the random combination of the training images. In the probabilistic sparse representation network, the probabilities of each class of the sparse subspace that the occluded test images individually belong to are defined and calculated. The final classifications of the test images are determined by the joint maximum probability of the network nodes. Meanwhile the second-order gradient constraint is the first introduced in the probabilistic sparse representation network. It is found that the constraint uses the adjacent pixels of the face images to obtain the local texture similarity, and further use the local texture similarity to distinguish the occlusion and non-occlusion parts. Thus the constraint can reduce the influence of the occlusion part on face recognition. Extensive experiments with the 12 existing methods on the five face databases demonstrate that the recognition rate of the proposed method is the best than the non-deep learning methods compared, and the proposed method can obtain nearly the same recognition rate with an advantage of a very less time consumption compared to the state-of-the-art deep learning methods.

Geometric approach to machine exploitation efficiency : modelling and assessment

This article presents a new approach to the exploitation assessment of machines and devices. A key aspect of this approach is the construction of the assessment model based on the geometric representation of measures associated with each other, which covers the full specifics of the exploitation process. This approach is successfully implemented by the Overall Equipment Effectiveness (OEE) model, which is fully susceptible to the geometric modelling process due to the three-way system of assessed exploitation aspects. The result of this approach is the vectored OEE model and its interpretation in terms of time series of changes in values of components. Methods of determining vector calculus measures were developed, including the second-order tensor and gradient. This is the subject of the variability of the reliability conditions of machines or production processes. It allows for the realisation of an exploitation assessment based on dynamic changes in the values of their components in the time domain. This is a significant difference to the classical static approach to such an assessment. The developed new geometric OEE model was confirmed by verification tests using the LabView software, based on two parallel data sets obtained with analytical and simulation methods using the FlexSim software.

Low-Light Image Enhancement via Gradient Prior-Aided Network

Low-light images have low brightness and low contrast, which bring huge obstacles to the intelligent video surveillance system. The enhancement of low-light images must simultaneously consider the interference of factors such as brightness, contrast, artifacts, and noise. To this end, in this study, we propose a gradient prior-aided low-light enhancement network (GPANet). The main idea is to improve the network's ability to extract edge features and remove unwanted noise by introducing first-order (i.e., Sobel Filter) and second-order gradient (i.e., Laplacian Filter) features. Unlike in previous methods, in the proposed study, we first extract the first-order and second-order gradient information of low-light images and concatenate them with low-light images for multi-view feature analysis in the multi-view fusion encoder (MFE). Then, we suggest the multi-branch topology module (MTM) to fuse and decompose the multi-view features. Finally, we reconstruct the multi-view features through multi-view decomposition decoders (MDDs, including three sub-decoders) to generate potentially normal-light images. The first- and second-order gradient decoders will provide the enhancement decoder with multi-scale gradient prior features. Furthermore, we suggest a residual network to speed up network convergence while ensuring stable enhancement performance.We conduct experiments on widely adopted datasets. The results demonstrate the advantages of our method compared to other methods from both qualitative and quantitative perspectives. The source code is available at https://github.com/LouisYuxuLu/GPANet.

Gesture recognition of wrist motion based on wearables sensors

This paper aims to evaluate two machine learning techniques using low-frequency photoplethysmography (PPG) associated with motion sensors, accelerometers and gyroscopes, from wearable devices such as smartwatches in gesture recognition from the wrist and fingers motion. The applied method consider the application of second-order gradient calculation on PPG to identify motion artifacts and then create segments that will be used gesture classification, the classification process used a support vector machine and random forests trained using statistical features extracted from PPG and motion sensor signals. Preliminary evaluations show that frequencies of 25 Hz are suitable for the recognition process, achieving an F1-score of 0.819 for seven gesture sets.

Underwater Image Enhancement With Hyper-Laplacian Reflectance Priors.

Underwater image enhancement aims at improving the visibility and eliminating color distortions of underwater images degraded by light absorption and scattering in water. Recently, retinex variational models show remarkable capacity of enhancing images by estimating reflectance and illumination in a retinex decomposition course. However, ambiguous details and unnatural color still challenge the performance of retinex variational models on underwater image enhancement. To overcome these limitations, we propose a hyper-laplacian reflectance priors inspired retinex variational model to enhance underwater images. Specifically, the hyper-laplacian reflectance priors are established with the l1/2 -norm penalty on first-order and second-order gradients of the reflectance. Such priors exploit sparsity-promoting and complete-comprehensive reflectance that is used to enhance both salient structures and fine-scale details and recover the naturalness of authentic colors. Besides, the l2 norm is found to be suitable for accurately estimating the illumination. As a result, we turn a complex underwater image enhancement issue into simple subproblems that separately and simultaneously estimate the reflection and the illumination that are harnessed to enhance underwater images in a retinex variational model. We mathematically analyze and solve the optimal solution of each subproblem. In the optimization course, we develop an alternating minimization algorithm that is efficient on element-wise operations and independent of additional prior knowledge of underwater conditions. Extensive experiments demonstrate the superiority of the proposed method in both subjective results and objective assessments over existing methods. The code is available at: https://github.com/zhuangpeixian/HLRP.

FOURTH-ORDER STRAIN GRADIENT BAR-SUBSTRATE MODEL WITH NONLOCAL AND SURFACE EFFECTS FOR THE ANALYSIS OF NANOWIRES EMBEDDED IN SUBSTRATE MEDIA

This paper presents a new analytical bar-substrate model for the analysis of an isotropic and homogeneous nanowire embedded in an elastic substrate. A fourth-order strain gradient model based on a thermodynamic approach is employed to represent the small-scale effect (nonlocal effect) while the Gurtin-Murdoch continuum model based on the surface elastic theory is used to account for the size-dependent effect (surface energy effect). The proposed model is derived from the virtual displacement principle, leading to the governing differential equations and its associated natural boundary conditions. The analytical solutions of the sixth-order governing differential equation for the nanowire-substrate element are provided, and were employed in numerical simulations. Two numerical simulations are used to demonstrate the performance and to investigate the characteristics of the fourth-order strain gradient model on nanowire responses, when compared to the classical model and the second-order strain gradient model. The first simulation investigates the influences of nonlocal and surface effects on the responses of a nanowire embedded in an elastic substrate, while the second simulation study assessed the sensitivity of system stiffness on parameters in the nanowire-substrate model.

A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements

In this paper, a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation is proposed. The basic idea consists in reconstructing the geometrical support of the unknown source from partial boundary measurements of the associated potential. A Kohn–Vogelius type shape functional is considered together with a regularization term penalizing the relative perimeter of the unknown set of anomalies. Identifiability result is derived and uniqueness of a minimizer is ensured. The shape functional measuring the misfit between the solutions of two auxiliary problems containing information about the boundary measurements is minimized with respect to a finite number of ball-shaped trial anomalies by using the topological derivative method. In particular, the second-order topological gradient is exploited to devise an efficient and fast noniterative reconstruction algorithm. Finally, some numerical experiments are presented, showing different features of the proposed approach in reconstructing multiple anomalies of varying shapes and sizes by taking noisy data into account.

Development of novel kinetic energy functional for orbital-free density functional theory applications

The development of novel Kinetic Energy (KE) functionals is an important topic in density functional theory (DFT). In particular, this happens by means of an analysis with newly developed benchmark sets. Here, I present a study of Laplacian-level kinetic energy functionals applied to metallic nanosystems. The nanoparticles are modeled using jellium sph eres of different sizes, background densities, and number of electrons. The ability of different functionals to reproduce the correct kinetic energy density and potential of various nanoparticles is investigated and analyzed in terms of semilocal descriptors. Most semilocal KE functionals are based on modifications of the second-order gradient expansion GE2 or GE4. I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles.

XGBLC: an improved survival prediction model based on XGBoost.

Survival analysis using gene expression profiles plays a crucial role in the interpretation of clinical research and assessment of disease therapy programs. Several prediction models have been developed to explore the relationship between patients' covariates and survival. However, the high-dimensional genomic features limit the prediction performance of the survival model. Thus, an accurate and reliable prediction model is necessary for survival analysis using high-dimensional genomic data. In this study, we proposed an improved survival prediction model based on XGBoost framework called XGBLC, which used Lasso-Cox to enhance the ability to analyze high-dimensional genomic data. The novel first- and second-order gradient statistics of Lasso-Cox were defined to construct the loss function of XGBLC. We extensively tested our XGBLC algorithm on both simulated and real-world datasets, and estimated the performance of models with 5-fold cross-validation. Based on 20 cancer datasets from The Cancer Genome Atlas (TCGA), XGBLC outperforms five state-of-the-art survival methods in terms of C-index, Brier score and AUC. The results show that XGBLC still keeps good accuracy and robustness by comparing the performance on the simulated datasets with different scales. The developed prediction model would be beneficial for physicians to understand the effects of patient's genomic characteristics on survival and make personalized treatment decisions. The implementation of XGBLC algorithm based on R language is available at: https://github.com/lab319/XGBLC. Supplementary data are available at Bioinformatics online.

Phase unwrapping of digital holographic microscopy using adaptive region segmentation and phase derivative calibration with respect to fringe density

Accurate phase unwrapping of the wrapped phase maps with high noise and uneven fringe densities is an essential problem for phase restoration in digital holographic microscopy. In this paper, a phase unwrapping algorithm using adaptive region segmentation and phase derivative calibration with respect to fringe density is proposed. The dense and sparse fringe regions of the wrapped phase map are adaptively segmented by using the sine/cosine spatial filtering and calculating the second-order phase gradient. Then, the first-order spatial wrapped phase derivative maps are divided into four phase derivative maps, and the phase anomalies on them are calibrated respectively. Finally, the four maps were recombined into two new phase derivative maps, and the unweighted least-squares iterative algorithm is implemented to obtain the continuous phase map. The advantage of our algorithm is that it can detect, calibrate and restore the phase anomalies based on fringe density automatically. Simulation and experimental results demonstrated that the proposed algorithm has better accuracy and effectiveness in dealing with the wrapped phase maps with high fringe density and high noise, which indicates that our algorithm is able to process the wrapped phase maps corrupted by coherent noise and phase aberration in the digital holographic microscopy.

A second-order gradient method for convex minimization

A second-order gradient method for convex minimization

Magnetic Object Positioning Based on Second-Order Magnetic Gradient Tensor System

Target positioning by the magnetic tracking system is extremely susceptible to the influence of the geomagnetic field. To accurately locate magnetic objects, we design a second-order magnetic gradient tensor (SMGT) system based on the plane-cross magnetic gradient tensor (MGT) system. With the constraint equation of MGT spatial invariants, the magnetic source position coordinates are solved by the SMGT and Euler deconvolution. The simulation shows when the Gaussian noise variance is less than 3 nT and a magnetic dipole with scalar 6000 Am <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> moment within 10 m distance, the positioning accuracy of the method can be controlled within the range of about 3 m root-mean-square error (RMSE); in actual measurement, after system calibration, the method realized a small magnet (diameter 5 cm, thickness 0.5 cm) positioning where the RMSE is suppressed in 14 cm in a 2.1 m heading-line detection interval.

Frequency-dependent AVO analysis: A potential seismic attribute for thin-bed identification

Identifying thinly bedded reservoirs is important in exploration, appraisal, and development. The thin beds that we are referring to are of meter scale or less. Conventional seismic attributes are not able to resolve thin-bed effects. A new frequency-dependent amplitude variation with offset (FAVO) seismic attribute is developed for the prediction of thin beds. It is based on seismic wave scattering theory for vertically inhomogeneous media, in which the seismic response from a laterally homogeneous interval is represented by the Born series. The Born series characterizes the P-P and P-SV wave reflections, transmissions, and interbed multiples within the target interval with different order terms. The newly derived attribute corresponds to the second-order term of the Born series, in which P-S wave reflection and transmission energy is taken into consideration, and it is called the second-order FAVO gradient attribute. In a thinly bedded interval where sand/shale interfaces are abundant, the P-SV wave mode conversions are numerous. This leads to a strong second-order FAVO gradient attribute response compared to that of a blocky sand, silt, or shale interval under the assumption that there is no significant rock- and fluid-property differences between the intervals. Therefore, the new seismic attribute has the potential to be a thin-bed interval indicator. We have adopted a strategy to estimate the new attribute using conventional P-wave seismic data. The attribute is extracted from seismic data at the frequency range at which the second-order scattering effect is the most prominent. Synthetic and field data examples from offshore Trinidad are studied to demonstrate the second-order scattering effect and the potential usage of the second-order FAVO attribute for thin-bed reservoir characterization.