Constrained Energy Minimization Research Articles

EXTRACTING FEATURE OF WATER FROM REMOTELY SENSED IMAGE

In the present work, different remote sensing techniques have been used to analyze remote sensing data spectrally using ENVI software. The majority of algorithms used in the Spectral Processing can be organized as target detection and classification. In this paper method of target detection has been studied constrained energy minimization on the Therthar Lakeand surrounding area has been done. Also the results that obtained from applying constrained energy minimization were more accurate than other method comparing with the real situation.

A Discrete‐Domain Approach to Three‐Phase Hysteresis in Porous Media

AbstractWe present a discrete‐domain approach to three‐phase displacements and hysteresis in porous media. In this method, constrained energy minimization leads to evolution equations for local saturations that describe a wide range of three‐phase displacements, including pressure‐ and saturation‐controlled displacement with or without preservation of one of the defending phases. Under action of global saturation constraints, irreversible displacements lead to significant fluid redistribution, as well as abrupt fluctuations of both the three‐phase saturation paths and the corresponding capillary pressures. These features are a consequence of Haines jumps with cooperative behavior that occur at pore scale in three‐phase systems. The method is a fast and convenient way to investigate hysteresis behavior of three‐phase displacement in porous media. As free energy is an extensive property, the framework links pore and core scales and provide a means to achieve upscaled three‐phase displacements for higher‐order hysteresis loops, which rarely is obtained in time‐consuming three‐phase measurements or pore‐scale simulations.

Sparse Channel Estimation via Hierarchical Hybrid Message Passing for Massive MIMO-OFDM Systems

In this paper, we investigate a sparse channel estimation problem for broadband massive multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We propose a hidden Markov model to capture the structured sparsity and temporal dependency characteristic of massive MIMO-OFDM channels in the angle-delay domain, and this probability model exhibits extensive adaptability to different realistic propagation scenarios. Then we solve the channel estimation problem based on a novel optimization framework named constrained Bethe free energy (BFE) minimization, which is valid for a generic statistical model. Under this systematic theoretical framework, a hierarchical hybrid message passing (HHMP) algorithm is proposed to track dynamic channel parameters recursively. The proposed method can adaptively learn the sparse structure and temporal correlation of multiuser channels without requiring the knowledge of hidden Markov channel parameters. Numerical simulations demonstrate that the proposed HHMP algorithm can accurately estimate angle-delay domain channels with reduced iteration times and pilot overhead.

Multispatial Filtering Module Cascaded System for Hyperspectral Image Classification

This article presents a multispatial filtering module cascaded system (MSFMCS) for hyperspectral image classification (HSIC), which can serve as a paradigm to improve spectral–spatial classification. It includes multiple spatial filtering modules (SFMs) that are cascaded to particularly capture spatial information from the classification maps generated from the preceding modules. As a result, any spectral classifier (SC) can be used as an input to an initial/input module (IM). Through MSFMCS, its classification performance keeps improving as more SFMs are processed. To terminate MSFMCS, an automatic stopping rule is particularly designed by support vector machine (SVM) which is used not only as a classifier but also as a decision-maker. So, once an SC cannot be further improved, MSFMCS is terminated. One major benefit resulting from MSFMCS is its framework which can implement any arbitrary SC as its initial classifier in IM. Another is its ability in capturing additional spatial classification information module by module as the process progresses. A third one is no weights connected between modules so that no training phase is required like a feedforward neural network. Finally, the number of modules used in MSFMCS can be automatically determined by its stopping rule not predetermined empirically. To illustrate full advantages of MSFMCS in HSIC, three types of heterogeneous classifiers, pure-pixel-based SVM, mixed-pixel-based constrained energy minimization (CEM), and feature-extraction-based classifier—orthogonal total variation component analysis (OTVCA)—are used for experiments to demonstrate how MSFMCS can improve their classification performance.

Identify Informative Bands for Hyperspectral Target Detection Using the Third-Order Statistic

Constrained energy minimization (CEM) has been proposed and widely researched in the field of hyperspectral target detection. Generally, it selects one of the target spectra as the representative and then keeps its output constant while minimizing the average filter output energy of the data. However, it has been proven that as the number of bands (L) increases, CEM will gradually lower the average filter output energy when keeping the representative’s output constant. Unavoidably, due to the inherent spatial and temporal variation of the spectra, this will lead to an unreasonable phenomenon, i.e., if L is particularly large, when adding more bands, CEM will suppress more and more pixels, even including the target pixels. This means that the optimal solution of CEM may not correspond to the target detection result that we desire. To deal with this, in this paper, we introduce the third-order statistic (skewness) of the CEM model, served as an auxiliary index to determine whether a band is beneficial to target detection or not. Theoretically, we prove that the skewness index can always exclude the noisy bands with Gaussian distribution. In addition, experiments on several widely used remote sensing data indicate that the index can also efficiently identify informative bands for a better target detection performance.

Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations

In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the method is based on two multiscale spaces: pressure multiscale space and velocity multiscale space. The pressure space is constructed via a set of well-designed local spectral problems, which can be solved independently. Based on the computed pressure multiscale space, we will construct the velocity multiscale space by applying constrained energy minimization. The convergence of the proposed method is proved. In particular, we prove that the convergence of the method depends only on the coarse grid size, and is independent of the heterogeneities and contrast of the diffusion coefficient. Four typical types of permeability fields are exploited in the numerical simulations, and the results indicate that our proposed method works well and gives efficient and accurate numerical solutions.

Orthogonal Subspace Projection Using Data Sphering and Low-Rank and Sparse Matrix Decomposition for Hyperspectral Target Detection

Orthogonal subspace projection (OSP) has been widely used in many applications for hyperspectral data exploitation. However, its performance is sensitive to its used prior target knowledge, which is significantly affected by target background (BKG). To resolve this issue, this article develops three approaches to extend OSP in improving its performance. One is data sphering which can suppress BKG via removing the first- and second-order data statistics. Another takes advantage of a recently developed low-rank and sparse matrix decomposition (LRaSMD) to separate BKG and target signal sources in two subspaces characterized by the low-rank matrix and sparse matrix, respectively, and then annihilates BKG via the low-rank matrix, referred to as BKG-annihilated OSP (BA-OSP). A third approach combines data sphering and LRaSMD to further improve OSP over target detectability and BKG suppressibility. Experiments show that implementing OSP in conjunction with data sphering and LRaSMD significantly improves OSP in target detection and BKG suppression, and also performs as well as a widely used constrained energy minimization (CEM)-based subpixel target detection.

Unifying Message Passing Algorithms Under the Framework of Constrained Bethe Free Energy Minimization

Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating on graphical models, this article unifies them under an optimization framework, namely, Bethe free energy minimization with differently and appropriately imposed constraints. This new perspective in terms of constraint manipulation can offer additional insights on the connection between different message passing algorithms and is valid for a generic statistical model. It also founds a theoretical framework to systematically derive message passing variants. Taking the sparse signal recovery (SSR) problem as an example, a low-complexity EP variant can be obtained by simple constraint reformulation, delivering better estimation performance with lower complexity than the standard EP algorithm. Furthermore, we can resort to the framework for the systematic derivation of hybrid message passing for complex inference tasks. Notably, a hybrid message passing algorithm is exemplarily derived for joint SSR and statistical model learning with near-optimal inference performance and scalable complexity.

Joint Hapke Model and Spatial Adaptive Sparse Representation with Iterative Background Purification for Martian Serpentine Detection

Visible and infrared imaging spectroscopy have greatly revolutionized our understanding of the diversity of minerals on Mars. Characterizing the mineral distribution on Mars is essential for understanding its geologic evolution and past habitability. The traditional handcrafted spectral index could be ambiguous as it may denote broad mineralogical classes, making this method unsuitable for definitive mineral investigation. In this work, the target detection technique is introduced for specific mineral mapping. We have developed a new subpixel mineral detection method by joining the Hapke model and spatially adaptive sparse representation method. Additionally, an iterative background dictionary purification strategy is proposed to obtain robust detection results. Laboratory hyperspectral image containing Mars Global Simulant and serpentine mixtures was used to evaluate and tailor the proposed method. Compared with the conventional target detection algorithms, including constrained energy minimization, matched filter, hierarchical constrained energy minimization, sparse representation for target detection, and spatially adaptive sparse representation method, the proposed algorithm has a significant improvement in accuracy about 30.14%, 29.67%, 29.41%, 9.13%, and 8.17%, respectively. Our algorithm can detect subpixel serpentine with an abundance as low as 2.5% in laboratory data. Then the proposed algorithm was applied to two well-studied Compact Reconnaissance Imaging Spectrometer for Mars images, which contain serpentine outcrops. Our results are not only consistent with the spatial distribution of Fe/Mg phyllosilicates derived by spectral indexes, but also denote what the specific mineral is. Experimental results show that the proposed algorithm enables the search for subpixel, low-abundance, and scientifically valuable mineral deposits.

Quasi-static anti-plane shear crack propagation in nonlinear strain-limiting elastic solids using phase-field approach

We study a quasi-static evolution of anti-plane crack with the nonlinear strain-limiting model using the phase-field approach. The nonlinear strain-limiting models, a subclass of the implicit constitutive relations, allow the linearized strain value to remain small even if the stress value tends to infinity. To compute the quasi-static crack, we solve the constrained energy minimization for the nonlinear bulk energy coupled with diffusive crack energy. An iterative staggered scheme (L-scheme) is employed for coupling the nonlinear mechanics and phase-field, and augmented Lagrangian is utilized to accommodate crack irreversibility. Several numerical experiments of the proposed framework substantiate the bounded strain in the neighborhood of the crack-tip for both static and quasi-static cracks. The comparisons of bulk and the crack energies and the discrete crack-tip speed between the LEFM and our model are presented.

Secrecy Energy‐Efficient UAV Communication via Trajectory Design and Power Control

This paper investigates the problem of maximizing the secrecy energy efficiency (SEE) for unmanned aerial vehicle‐ (UAV‐) to‐ground wireless communication system, in which a fixed‐wing UAV tries to transmit covert information to a terrestrial legitimate destination receiver with multiple terrestrial eavesdroppers. In particular, we intend to maximize the worst‐case SEE of UAV by jointly optimizing UAV’s flight trajectory and transmit power over a finite flight period. However, the formulated problem is challenging to solve because of its large‐scale nonconvexity. For efficiently solving this problem, we first decouple the above optimization problem into two subproblems and then propose an alternating iterative algorithm by adopting block coordinate descent method and Dinkelbach’s algorithm as well as successive convex approximation technique to seek a suboptimal solution. For the sake of performance comparison, two benchmark schemes, the secrecy rate maximization (SRM) scheme and constrained energy minimization (CEM) scheme are considered to obtain more useful insights. Finally, simulation results are executed to verify that our proposed SEE maximization (SEEM) algorithm is superior to two benchmark schemes for the UAV‐ground communication system.

Surface Defect Detection of Wet-Blue Leather Using Hyperspectral Imaging

Detection of surface defects on wet-blue leather is much more challenging than raw-hide leather. Since wet-blue leather turns blue and contains moisture after pre-treatment, it is a semi-product of the cowhide processing. At present, the defect detection of wet-blue leather is mostly carried out manually and is time-consuming and labor-intensive for professional inspectors. This paper is the first to use hyperspectral imaging (HSI) to implement the surface inspection of five wet-blue leather defects including brand masks, rotten grain, rupture, insect bites, and scratches in the pixel level detection. Hyperspectral Leather Defect Detection Algorithm (HLDDA) including Hyperspectral Target Detection (HTD) and Deep Learning (DL) techniques was proposed in this paper. In HTD, Weighted Background Suppression Constrained Energy Minimization (WBS-CEM) and WBS-Hierarchical CEM (WBS-hCEM) were developed in this paper by using weighting to suppress the background and enhance the contrast between the target and background. Experimental results showed that the overall performance of WBS was better than the original CEM. In the DL part, 1D-Convolutional Neural Network (CNN), 2D-Unet and 3D-UNet architectures were designed to segment defect areas. For various characteristics of defects, 1D-CNN emphasizes on defects with spectral features, 2D-Unet emphasizes on defects with spatial features, and 3D-Unet can simultaneously process spatial and spectral information in HSI. The experimental results verified that the proposed HLDDA could effectively quantify and estimate the size of the defect, thereby accelerating the leather inspection process by professional inspectors and develop an automated leather grading system towards Industry 4.0.

Bayesian Constrained Energy Minimization for Hyperspectral Target Detection

For better performance of hyperspectral target detectors, the prior target spectrum is expected to be accurate and consistent with the target spectrum in the hyperspectral image to be detected. The existing hyperspectral target detection algorithms usually assume that the prior target spectrum is highly reliable. However, the label obtained is not always precise in practice, and pixels of the same object may have quite different spectra. Since it is hard to acquire a highly reliable prior target spectrum in some application scenarios, we propose a Bayesian constrained energy minimization (B-CEM) method for hyperspectral target detection. Instead of the point estimation of the target spectrum, we infer the posterior distribution of the true target spectrum based on the prior target spectrum. Specifically, considering the characteristics of hyperspectral image and target detection task, we adopt the Dirichlet distribution to approximate the true target spectrum. Experimental results on three datasets demonstrate the effectiveness of the proposed B-CEM when the known target spectrum is noisy or inconsistent with the true target spectrum. The necessity to approximate the true target spectrum is also proved. Generally, the distributional estimate achieves better performance than using the known target spectrum directly.

Nonconvex and Bound Constraint Zeroing Neural Network for Solving Time-Varying Complex-Valued Quadratic Programming Problem

Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this study, a nonconvex and bound constraint zeroing neural network (NCZNN) model is designed and theorized to solve the time-varying complex-valued QP with linear equation constraint. Besides, we construct several new types of nonconvex and bound constraint complex-valued activation functions by extending real-valued activation functions to the complex domain. Subsequently, corresponding simulation experiments are conducted, and the simulation results verify the effectiveness and robustness of the proposed NCZNN model. Moreover, the model proposed in this article is further applied to solve the issue of small target detection in remote sensing images, which is modeled to QP problem with linear equation constraint by a serial of conversions based on constrained energy minimization algorithm.

Identification of Phyllosilicates in the Antarctic Environment Using ASTER Satellite Data: Case Study from the Mesa Range, Campbell and Priestley Glaciers, Northern Victoria Land

In Antarctica, spectral mapping of altered minerals is very challenging due to the remoteness and inaccessibility of poorly exposed outcrops. This investigation evaluates the capability of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) satellite remote sensing imagery for mapping and discrimination of phyllosilicate mineral groups in the Antarctic environment of northern Victoria Land. The Mixture-Tuned Matched-Filtering (MTMF) and Constrained Energy Minimization (CEM) algorithms were used to detect the sub-pixel abundance of Al-rich, Fe3+-rich, Fe2+-rich and Mg-rich phyllosilicates using the visible and near-infrared (VNIR), short-wave infrared (SWIR) and thermal-infrared (TIR) bands of ASTER. Results indicate that Al-rich phyllosilicates are strongly detected in the exposed outcrops of the Granite Harbour granitoids, Wilson Metamorphic Complex and the Beacon Supergroup. The presence of the smectite mineral group derived from the Jurassic basaltic rocks (Ferrar Dolerite and Kirkpatrick Basalts) by weathering and decomposition processes implicates Fe3+-rich and Fe2+-rich phyllosilicates. Biotite (Fe2+-rich phyllosilicate) is detected associated with the Granite Harbour granitoids, Wilson Metamorphic Complex and Melbourne Volcanics. Mg-rich phyllosilicates are mostly mapped in the scree, glacial drift, moraine and crevasse fields derived from weathering and decomposition of the Kirkpatrick Basalt and Ferrar Dolerite. Chlorite (Mg-rich phyllosilicate) was generally mapped in the exposures of Granite Harbour granodiorite and granite and partially identified in the Ferrar Dolerite, the Kirkpatrick Basalt, the Priestley Formation and Priestley Schist and the scree, glacial drift and moraine. Statistical results indicate that Al-rich phyllosilicates class pixels are strongly discriminated, while the pixels attributed to Fe3+-rich class, Fe2+-rich and Mg-rich phyllosilicates classes contain some spectral mixing due to their subtle spectral differences in the VNIR+SWIR bands of ASTER. Results derived from TIR bands of ASTER show that a high level of confusion is associated with mafic phyllosilicates pixels (Fe3+-rich, Fe2+-rich and Mg-rich classes), whereas felsic phyllosilicates (Al-rich class) pixels are well mapped. Ground truth with detailed geological data, petrographic study and X-ray diffraction (XRD) analysis verified the remote sensing results. Consequently, ASTER image-map of phyllosilicate minerals is generated for the Mesa Range, Campbell and Priestley Glaciers, northern Victoria Land of Antarctica.

Adaptive Iterated Shrinkage Thresholding-Based Lp-Norm Sparse Representation for Hyperspectral Imagery Target Detection

In recent years, with the development of compressed sensing theory, sparse representation methods have been concerned by many researchers. Sparse representation can approximate the original image information with less space storage. Sparse representation has been investigated for hyperspectral imagery (HSI) detection, where approximation of testing pixel can be obtained by solving l1-norm minimization. However, l1-norm minimization does not always yield a sufficiently sparse solution when a dictionary is not large enough or atoms present a certain level of coherence. Comparatively, non-convex minimization problems, such as the lp penalties, need much weaker incoherence constraint conditions and may achieve more accurate approximation. Hence, we propose a novel detection algorithm utilizing sparse representation with lp-norm and propose adaptive iterated shrinkage thresholding method (AISTM) for lp-norm non-convex sparse coding. Target detection is implemented by representation of the all pixels employing homogeneous target dictionary (HTD), and the output is generated according to the representation residual. Experimental results for four real hyperspectral datasets show that the detection performance of the proposed method is improved by about 10% to 30% than methods mentioned in the paper, such as matched filter (MF), sparse and low-rank matrix decomposition (SLMD), adaptive cosine estimation (ACE), constrained energy minimization (CEM), one-class support vector machine (OC-SVM), the original sparse representation detector with l1-norm, and combined sparse and collaborative representation (CSCR).

Multitarget Detection Algorithms for Multitemporal Remote Sensing Data

Target detection is always an important topic in the field of hyper/multispectral remote sensing image processing. At present, target detection algorithms in this field are generally limited to processing single-temporal remote sensing data, and they cannot obtain satisfactory results when the spectra of target and background are similar to each other. Recently, a target detection algorithm called filter tensor analysis (FTA), which is specially designed for multitemporal remote sensing data, has been reported and has achieved better detection results in many cases than the traditional single-temporal methods. However, FTA can only extract one target of interest at a time, and it cannot work when there are multiple targets of interest in the image. Therefore, considering that the matrix form of the FTA method is similar to that of the constrained energy minimization (CEM) model, it naturally comes to us that we can combine the tensor filter in FTA and the multiple target constraints to detect multiple targets by fully exploiting the time-series information in multitemporal data. To be specific, through: 1) adding the ``output to one'' constraints to the multiple targets in FTA; 2) applying linear/nonlinear function to the outputs of FTA for the multiple targets; and 3) modifying the autocorrelation matrix in FTA, four multitarget detection algorithms for multitemporal remote sensing data are proposed in this article. Experiments with simulation data and real data both show the effectiveness and superiority of the proposed methods.

Synergistic use of ASTER, L-band ALOS PALSAR, and hyperspectral AVIRIS-NG data for exploration of lode type gold deposit – A study in Hutti Maski Schist Belt, India

In this study, we have explored the utility of advanced hyperspectral, dual-polarized microwave, and advanced multispectral data to delineate potential areas of mineralization associated with the lode type gold deposit in Hutti-Maski Schist Belt Karnataka, India. We derived different image-enhanced products using visible-near-infrared (VNIR) and short-wave infrared (SWIR) spectral bands of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor to delineate major rock types of gold-bearing greenstone belt such as metabasalt, amphibolite, younger alkali feldspar rich granite, granodiorite, and tonalitic-granodioric gneiss (TTG). The principal component (PC) image composite of ASTER VNIR-SWIR bands was not only used to distinguish different granitoids but also confirmed their sharp instructive nature of contact with the greenstone rocks. We also used an index image composite using ASTER SWIR bands to discriminate granitoid, basalt and amphibolite. We could demarcate few lineaments extending through the mineralized zone (e.g., Hutti, Heera-Buddine mines, etc.) using the fused products of ASTER and two polarization channels of the Phased-array L band Synthetic Aperture Radar (PALSAR) sensor of the Advanced Land Observation Satellite (ALOS). All these image-enhanced products are validated using the reference geological map of the study area and field data collected along selected field -traverses. The mineralogical and petrographical data of the altered rocks from the study site revealed the formation of calcite, scapolite, and other minerals. Represenattive reflectance spectrum of the altered rock was used to spatially delineate the surface distribution of the patchy and small alteration zones using airborne hyperspectral data of the Advanced Visible Infrared Imaging Spectrometer Next Generation (AVIRIS-NG) sensor. In this regard, a unified spectral map of altered rocks was derived by integrating two alteration maps prepared independently using two different partial sub-pixel algorithms (constrained energy minimization and matched filtering). Occurrences of altered rocks in the vicinity to favorable geological lineaments and their spatial proximity to metavolcanic-younger felsic intrusive contacts suggest their importance as the potential sites for detailed exploration.

Inextensibility and Its Effect on the Number of Equilibria of Shallow Buckled Beams

Abstract A buckled beam with shallow rise under lateral constraint is considered. The initial rise results from a prescribed end displacement. The beam is modeled as inextensible, and analytical solutions of the equilibria are obtained from a constrained energy minimization problem. For simplicity, the results are derived for the archetypal beam with pinned ends. It is found that there are an infinite number of zero lateral-load equilibria, each corresponding to an Euler buckling mode. A numerical model is used to verify the accuracy of the model and also to explore the effects of extensibility.

A reconfigurable multi-mode implementation of hyperspectral target detection algorithms

Hyperspectral images obtained by imaging spectrometer contain a large data amount that requires techniques such as target detection for information extraction. The proposed multi-mode FPGA implementation combines matrix correlation and inversion matrix computations by using the Sherman-Morrison method to achieve real-time operation. The implementation supports Constrained Energy Minimization (CEM), Adjusted Spectral Matched Filter (ASMF) and modified Adaptive Cosine Estimator (ACE) detectors. The detection performance of the algorithms is evaluated using standard detection metrics. The proposed implementation has been realized on Zynq family SoCs and verified against the MATLAB reference software. The detection results for different fixed-point data types and target detection algorithms are reported. Finally, the proposed implementation is compared with state-of-the-art designs in terms of both throughput and resource utilization.