Smoothness Constraint Research Articles

1.5D Time Domain Electromagnetic Inversion Using Global Optimization Methods and Parallel Processing

An innovative comparative study among three different global optimization methods (GOMs) to invert time domain electromagnetic data (TDEM), was applied in the 1.5D subsurface resistivity imaging. These stochastic methods allow the incorporation of different kinds of constraints in the objective function, due to the easiness of implementation in their algorithms and their computational efficiency. Nevertheless, global optimization methods, like any other based on swarm intelligence cost much computational time, including problems with a high number of unknown parameters and when the forward modeling involves time-consuming calculations such as Gaver-Stehfest inverse transforms, Hankel transforms, and others. To overcome this difficulty, we developed a parallel pure MPI version of each GOM, allowing the distribution of the computation among several cores of a cluster. The performances of the classic version of particle swarm optimization (PSO), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) using MPI parallelism for solving 1.5D TDEM inverse problems are compared here in a set of synthetic and real data. The principal outcomes show: (1) These GOMs reproduce quite well the distribution of subsurface resistivity either synthetic models or real data, (2) WOA and PSO exhibit better computational performances, converging first than GWO, (3) WOA provided better performance in the final value achieved of the cost function than PSO and GWO, and (4) pure MPI parallelism provided a 17x and 50x speedup in the computation time for both synthetic and real data, respectively. In a better way to classify this comparison, we analyzed the solutions using total variation (TV) and Global smoothness (GS) constraints, to identify smooth and sharp structures. Additionally, we have diminished the computational time execution with the parallel solution (MPI version of each stochastic traditional method) against the sequential processing.

Mitigating undersampling errors in MR fingerprinting bysequence optimization.

To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account. A predictive model for the undersampling error leveraging on perturbation theory was exploited to optimize the MRF flip angle sequence for improved robustness against undersampling artifacts. In this framework parameter maps from a previously acquired MRF scan were used as reference. Sequences were optimized for different sequence lengths, smoothness constraints and undersampling factors. Numerical simulations and in vivo measurements in eight healthy subjects were performed to assess the effect of the performed optimization. The optimized MRF sequences were compared to a conventionally shaped flip angle pattern and an optimized pattern based on the Cramér-Rao lower bound (CRB). Numerical simulations and in vivo results demonstrate that the undersampling errors can be suppressed by flip angle optimization. Analysis of the in vivo results show that a sequence optimized for improved robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors in : and : compared to the conventional ( : , : ) and CRB-based ( : , : ) sequences. The proposed method is able to optimize the MRF flip angle pattern such that significant mitigation of the artifacts from strong k-space undersampling in MRF is achieved.

Pyramidal Semantic Correspondence Networks

This paper presents a deep architecture, called pyramidal semantic correspondence networks (PSCNet), that estimates locally-varying affine transformation fields across semantically similar images. To deal with large appearance and shape variations that commonly exist among different instances within the same object category, we leverage a pyramidal model where the affine transformation fields are progressively estimated in a coarse-to-fine manner so that the smoothness constraint is naturally imposed. Different from the previous methods which directly estimate global or local deformations, our method first starts to estimate the transformation from an entire image and then progressively increases the degree of freedom of the transformation by dividing coarse cell into finer ones. To this end, we propose two spatial pyramid models by dividing an image in a form of quad-tree rectangles or into multiple semantic elements of an object. Additionally, to overcome the limitation of insufficient training data, a novel weakly-supervised training scheme is introduced that generates progressively evolving supervisions through the spatial pyramid models by leveraging a correspondence consistency across image pairs. Extensive experimental results on various benchmarks including TSS, Proposal Flow-WILLOW, Proposal Flow-PASCAL, Caltech-101, and SPair-71k demonstrate that the proposed method outperforms the lastest methods for dense semantic correspondence.

Joint spectral quantification of MR spectroscopic imaging using linear tangent space alignment-based manifold learning.

To develop a manifold learning-based method that leverages the intrinsic low-dimensional structure of MR Spectroscopic Imaging (MRSI) signals for joint spectral quantification. A linear tangent space alignment (LTSA) model was proposed to represent MRSI signals. In the proposed model, the signals of each metabolite were represented using a subspace model and the local coordinates of the subspaces were aligned to the global coordinates of the underlying low-dimensional manifold via linear transform. With the basis functions of the subspaces predetermined via quantum mechanics simulations, the global coordinates and the matrices for the local-to-global coordinate alignment were estimated by fitting the proposed LTSA model to noisy MRSI data with a spatial smoothness constraint on the global coordinates and a sparsity constraint on the matrices. The performance of the proposed method was validated using numerical simulation data and in vivo proton-MRSI experimental data acquired on healthy volunteers at 3T. The results of the proposed method were compared with the QUEST method and the subspace-based method. In all the compared cases, the proposed method achieved superior performance over the QUEST and the subspace-based methods both qualitatively in terms of noise and artifacts in the estimated metabolite concentration maps, and quantitatively in terms of spectral quantification accuracy measured by normalized root mean square errors. Joint spectral quantification using linear tangent space alignment-based manifold learning improves the accuracy of MRSI spectral quantification.

Path Planning For Unmanned Surface Vehicles Based On Modified Artificial Fish Swarm Algorithm With Local Optimizer

The appeal for safe navigation of autonomous surface vessels (ASVs) has deemed the path planning problem as an attractive research interest. However, most of the previous works to solve the path planning problem focus on finding the shortest and collision-free path, but the solutions are scarcely satisfied by the safety requirements and constraints related to the USVs’ mechanical systems. To address this challenge, we present a novel path planning method based on a modified artificial fish swarm algorithm in combination with a path optimizer. The modifications are made from two perspectives: (1) Four customized operators and an adaptive factor are applied to improve the convergence performance of the algorithm. (2) A local path optimizer is proposed to enhance its feasibility of cooperating with the USV control system. Path safety, path smoothness, and nonholonomic constraints are considered. The path planning benchmark experiments have demonstrated its superior performance in terms of efficiency and path quality compared to other state-of-the-art algorithms. Moreover, the proposed method is also integrated into the USV’s control system in a practical environment with satisfactory feasibility. The simulation results provide strong evidence that the proposed method can be regarded as a practical approach for USV path planning problems.

Spectral Reflectance Estimation with Smoothness Constraint

We consider the problem of estimating surface-spectral reflectance with a smoothness constraint from image data. The total variation of a spectral reflectance over the visible wavelength range is defined as the measure of smoothness. A penalty on roughness, equivalent to smoothness, is added to the performance index to estimate the spectral reflectance functions. The optimal estimates of the spectral reflectance functions are determined to minimize a total cost function consisting of the estimation error and the roughness of the spectral functions. An RGB camera and multiple LED light sources are used to construct the multispectral image acquisition system. We model the observed images using spectral sensitivities, illuminant spectrum, unknown spectral reflectance, a gain parameter, and an additive noise term. The estimation algorithms are developed for the two estimation methods of PCA and LMMSE. The optimal estimators are derived based on the least-square criterion for PCA and the mean squared error minimization criterion for LMMSE. The feasibility of the proposed method is shown in an experiment using three mobile phone cameras. It is confirmed that the optimal estimators improve the accuracy for both original PCA and LMMS estimators.

An Improved 3D Magnetization Inversion Based on Smoothness Constraints in Spherical Coordinates

In the inverse problem, the traditional way to obtain a stable solution is based on the maximum smoothness criteria. However, this approach cannot generate clearer and more focused images. In this study, we propose an improved inversion method based on the smoothness constraints. In the algorithm, the model weighting functions are updated by adding a model’s total gradient module matrix, which can effectively constrain the boundary of the recovery model in the iterative operation. We invert the 3D magnetization intensity for the three-component magnetic data in the spatial domain by spherical coordinates. The preconditional conjugate gradient algorithm is introduced to improve the efficiency of the solutions. We design two sets of synthetic examples to evaluate the inversion effects, which show that the improved method is more reliable than the smoothness constraint method. The boundary of the magnetic bodies is more precise, and the magnetization ranges are more focused. The method does not rely on the initial model and is suitable for magnetic vector data inversion. We also apply the algorithm to a set of Dabie orogen three-component magnetic data derived from a geomagnetic field model and verify the effectiveness of the inversion method.

Fast Nonsingular Fixed-Time Fuzzy Fault-Tolerant Control for HFVs With Guaranteed Time-Varying Flight State Constraints

This article proposes a fuzzy adaptive fault-tolerant control strategy solving the fast fixed-time constrained tracking problem for hypersonic flight vehicles. To handle the actuator faults, a two-step design method is first proposed that only needs to estimate the upper and lower bounds of actuator parameters, under which the adverse influences of actuator faults (e.g., lock-in-place, loss of effectiveness, etc.) have been compensated via an adaptive fashion instead of conventional robust ways. In comparison with the state-of-the-art, a new fixed-time corollary that has proved a smaller upper bound of convergence time under the same condition of conventional fixed-time stability is presented. To avoid singularity issues often encountered in fixed-time designs, a piecewise but differentiable switching control laws whose continuity and differentiability are guaranteed everywhere through an appropriate design is introduced. Such a design not only preserves the continuity and differentiability of virtual and actual control laws, but also ensures the continuity of their time derivatives. Fuzzy logic systems are exploited to tackle continuous unknown dynamics and asymmetric time-varying barrier functions are utilized to confine flight states within some predefined compact sets all the time provided their initial conditions remain therein. This property is of great significance in dealing with the challenge that the operating regions of the flight state variables are asymmetric and time-varying in practice, especially when executing various flight missions. Comparative simulations have been performed to validate the effectiveness of the proposed control scheme in terms of fixed-time convergence, smoothness, and time-varying constraints satisfaction.

Bayesian Inversion of Time Domain Electromagnetic (TDEM) Synthetic Data using Langevin Monte Carlo (LMC)

The inversion of time domain electromagnetic (TDEM) data is an ill-posed problem. This makes the standard inversion procedure, which is to linearize the related objective function. Then take a deterministic approach to determine a solution that can minimize the said objective function, which has the potential to be trapped in a local minimum. In this study, we solved the problem of TDEM data inversion using the Bayesian framework by generating a sample from the posterior distribution. The posterior distribution contains information related to the uncertainty of the TDEM data and the results of the forward modeling formulation, and prior information about the subsurface parameter model. In conducting the sampling process, we use the Langevin Monte Carlo (LMC) algorithm, one of many gradient-based Markov chain Monte Carlo (MCMC) sampling algorithms. Bayesian inversion was performed on synthetic data generated through the forward modeling of several test models. We used a model with varying thickness and resistivity values for inversion. We also added a prior probability distribution related to the smoothness constraint between resistivity values in adjacent layers allowing sharp and smooth transitions.

Elastic moduli parameterization and inversion considering nanopores effects in shale

Nanopores are widely developed in organic kerogen in shale. Due to the large surface-bulk ratio, nanopores cause significant surface effects that affect the overall elastic properties of shale. It is essential to consider the effects of nanopores when applying the prestack seismic inversion technique for shale reservoir prediction. Based on classical elastic theory, the technique of amplitude variation with offset (AVO) can usually extract velocity of the longitudinal wave and shear wave, elastic modulus, and density in shale reservoir from prestack seismic amplitudes but often ignores the surface effects of nanopores. For this reason, we have derived a new AVO parameterization combining the nanoporoelasticity theory and AVO technique. The newly derived parameterization contains four parameters (shear modulus of matrix, nanopores-related parameter, shear modulus of saturated rock, and density) which can be used to estimate the nanopore properties of shale. The model test and real seismic data examples verify the feasibility and suitability of the proposed method by applying the Bayesian inversion technique with smooth background constraint.

Pointwise mutual information sparsely embedded feature selection

Feature selection is an effective approach to dimensionality reduction. Feature selection based on rough sets and fuzzy rough sets is extensively realized by introducing diversified heuristic information. Most existing heuristic feature selection methods ignore the fact that different features have distinct classification abilities when constructing feature evaluation functions. Due to the limitations of search strategies, locally optimal feature subsets are probably selected out. Embedded feature selection based on regression analysis can avoid falling into locally optimal feature subsets to a certain extent. However, only linear relationships between feature space and decision space have been involved. To overcome those problems, a pointwise mutual information sparsely embedded feature selection model (PMISEFS) is proposed in this paper. In this model, the pointwise fuzzy mutual information matrix is constructed based on fuzzy information granules to characterize the discernibility of features as well as the nonlinear relationship between the feature space and decision space for a data set. A classification information matrix is introduced to further describe the consistency between the predicted decision and real decisions of samples. The fuzzy mutual information tensor is embedded sparsely into the decision matrix and the sparsely embedded coefficients, called information fusion coefficients (IFCs) of features, are adaptively learnt by imposing a smooth constraint to avoid over-fitting. An embedded feature selection algorithm is designed to adaptively learn optimal IFCs. Extensive experiments on various benchmark data sets are conducted and experimental results demonstrate the superiority of the proposed model over the state-of-the-art heuristic as well as embedded feature selection methods.

Noise Robust Face Hallucination Based on Smooth Correntropy Representation.

Face hallucination technologies have been widely developed during the past decades, among which the sparse manifold learning (SML)-based approaches have become the popular ones and achieved promising performance. However, these SML methods always failed in handling noisy images due to the least-square regression (LSR) they used for error approximation. To this end, we propose, in this article, a smooth correntropy representation (SCR) model for noisy face hallucination. In SCR, the correntropy regularization and smooth constraint are combined into one unified framework to improve the resolution of noisy face images. Specifically, we introduce the correntropy induced metric (CIM) rather than the LSR to regularize the encoding errors, which admits the proposed method robust to noise with uncertain distributions. Besides, the fused LASSO penalty is added into the feature space to ensure similar training samples holding similar representation coefficients. This encourages the SCR not only robust to noise but also can well exploit the inherent typological structure of patch manifold, resulting in more accurate representations in noise environment. Comparison experiments against several state-of-the-art methods demonstrate the superiority of SCR in super-resolving noisy low-resolution (LR) face images.

Improving moisture content estimation from field resistivity measurements with subsurface structure information

• Smoothness constraint in regularized resistivity inversion is removed at structural boundaries. • Structural unit-specific petrophysical models are used for moisture interpretation. • Moisture content is better estimated from resistivity with the new method. In Earth sciences, the measurement of soil and rock moisture content is essential in improving our understanding of various hydrologic processes. Recently, the electrical resistivity method has been frequently used to estimate the moisture content in the field. The uncertainty associated with resistivity-estimated moisture content is mainly from two sources: regularized inversion and petrophysical interpretation. In this study, to reduce the uncertainty, we propose (1) to use subsurface structural information from seismic refraction measurements to relax the smoothness-based regularization at structural boundaries and (2) to use structural unit-specific petrophysical relationships to translate resistivity into moisture content. The proposed methods are tested on a synthetic subsurface model featuring three distinct layers of a granitic critical zone (CZ). The results of the synthetic example show that both the spatial pattern and the moisture content values estimated with the new method are very close to the true model with low uncertainty. Compared to the traditional method, the estimation is significantly improved, particularly at the CZ boundaries, such as the regolith-fractured bedrock interface. We also apply the new method to a granitic hillslope to estimate the moisture content distribution from field resistivity measurements. Although no ground truth is available for validation, the estimated moisture content distributions exhibit some typical hydrological features in hillslopes, such as the perched water at the soil/rock interface and preferential flow path in fractured rocks. Therefore, it is concluded that incorporating structural information in resistivity inversion and using structural unit-specific petrophysical models can improve moisture content estimation from field resistivity measurements.

An integrated two‐dimensional merging trajectory optimization model for automated vehicles considering mixed traffic flow

Recently, automated vehicles have been recognized as a promising tool to address the problem of on-ramp merging. However, the complexity of the problem includes ignorance of the vehicle's lateral dynamics, the limitation of the fixed merging point, the mismatch problem caused by the sequential optimization scheme, and the fixed terminal states assumption. These factors make it intractable in practical driving scenarios. This paper proposed an integrated optimization model for on-ramp automated vehicles, which can guide the vehicle to complete the merging behaviour from the ramp lane to the main lane safely and efficiently. A merging path is first constructed in the two-dimensional plane with two critical parameters recommended by a neural network predictor, enabling it to incorporate both longitudinal and lateral dynamics. Then, an integrated Mixed Integer Quadratic Program (MIQP) model is built to determine the optimal velocity profiles and merging gap simultaneously while considering the safety and efficiency factors. Specifically, with the introduction of discretization and linearization techniques, linear collision avoidance constraints and smooth transition constraints can be built, which can address the challenging computational problem. The effectiveness of the proposed model is validated through the microscopic and macroscopic numerical results under different levels of mixed traffic.

Robust Video Stabilization based on Motion Decomposition

Video stabilization aims to eliminate camera jitter and improve the visual experience of shaky videos. Video stabilization methods often ignore the active movement of the foreground objects and the camera, and may result in distortion and over-smoothing problems. To resolve these issues, this paper proposes a novel video stabilization method based on motion decomposition. Since the inter-frame movement of foreground objects is different from that of the background, we separate foreground feature points from background feature points by modifying the classic density based spatial clustering method of applications with noise (DBSCAN). The movement of background feature points is consistent with the movement of the camera, which can be decomposed into the camera jitter and the active movement of the camera. And the movement of foreground feature points can be decomposed into the movement of the camera and the active movement of foreground objects. Based on motion decomposition, we design first-order and second-order trajectory smoothing constraints to eliminate the high-frequency and low-frequency components of the camera jitter. To reduce content distortion, shape-preserving constraints, and regularization constraints are taken to generate stabilized views of all feature points. Experimental results demonstrate the effectiveness and robustness of the proposed video stabilization method on a variety of challenging videos.

Solving Shape-From-Shading problem through shape and depth joint optimization

Objective:Shape-From-Shading (SFS) is one unique and long-standing problem aiming to reconstruct shape/depth from only one image. The SFS problem can be regarded as an inverse process of image rendering, i.e., solving the Bi-directional Reflection Distribution Function (BRDF) model with the given image. Among various BRDF models, physically based perspective Cook-Torrance BRDF model is generally used because of its universality. However, the solution of Cook-Torrance BRDF model based SFS problem has not been properly addressed because the model is very complicated and non-convex. Method:In this paper, we present a shape and depth joint optimization method under the neural network framework to solve this kind of SFS problem. Our method has three aspects of contributions. Firstly, we remove the unrealistic surface smoothness constraint imposed on the solution of SFS. Secondly, the design of shape and depth joint optimization provides the method with a higher probability of bypassing local optimum and finding the global optimum. Thirdly, the neural network framework enables our method with the ability of performing point-wise optimization, that is, the optimization does not subject to the approximation on the discrete domain. Result:Through experiments, we prove that our method can solve Cook-Torrance BRDF model based SFS problem with good accuracy. The maximum Mean Absolute Error, Mean Relative Error and Root-mean-square error of depth results are 0.8 mm, 1.0% and 1.23 mm respectively, which outperforms related methods.

Windowed 4D inversion for near real-time geoelectrical monitoring applications

Many different approaches have been developed to regularise the time-lapse geoelectrical inverse problem. While their advantages and limitations have been demonstrated using synthetic models, there have been few direct comparisons of their performance using field data. We test four time-lapse inversion methods (independent inversion, temporal smoothness-constrained 4D inversion, spatial smoothness constrained inversion of temporal data differences, and sequential inversion with spatial smoothness constraints on the model and its temporal changes). We focus on the applicability of these methods to automated processing of geoelectrical monitoring data in near real-time. In particular, we examine windowed 4D inversion, the use of short sequences of time-lapse data, without which the 4D method would not be suitable in the near real-time context. We develop measures of internal consistency for the different methods so that the effects of the use of short time windows or the choice of baseline data set can be compared. The resulting inverse models are assessed against qualitative and quantitative ground truth information. Our findings are that 4D inversion of the full data set performed best, and that windowed 4D inversion retained the majority of its benefits while also being applicable to applications requiring near real-time inversion.

MMatch: Semi-Supervised Discriminative Representation Learning for Multi-View Classification

Semi-supervised multi-view learning has been an important research topic due to its capability to exploit complementary information from unlabeled multi-view data. This work proposes MMatch, a new semi-supervised discriminative representation learning method for multi-view classification. Unlike existing multi-view representation learning methods that seldom consider the negative impact caused by particular views with unclear classification structures (weak discriminative views). MMatch jointly learns view-specific representations and class probabilities of training data. The representations concatenated to integrate multiple views’ information to form a global representation. Moreover, MMatch performs the smoothness constraint on the class probabilities of the global representation to improve pseudo labels, whereas the pseudo labels regularize the structure of view-specific representations. A discriminative global representation is mined with the training process, and the negative impact of weak discriminative views is overcome. Besides, MMatch learns consistent classification while preserving diverse information from multiple views. Experiments on several multi-view datasets demonstrate the effectiveness of MMatch.

Algebraic methods to study the dimension of supersmooth spline spaces

Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation theory, and computer aided geometric design. In this paper we address various challenges arising in the study of splines with enhanced mixed (super-)smoothness conditions at the vertices and across interior faces of the partition. Such supersmoothness can be imposed but can also appear unexpectedly on certain splines depending on the geometry of the underlying polyhedral partition. Using algebraic tools, a generalization of the Billera–Schenck–Stillman complex that includes the effect of additional smoothness constraints leads to a construction which requires the analysis of ideals generated by products of powers of linear forms in several variables. Specializing to the case of planar triangulations, a combinatorial lower bound on the dimension of splines with supersmoothness at the vertices is presented, and we also show that this lower bound gives the exact dimension in high degree. The methods are further illustrated with several examples.

Evaluation of the 3D Near-Surface Velocity Structure in an Urban Environment from Ambient Noise Array Tomography: The Case of the City of Thessaloniki (Northern Greece)

Abstract We examine the implementation of ambient noise array tomography in an urban environment to assess the 3D near-surface shear wave velocity (VS) structure at an intermediate spatial scale (∼1 km2, depth range 200–300 m). The application employs cross correlation traces of vertical component ambient noise recordings from a local network installed in Thessaloniki city (Northern Greece), allowing the determination of Rayleigh wave travel times for the frequency range of 1.5–14 Hz. The results confirm the presence of a complex subsurface with strong lateral variations in the geology, with travel times varying up to almost one order of magnitude. A surface wave travel time tomography approach was applied for each frequency to determine the spatial variability of the group velocity, involving the use of approximate Fresnel volumes, as well as damping and spatial smoothing constraints to stabilize the results. We also employed an interfrequency smoothing scheme to obtain smooth but data-compatible dispersion curves at the cost of inverting all travel time data simultaneously. Following the application of several quality cutoff criteria, we reconstructed local group slowness dispersion curves for a predefined tomographic grid in the study area. The final 3D velocity model was determined by a modified Monte Carlo inversion of these dispersion curves and the spatial integration of the obtained 1D VS profiles. Different model parameterizations were tested for the inversion to determine the optimal datafit. The final 3D velocity model is in a very good agreement with the local geology, previous larger scale studies, and other geophysical surveys, providing additional structural constraints (such as hidden fault identification) for the complex sedimentary deposits and bedrock formation in Thessaloniki, up to the depth of ∼250–300 m. The introduction of the aforementioned modifications to the ambient noise array tomography suggests that it can be efficiently adjusted and employed as a reliable tool for imaging the 3D seismic structure in urban environments with complex geology.