Search Results (25)

Joint inversion of gravity and gravity gradient data are of paramount importance in geophysical exploration, as the integration of these datasets enhances subsurface resolution and facilitates the accurate delineation of ore body shapes and boundaries. Conventional regularization methods, such as the L₂-norm, frequently yield excessively smooth solutions, which complicates the recovery of sharp boundaries. Furthermore, disparities in data units, magnitudes, and noise levels introduce additional complexities in selecting appropriate weighting functions and inversion parameters. To address these challenges, this study proposes a greedy inversion method based on cosine similarity, which identifies the most relevant cells and reduces the complexity involved in data weighting and parameter selection. Additionally, it incorporates prior information on density limits to achieve a high-resolution and sparse solution. To further enhance the stability and accuracy of the inversion process, a pruning mechanism is introduced to dynamically detect and remove erroneously selected cells, thereby suppressing error propagation. Synthetic model experiments demonstrate that incorporating the pruning mechanism significantly improves inversion accuracy. The method not only accurately resolves models of varying volumes while avoiding local convergence issues in the presence of major anomalies, but also exhibits strong robustness against noise, successfully delineating clear boundaries even when applied to complex composite models contaminated with 10% Gaussian noise. Finally, when applied to the joint inversion of measured gravity and gravity gradient tensor data from the Vinton salt dome, the results closely align with previous studies and actual geological observations. Full article

Compared to conventional single-aperture infrared cameras, the bio-inspired infrared compound eye camera integrates the advantages of infrared imaging technology with the benefits of multi-aperture systems, enabling simultaneous information acquisition from multiple perspectives. This enhanced detection capability demonstrates unique performance in applications such as autonomous driving, surveillance, and unmanned aerial vehicle reconnaissance. Current single-aperture small target detection algorithms fail to exploit the spatial relationships among compound eye apertures, thereby underutilizing the inherent advantages of compound eye imaging systems. This paper proposes a low-rank and sparse decomposition method based on bio-inspired infrared compound eye image features for small target detection. Initially, a compound eye structural weighting operator is designed according to image characteristics, which enhances the sparsity of target points when combined with the reweighted $l_1$-norm. Furthermore, to improve detection speed, the structural tensor of the effective imaging region in infrared compound eye images is reconstructed, and the Representative Coefficient Total Variation method is employed to avoid complex singular value decomposition and regularization optimization computations. Our model is efficiently solved using the Alternating Direction Method of Multipliers (ADMM). Experimental results demonstrate that the proposed model can rapidly and accurately detect small infrared targets in bio-inspired compound eye image sequences, outperforming other comparative algorithms. Full article

Accurate and efficient white-spot defects detection for the surface of galvanized strip steel is one of the most important guarantees for the quality of steel production. It is a fundamental but “hard” small target detection problem due to its small pixel occupation in low-contrast images. By fully exploiting the low-rank and sparse prior information of a surface defect image, a Schatten-p norm-based low-rank tensor decomposition (SLRTD) method is proposed to decompose the defect image into low-rank background, sparse defect, and random noise. Firstly, the original defect images are transformed into a new patch-based tensor mode through data reconstruction for mining valuable information of the defect image. Then, considering the over-shrinkage problem in the low-rank component estimation caused by a vanilla nuclear norm and a weighted nuclear norm, a nonlinear reweighting strategy based on a Schatten $p$-norm is incorporated to improve the decomposition performance. Finally, a solution framework is proposed via a well-designed alternating direction method of multipliers to obtain the white-spot defect target image by a simple segmenting algorithm. The white-spot defect dataset from a real-world galvanized strip steel production line is constructed, and the experimental results demonstrate that the proposed SLRTD method outperforms existing state-of-the-art methods qualitatively and quantitatively. Full article

Temporal random noise (TRN) in uncooled infrared detectors significantly degrades image quality. Existing denoising techniques primarily address fixed-pattern noise (FPN) and do not effectively mitigate TRN. Therefore, a novel TRN denoising approach based on total variation regularization and low-rank tensor decomposition is proposed. This method effectively suppresses temporal noise by introducing twisted tensors in both horizontal and vertical directions while preserving spatial information in diverse orientations to protect image details and textures. Additionally, the Laplacian operator-based bidirectional twisted tensor truncated nuclear norm (bt-LPTNN), is proposed, which is a norm that automatically assigns weights to different singular values based on their importance. Furthermore, a weighted spatiotemporal total variation regularization method for nonconvex tensor approximation is employed to preserve scene details. To recover spatial domain information lost during tensor estimation, robust principal component analysis is employed, and spatial information is extracted from the noise tensor. The proposed model, bt-LPTVTD, is solved using an augmented Lagrange multiplier algorithm, which outperforms several state-of-the-art algorithms. Compared to some of the latest algorithms, bt-LPTVTD demonstrates improvements across all evaluation metrics. Extensive experiments conducted using complex scenes underscore the strong adaptability and robustness of our algorithm. Full article

Seismic data are easily contaminated by random noise, impairing subsequent geological interpretation tasks. Existing denoising methods like low-rank approximation (LRA) and deep learning (DL) show promising denoising capabilities but still have limitations; for instance, LRA performance is parameter-sensitive, and DL networks lack interpretation. As an alternative, this paper introduces the low-rank tensor network (LRTNet), an innovative approach that integrates low-rank tensor approximation (LRTA) with DL. Our method involves constructing a noise attenuation model that leverages LRTA, total variation (TV) regularization, and weighted tensor nuclear norm minimization (WTNNM). By applying the alternating direction method of multipliers (ADMM), we solve the model and transform the iterative schemes into a DL framework, where each iteration corresponds to a network layer. The key learnable parameters, including weights and thresholds, are optimized using labeled data to enhance performance. Quantitative evaluations on synthetic data reveal that LRTNet achieves an average signal-to-noise ratio (SNR) of 9.37 dB on the validation set, outperforming Pyseistr (6.46 dB) and TNN-SSTV (6.10 dB) by 45.0% and 53.6%, respectively. Furthermore, tests on real field datasets demonstrate consistent enhancements in noise suppression while preserving critical stratigraphic structures and fault discontinuities. The embedded LRTA mechanism not only improves network interpretability, but also reduces parameter sensitivity compared to conventional LRA methods. These findings position LRTNet as a robust, physics-aware solution for seismic data restoration. Full article

Purpose: Accurate and precise navigation in space and postural stability rely on the central integration of multisensory input (vestibular, proprioceptive, visual), weighted according to its reliability, to continuously update the internal estimate of the direction of gravity. In this study, we examined both peripheral and central vestibular functions in a world-renowned 53-year-old male tightrope walker and investigated the extent to which his exceptional performance was reflected in our findings. Methods: Comprehensive assessments were conducted, including semicircular canal function tests (caloric irrigation, rotatory-chair testing, video head impulse testing of all six canals, dynamic visual acuity) and otolith function evaluations (subjective visual vertical, fundus photography, ocular/cervical vestibular-evoked myogenic potentials [oVEMPs/cVEMPs]). Additionally, static and dynamic posturography, as well as video-oculography (smooth-pursuit eye movements, saccades, nystagmus testing), were performed. The participant’s results were compared to established normative values. High-resolution diffusion tensor magnetic resonance imaging (DT-MRI) was utilized to assess motor tract integrity. Results: Semicircular canal testing revealed normal results except for a slightly reduced response to right-sided caloric irrigation (26% asymmetry ratio; cut-off = 25%). Otolith testing, however, showed marked asymmetry in oVEMP amplitudes, confirmed with two devices (37% and 53% weaker on the left side; cut-off = 30%). Bone-conducted cVEMP amplitudes were mildly reduced bilaterally. Posturography, video-oculography, and subjective visual vertical testing were all within normal ranges. Diffusion tensor MRI revealed no structural abnormalities correlating with the observed functional asymmetry. Conclusions: This professional tightrope walker’s exceptional balance skills contrast starkly with significant peripheral vestibular (otolithic) deficits, while MR imaging, including diffusion tensor imaging, remained normal. These findings highlight the critical role of central computational mechanisms in optimizing multisensory input signals and fully compensating for vestibular asymmetries in this unique case. Full article

Anomaly detection (AD) is an important topic in remote sensing, aiming to identify unusual or abnormal features within the data. However, most existing low-rank representation methods usually use the nuclear norm for background estimation, and do not consider the different contributions of different singular values. Besides, they overlook the spatial relationships of abnormal regions, particularly failing to fully leverage the 3D structured information of the data. Moreover, noise in practical scenarios can disrupt the low-rank structure of the background, making it challenging to separate anomaly from the background and ultimately reducing detection accuracy. To address these challenges, this paper proposes a weighted multidirectional sparsity regularized low-rank tensor representation method (WMS-LRTR) for AD. WMS-LRTR uses the weighted tensor nuclear norm for background estimation to characterize the low-rank property of the background. Considering the correlation between abnormal pixels across different dimensions, the proposed method introduces a novel weighted multidirectional sparsity (WMS) by unfolding anomaly into multimodal to better exploit the sparsity of the anomaly. In order to improve the robustness of AD, we further embed a user-friendly plug-and-play (PnP) denoising prior to optimize the background modeling under low-rank structure and facilitate the separation of sparse anomalous regions. Furthermore, an effective iterative algorithm using alternate direction method of multipliers (ADMM) is introduced, whose subproblems can be solved quickly by fast solvers or have closed-form solutions. Numerical experiments on various datasets show that WMS-LRTR outperforms state-of-the-art AD methods, demonstrating its better detection ability. Full article

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space (${\mathcal{l}}^{\mathtt{q}(·)}\left({\mathtt{L}}^{\mathtt{p}(·)}\right)$). Moreover, it was developed using classical Lebesgue space (${\mathtt{L}}_{\mathtt{p}}$) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. Full article

Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the ${\ell }_{2,1}$ norm to depict the sparsity of the error matrix, and they usually ignore the global structure embedded in each single view, compromising the clustering performance. Here, we design a robust tensor learning method for multi-view spectral clustering (RTL-MSC), which employs the weighted tensor nuclear norm to regularize the essential tensor for exploiting the high-order correlations underlying multiple views and adopts the nuclear norm to constrain each frontal slice of the essential tensor as the block diagonal matrix. Simultaneously, a novel column-wise sparse norm, namely, ${\ell }_{2,p}$, is defined in RTL-MSC to measure the error tensor, making it sparser than the one derived by the ${\ell }_{2,1}$ norm. We design an effective optimization algorithm to solve the proposed model. Experiments on three widely used datasets demonstrate the superiority of our method. Full article

Discrete spectral clustering directly obtains the discrete labels of data, but existing clustering methods assume that the real-valued indicator matrices of different views are identical, which is unreasonable in practical applications. Moreover, they do not effectively exploit the spatial structure and complementary information embedded in views. To overcome this disadvantage, we propose a tensorized discrete multi-view spectral clustering model that integrates spectral embedding and spectral rotation into a unified framework. Specifically, we leverage the weighted tensor nuclear-norm regularizer on the third-order tensor, which consists of the real-valued indicator matrices of views, to exploit the complementary information embedded in the indicator matrices of different views. Furthermore, we present an adaptively weighted scheme that takes into account the relationship between views for clustering. Finally, discrete labels are obtained by spectral rotation. Experiments show the effectiveness of our proposed method. Full article

Hyperspectral anomaly detection is an important unsupervised binary classification problem that aims to effectively distinguish between background and anomalies in hyperspectral images (HSIs). In recent years, methods based on low-rank tensor representations have been proposed to decompose HSIs into low-rank background and sparse anomaly tensors. However, current methods neglect the low-rank information in the spatial dimension and rely heavily on the background information contained in the dictionary. Furthermore, these algorithms show limited robustness when the dictionary information is missing or corrupted by high level noise. To address these problems, we propose a novel method called multi-dimensional low-rank (MDLR) for HSI anomaly detection. It first reconstructs three background tensors separately from three directional slices of the background tensor. Then, weighted schatten p-norm minimization is employed to enforce the low-rank constraint on the background tensor, and $L_{F,1}$-norm regularization is used to describe the sparsity in the anomaly tensor. Finally, a well-designed alternating direction method of multipliers (ADMM) is employed to effectively solve the optimization problem. Extensive experiments on four real-world datasets show that our approach outperforms existing anomaly detection methods in terms of accuracy. Full article

Graph-based semi-supervised multi-view clustering has demonstrated promising performance and gained significant attention due to its capability to handle sample spaces with arbitrary shapes. Nevertheless, the ordinary graph employed by most existing semi-supervised multi-view clustering methods only captures the pairwise relationships between samples, and cannot fully explore the higher-order information and complex structure among multiple sample points. Additionally, most existing methods do not make full use of the complementary information and spatial structure contained in multi-view data, which is crucial to clustering results. We propose a novel hypergraph learning-based semi-supervised multi-view spectral clustering approach to overcome these limitations. Specifically, the proposed method fully considers the relationship between multiple sample points and utilizes hypergraph-induced hyper-Laplacian matrices to preserve the high-order geometrical structure in data. Based on the principle of complementarity and consistency between views, this method simultaneously learns indicator matrices of all views and harnesses the tensor Schatten p-norm to extract both complementary information and low-rank spatial structure within these views. Furthermore, we introduce an auto-weighted strategy to address the discrepancy between singular values, enhancing the robustness and stability of the algorithm. Detailed experimental results on various datasets demonstrate that our approach surpasses existing state-of-the-art semi-supervised multi-view clustering methods. Full article

Methods for detecting small infrared targets in complex scenes are widely utilized across various domains. Traditional methods have drawbacks such as a poor clutter suppression ability and a high number of edge residuals in the detection results in complex scenes. To address these issues, we propose a method based on a joint new norm and self-attention mechanism of low-rank sparse inversion. Firstly, we propose a new tensor nuclear norm based on linear transformation, which globally constrains the low-rank characteristics of the image background and makes full use of the structural information among tensor slices to better approximate the rank of the non-convex tensor, thus achieving effective background suppression. Secondly, we construct a self-attention mechanism in order to constrain the sparse characteristics of the target, which further eliminates any edge residuals in the detection results by transforming the local feature information into a weight matrix to further constrain the target component. Finally, we use the alternating direction multiplier method to decompose the newly reconstructed objective function and introduce a reweighted strategy to accelerate the convergence speed of the model. The average values of the three evaluation metrics, SSIM, BSF, and SNR, for the algorithm proposed in this paper are 0.9997, 467.23, and 11.72, respectively. Meanwhile, the proposed detection method obtains a higher detection rate compared with other algorithms under the same false alarm rate. Full article

Infrared maritime target detection is a key technology in the field of maritime search and rescue, which usually requires high detection accuracy. Despite the promising progress of principal component analysis methods, it is still challenging to detect small targets of unknown polarity (bright or dark) with strong edge interference. Using the partial sum of tubal nuclear norm to estimate low-rank background components and weighted $l_1$ norm to estimate sparse components is an effective method for target extraction. In order to suppress the strong edge interference, considering that the uniformity of the target scattering field is significantly higher than that of the background scattering field in the eigenvalue of the structure tensor, a prior weight based on the multidirectional uniformity of structure tensor eigenvalue was proposed and applied to the optimization model. In order to detect targets with unknown polarity, the images with opposite polarity were substituted into the optimization model, respectively, and the sparse-weight similarity is used to judge the polarity of the target. In order to make the method more efficient, the polarity judgment is made in the second iteration, and then, the false iteration will stop. The proposed method is compared with nine advanced baseline methods on 14 datasets and shows significant strong robustness, which is beneficial to engineering applications. Full article

In this paper, we proposed an image inpainting algorithm, including an interpolation step and a non-local tensor completion step based on a weighted tensor nuclear norm. Specifically, the proposed algorithm adopts the triangular based linear interpolation algorithm firstly to preform the observation image. Second, we extract the non-local similar patches in the image using the patch match algorithm and rearrange them to a similar tensor. Then, we use the tensor completion algorithm based on the weighted tensor nuclear norm to recover the similar tensors. Finally, we regroup all these recovered tensors to obtain the final recovered image. From the image inpainting experiments on color RGB images, we can see that the performance of the proposed algorithm on the peak signal-to-noise ratio (PSNR) and the relative standard error (RSE) are significantly better than other image inpainting methods. Full article