Representation Coefficients Research Articles

Integrating progressive screening strategy-based continuous wavelet transform with EfficientNetV2 for enhanced near-infrared spectroscopy

Near-infrared (NIR) spectroscopy has gained wide acceptance across various fields as a result of advances in portable equipment that can record spectra on site or at production lines. Continuous wavelet transform (CWT) can transform traditional one-dimensional (1D) NIR spectra into more informative two-dimensional (2D) spectrograms, thus enhancing the analysis and interpretation of spectral information. This study introduces a high-efficiency 2D CWT-EfficientNetV2 regression model to optimize NIR spectroscopy applications. A novel progressive screening strategy is employed to select the optimal wavelet functions and scales for CWT, which are then used to transform the features into wavelet coefficient matrices. Direct digital mapping (DDM) with Gray colormap generates 2D spectrograms from matrices, significantly preserving the representation of wavelet coefficients. The 2D CWT-EfficientNetV2 model was used to predict the content of five polyphenols in tobacco leaf samples with superior performance compared to partial least squares regression (PLSR) and other high-efficiency models. Moreover, to further validate the robustness and reliability of the proposed method, two additional public NIR spectral datasets were included in this study. The model achieves lower root mean square error of prediction (RMSEP), as well as higher coefficient of determination of prediction (RP2) and the ratio of the standard error of prediction to the standard deviation of the reference values (RPD) on the test datasets. These results demonstrate that the 2D CWT-EfficientNetV2 model is a robust and efficient approach for the accurate quantification of various target compounds utilizing NIR spectroscopy.

Analysis for sparse channel representation based on dictionary learning in massive MIMO systems

AbstractThe accuracy analysis of dictionary sparse representation for channels in massive MIMO systems is a relatively unexplored field. Existing research has primarily focused on investigating the accuracy of dictionary sparse representation using simulation in massive MIMO systems, but has not provided quantitative accuracy analysis. To address this gap, the correlation numerical proportional factor is proposed to represent the accuracy performance of non‐zero elements in the coefficient matrix. Additionally, a qualitative analytical formula for dictionary sparse representation accuracy is provided and an optimal upper bound for the correlation numerical proportional factor is established. Furthermore, the innovation indicates that the accuracy of dictionary sparse representation is mainly influenced by the cross‐correlation between the pilots matrix and the dictionary matrix, as well as sparsity. The author has also developed a method for minimizing the correlation numerical proportional factor. In order to obtain an optimal sparse representation coefficient matrix, a cross‐correlation matrix is constructed and an analytical expression is derived for it as well as its use as an optimal hard decision threshold is determined. Finally, a sparse representation coefficient optimization algorithm is proposed using this optimal threshold. Simulation results demonstrate that this algorithm can significantly improve channel sparse dictionary representation accuracy.

Combining Low-Rank and Deep Plug-and-Play Priors for Snapshot Compressive Imaging.

Snapshot compressive imaging (SCI) is a promising technique that captures a 3-D hyperspectral image (HSI) by a 2-D detector in a compressed manner. The ill-posed inverse process of reconstructing the HSI from their corresponding 2-D measurements is challenging. However, current approaches either neglect the underlying characteristics, such as high spectral correlation, or demand abundant training datasets, resulting in an inadequate balance among performance, generalizability, and interpretability. To address these challenges, in this article, we propose a novel approach called LR2DP that integrates the model-driven low-rank prior and data-driven deep priors for SCI reconstruction. This approach not only captures the spectral correlation and deep spatial features of HSI but also takes advantage of both model-based and learning-based methods without requiring any extra training datasets. Specifically, to preserve the strong spectral correlation of the HSI effectively, we propose that the HSI lies in a low-rank subspace, thereby transforming the problem of reconstructing the HSI into estimating the spectral basis and spatial representation coefficient. Inspired by the mutual promotion of unsupervised deep image prior (DIP) and trained deep denoising prior (DDP), we integrate the unsupervised network and pre-trained deep denoiser into the plug-and-play (PnP) regime to estimate the representation coefficient together, aiming to explore the internal target image prior (learned by DIP) and the external training image prior (depicted by pre-trained DDP) of the HSI. An effective half-quadratic splitting (HQS) technique is employed to optimize the proposed HSI reconstruction model. Extensive experiments on both simulated and real datasets demonstrate the superiority of the proposed method over the state-of-the-art approaches.

Improving the sparse coding model via hybrid Gaussian priors

Sparse Coding (SC) imposes a sparse prior on the representation coefficients under a dictionary or a sensing matrix. However, the sparse regularization, approximately expressed as the L1-norm, is not strongly convex. The uniqueness of the optimal solution requires the dictionary to be of low mutual coherence. As a specialized form of SC, Convolutional Sparse Coding (CSC) encounters the same issue. Inspired by the Elastic Net, this paper proposes to learn an additional anisotropic Gaussian prior for the sparse codes, thus improving the convexity of the SC problem and enabling the modeling of feature correlation. As a result, the SC problem is modified by the proposed elastic projection. We thereby analyze the effectiveness of the proposed method under the framework of LISTA and demonstrate that this simple technique has the potential to correct bad codes and reduce the error bound, especially in noisy scenarios. Furthermore, we extend this technique to the CSC model for the vision practice of image denoising. Extensive experimental results show that the learned Gaussian prior significantly improves the performance of both the SC and CSC models. Source codes are available at https://github.com/eeejyang/EPCSCNet.

Eigenimage2Eigenimage (E2E): A Self-Supervised Deep Learning Network for Hyperspectral Image Denoising.

The performance of deep learning-based denoisers highly depends on the quantity and quality of training data. However, paired noisy-clean training images are generally unavailable in hyperspectral remote sensing areas. To solve this problem, this work resorts to the self-supervised learning technique, where our proposed model can train itself to learn one part of noisy input from another part of noisy input. We study a general hyperspectral image (HSI) denoising framework, called Eigenimage2Eigenimage (E2E), which turns the HSI denoising problem into an eigenimage (i.e., the subspace representation coefficients of the HSI) denoising problem and proposes a learning strategy to generate noisy-noisy paired training eigenimages from noisy eigenimages. Consequently, the E2E denoising framework can be trained without clean data and applied to denoise HSIs without the constraint with the number of frequency bands. Experimental results are provided to demonstrate the performance of the proposed method that is better than the other existing deep learning methods for denoising HSIs. A MATLAB demo of this work is available at https://github.com/LinaZhuang/HSI-denoiser-Eigenimage2Eigenimage for the sake of reproducibility.

Construction and non-vanishing of a family of vector-valued Siegel Poincaré series

Using Poincaré series of K-finite matrix coefficients of integrable antiholomorphic discrete series representations of Sp2n(R), we construct a spanning set for the space Sρ(Γ) of Siegel cusp forms of weight ρ for Γ, where ρ is an irreducible polynomial representation of GLn(C) of highest weight ω∈Zn with ω1≥…≥ωn>2n, and Γ is a discrete subgroup of Sp2n(R) commensurable with Sp2n(Z). Moreover, using a variant of Muić's integral non-vanishing criterion for Poincaré series on unimodular locally compact Hausdorff groups, we prove a result on the non-vanishing of constructed Siegel Poincaré series.

Bearing fault diagnosis by sparse frequency spiral spectrum driven NAF-LDM under strong noise and small samples

Abstract The complexity of background noise and the scarcity of real fault samples seriously affect the diagnostic accuracy of the model. To address this, a noise-robust two-dimensional feature map, the sparse frequency spiral spectrum (SFSM), based on sparse representation theory, is proposed. A bridge penalty coefficient is applied to the sparse representation model to accurately select impact components, and the fast iterative shrinkage threshold algorithm is used to solve for sparse representation coefficients. Sparse reconstructed signals are obtained by convolving the impact patterns with these coefficients, leading to a sparse reconstruction algorithm with reduced computational complexity. Furthermore, the novel non-linear activation-free blocks (NAF Blocks) are embedded into the latent diffusion model to augment small samples, significantly improving image generation speed and quality. The integration of the Swin transformer for feature extraction and classification further enhances diagnostic performance. The superiority of this method is validated on the XJTU-SY dataset, a bearing experimental platform dataset, and enterprise engineering dataset. Experimental results demonstrate that the structural and generalization advantages of NAF Blocks are crucial for improving image quality and inference speed. The noise suppression capability of the proposed method, facilitated by the SFSM feature processing technique, is confirmed through ablation and noise robustness tests. Finally, the Swin transformer’s excellent feature extraction and classification capabilities for SFSM are verified. The proposed method achieves diagnostic accuracies of 99.10% and 98.7% on the XJTU-SY and experimental platform datasets, respectively.

Beyond the root: Geometric characterization for the diagnosis of syndromic heritable thoracic aortic diseases

Syndromic heritable thoracic aortic diseases (sHTAD), such as Marfan (MFS) or Loeys–Dietz (LDS) syndromes, involve high risk of life threatening aortic events. Diagnosis of syndromic features alone is difficult, and negative genetic tests do not necessarily exclude a genetic or hereditary condition. Periodic 3D imaging of the aorta is recommended in patients with aortic disease. Thus, an imaging-based approach aimed at identifying unique features of aortic geometry can be highly effective for diagnosing sHTAD and assessing risk. In this study, we present a method that can help identify the manifestations of sHTAD by focusing on the entire geometry of the thoracic aorta, rather than only using measurements of dilation of the aortic root. We analyze the geometric phenotype of 97 patients with genetically confirmed sHTAD (79 MF and 18 LDS) and of 45 healthy volunteers, using 3D aorta meshes obtained from phase contrast-enhanced magnetic resonance angiograms computed from 4D flow cardiac magnetic resonance. We build a geometric encoding of the aorta, based on a vessel coordinate system, and use several mathematical models to discriminate between controls and patients with sHTAD: a baseline scenario, based on aortic root dimensions only, a descriptor typically used in sHTAD patients; a low dimensional scenario, with a reduce encoding using principal component analysis; and a high-dimensional scenario, which included the full coefficient representation for geometry encoding, aiming to capture finer geometric details. The results indicate that considering the anatomy of the whole thoracic aorta can improve predictive ability. We achieve precision and sensitivity values over 0.8, with a specificity of over 70% in all the models used, while a single value classifiers (based only on aortic root diameter) demonstrated a trade-off between sensitivity and specificity. Using the mathematical properties of the vessel coordinate system representation, feature importance is mapped onto a set of anatomical traits that are used by the models to do the classification, thus providing interpretability of the results. This analysis indicates that in addition to the diameter of the aortic root, aortic elongation and a narrowing of the descending thoracic aorta may be markers of positive sHTAD.

A clustered federated learning framework for collaborative fault diagnosis of wind turbines

Data-driven approaches demonstrate significant potential in accurately diagnosing faults in wind turbines. To enhance diagnostic performance and reduce communication costs in federated learning with data heterogeneity among different clients, we introduce a clustered federated learning framework to wind turbine fault diagnosis. Initially, a lightweight multiscale separable residual network (LMSRN) model is proposed for each local client. The LMSRN model integrates a multiscale spatial feature derivation unit and a depthwise separable feature extraction unit. Subsequently, to tackle data heterogeneity among clients, canonical correlation coefficients of representations are extracted from the intermediate layers of local LMSRN models, and a representational canonical correlation clustering (RCCC) method is proposed to assess the similarity of local LMSRN models and group them into clusters. Finally, a global model is trained for each cluster. Real-world wind turbine data experiments showcase the superior performance of the proposed clustered federated learning framework over traditional methods in terms of diagnostic accuracy and computational speed. Additionally, the optimal choice of the number of clusters is also discussed.

Fekete-Szegö and Hankel inequalities related to the sine function

ABSTRACT The Fekete-Szegö inequality is one of the inequalities for the coefficients which associated with the famous Bieberbach conjecture. Other issues associated with this inequality are determining the Hankel determinant denoted as Hd inequalities which are involved in the study of the singularities and integral coefficients in the Taylor series representations. In this investigation, we discuss such inequalities for certain mappings g for which ( g ′ ( z ) ) α [ 2 z g ′ ( z ) g ( z ) − g ( − z ) ] ( 1 − α ) ≺ 1 + sin ⁡ z , ( 0 ≤ α ≤ 1 ) lies in the image domain starlike about 1 and symmetric about real axis. Particularly, we obtain certain inequality for functions involving Poisson distribution. Furthermore, we also find the second Hankel determinant and other inequalities related to this newly defined class.

Trapped acoustic waves and raindrops: High-order accurate integral equation method for localized excitation of a periodic staircase

We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We apply it to the accurate numerical study of acoustic radiation in the neighborhood of a sound-hard two-dimensional staircase modeled after the El Castillo pyramid. Such staircases support trapped waves which travel along the surface and decay exponentially away from it. We use the array scanning method (Floquet–Bloch transform) to recover the scattered field as an integral over the family of quasiperiodic solutions parameterized by on-surface wavenumber. Each such BIE solution requires the quasiperiodic Green's function, which we evaluate using an efficient integral representation of lattice sum coefficients. We avoid the singularities and branch cuts present in the array scanning integral by complex contour deformation. For each frequency, this enables a solution accurate to around 10 digits in a few seconds. We propose a residue method to extract the limiting powers carried by trapped modes far from the source. Finally, by computing the trapped mode dispersion relation, we use a simple ray model to explain an acoustic chirp-like time-domain response that is referred to in the literature as the “raindrop effect.”

Three-phase-lag analysis of transversely isotropic double porous thermoelastic waves with liquid medium

This manuscript presents a mathematical framework for a double porous, thermoelastic solid half-space with transverse isotropy in contact with an inviscid liquid half-space. The analysis takes into account the three-phase-lag model within thermoelasticity theory. To gain deeper insights, we formulate the governing equations in a two-dimensional representation and subsequently employ normal mode analysis for their rigorous solution. The governing equations are influenced by both types of voids, anisotropy, thermal effect, and inviscid liquid. It has been discovered that thermoelastic half-space exhibits five coupled longitudinal waves, and in the liquid half-space, there is one mechanical wave. Secular equations are obtained by using thermal and mechanical conditions, resulting in a compact representation of phase velocity, specific loss, penetrating depth, and attenuation coefficient. Analytical presentations have been made to showcase the effects of anisotropy, voids, and liquid on various wave parameters. These effects are compared by illustrating the results graphically using the MATLAB software, allowing for a visual understanding of the comparative outcomes. This study has practical applications in engineering, materials science, geophysics, and environmental studies, contributing to advancements in various industries and scientific fields.

Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension

We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients, refining methods used in (J. Differential Equations 137(2) (1997) 251–272) and (J. Funct. Anal. 178(2) (2000) 396–420).

Comparative Studies on the Radiative Heat Transfer in Arc Plasma and Its Impact in a Model of a Free-Burning Arc

The radiative heat transfer in arc plasma models is considered from the point of view of its description in terms of a net emission coefficient, the method of spherical harmonics in its lowest order, and the discrete ordinate method. Net emission coefficients are computed, applying approximate analytical and numerical approaches and a multi-band representation of the spectral absorption coefficient with three kinds of its averaging and two datasets. Self-consistent access to the radiative heat transfer is applied to a two-dimensional axisymmetric model of a free-burning arc in argon at atmospheric pressure. The results obtained from the models employing the net emission coefficient, the method of spherical harmonics, and the discrete ordinate method are compared.

Functional Bethe Ansatz for a sinh-Gordon Model with Real q

Recently, Bazhanov and Sergeev have described an Ising-type integrable model which can be identified as a sinh-Gordon-type model with an infinite number of states but with a real parameter q. This model is the subject of Sklyanin’s Functional Bethe Ansatz. We develop in this paper the whole technique of the FBA which includes: (1) Construction of eigenstates of an off-diagonal element of a monodromy matrix. The most important ingredients of these eigenstates are the Clebsh-Gordan coefficients of the corresponding representation. (2) Separately, we discuss the Clebsh-Gordan coefficients, as well as the Wigner’s 6j symbols, in details. The later are rather well known in the theory of 3D indices. Thus, the Sklyanin basis of the quantum separation of variables is constructed. The matrix elements of an eigenstate of the auxiliary transfer matrix in this basis are products of functions satisfying the Baxter equation. Such functions are called usually the Q-operators. We investigate the Baxter equation and Q-operators from two points of view. (3) In the model considered the most convenient Bethe-type variables are the zeros of a Wronskian of two well defined particular solutions of the Baxter equation. This approach works perfectly in the thermodynamic limit. We calculate the distribution of these roots in the thermodynamic limit, and so we reproduce in this way the partition function of the model. (4) The real parameter q, which is the standard quantum group parameter, plays the role of the absolute temperature in the model considered. Expansion with respect to q (tropical expansion) gives an alternative way to establish the structure of the eigenstates. In this way we classify the elementary excitations over the ground state.

On the coefficients of automorphic representations over polynomials

On the coefficients of automorphic representations over polynomials

Non-negative consistency affinity graph learning for unsupervised feature selection and clustering

Feature selection plays a crucial role in data mining and pattern recognition tasks. This paper proposes an efficient method for robust unsupervised feature selection, called joint local preserving and low-rank representation with nonnegative and symmetric constraint (JLPLRNS). This approach utilizes an indicator matrix instead of the row sparsity of the projection matrix to directly select some significant features from the original data and adaptively preserves the local geometric structure of original data into the low-dimensional embedded feature subspace via learned indicator matrix. By simultaneously imposing nonnegative symmetric and low-rank constraints on the representation coefficient matrix, it cannot only make this matrix discriminative, sparse and weight consistency for each pair of data, but also uncover the global structure of original data. These effectively will improve clustering performance. An algorithm based on the augmented Lagrange multiplier method with an alternating direction strategy is designed to resolve this model. Experimental results on various real datasets show that the proposed method can effectively identify some important features in data and outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering performance.

On the resonance frequency of the irregular shaped visco-acoustic Helmholtz cavity problem

In this paper we develop a closed-form mathematical solution for the resonance frequency of the axisymmetric irregular shaped visco-acoustic Helmholtz cavity problem. The solution is based on a conformal mapping that transforms the governing visco-acoustic equations of motion for the irregular cavity geometry into a new domain described by a set of orthogonal curvilinear coordinates. These orthogonal curvilinear coordinates have an important characteristic relative to the transformation of the physical boundary: the mapped domain is constructed such that the locus of all points for the length-wise profile of the physical boundary coincides with a constant value for a (quasi radial) coordinate in the new mapped domain. In these orthogonal curvilinear coordinates we obtain an analytical solution for the visco-acoustic equations of motion and exactly satisfy the no-slip fluid boundary conditions over the irregular shaped cavity walls by matching the coefficients of an orthogonal Legendre polynomial series representation for the non-uniform velocity on the cavity walls. The mathematical solution is an approximation to the extent that the scale factors chosen for the mapping consist of strictly the mutual-coupling terms of the true scale factors. Thus we analyze some results to understand the correlation of the analytical solution frequency response spectra with numerical finite element analyses of the idealized boundary conditions with various irregular shaped cavity geometries. The results for fundamental resonance frequency were found to exhibit good correlation with the results of finite element analyses over a significant range of fluid properties with different irregular cavity geometries. As the primary motivation for the derivation stems from the lack of a rapid yet accurate alternative to computationally intensive MultiPhysics FEA in the formulation of acoustic trendlines for sensor development, the solution’s acoustic impedance was applied as dispersive loading in a simple lumped parameter model of a fluid identification sensor for comparison. The resulting acoustic trendlines of the reduced (5 DOF) model were found to exhibit good correlation with the results of the MultiPhysics FEA (>105 DOF). Thus the solution was found to enable a closed-form analytical method for rapid construction of parametric studies in the practical design of fluid analysis sensors based on complex resonant cavity geometries.

On linear combinations of binomial OWA functions

We consider the binomial decomposition of ordered weighted averaging (OWA) functions proposed by Calvo and De Baets (1998) in the framework of Choquet integration. Our aim in the paper is to further investigate the equivalence between the two representations of OWA functions involved in the binomial decomposition: the usual canonical representation in terms of the order statistics, and the binomial representation in terms of the binomial OWA functions. We describe and discuss in detail the linear transformations that relate the coefficients of these two equivalent representations: the original expression of the weights in terms of the coefficients of the binomial representation, and its inverse, the expression of those coefficients in terms of the weights. In both cases simple and direct proofs are presented. Moreover, we consider the linear transformations between the two representations in the general linear algebra framework of unconstrained linear combinations of binomial OWA functions. In this perspective we obtain compact matrix expressions for the linear transformations, which also offer new insight on the geometry of the coefficient constraints in the binomial representation of OWA functions.

Robust sparse representation based on fitting error decomposition

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.