Sparse Basis Research Articles

Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring

Structural health monitoring (SHM) data have a large volume, increasing the cost of data storage and transmission and the difficulties of structural parameter identification. The compressed sensing (CS) theory provides a signal acquisition and analysis strategy. Signal reconstruction using limited measurements and CS has attracted significant interest. However, the dynamic responses obtained from civil engineering structures contain noise, resulting in sparse samples and reducing the signal reconstruction accuracy. Therefore, we propose an optimization algorithm for the measurement matrix integrating the Karhunen-Loeve transform (KLT) and approximate QR decomposition (KLT-QR) to improve the accuracy of dynamic response reconstruction of SHM data. The KLT reduces the correlation between the measurement matrix and the sparse basis. The approximate QR decomposition is used to improve the independence between the column vectors of the measurement matrix, optimizing the measurement matrix. The experimental results for a laboratory steel beam indicate that the proposed KLT-QR algorithm outperforms three other algorithms regarding the accuracy of dynamic response reconstruction (acceleration, displacement, and strain), especially at high compression ratios. The acceleration responses from the Ji’an Bridge are utilized to verify the advantages of the proposed algorithm. The results demonstrate that the KLT-QR algorithm has the highest accuracy of reconstructing the vibration signals and yields better Fourier spectra than the conventional Gaussian measurement matrix.

Separation of overlapping non-stationary signals and compressive sensing-based reconstruction using instantaneous frequency estimation

Compressive sensing uses an incomplete sample set to consider signal reconstruction with sparse basis representations over a specific transform domain. This work examines the difficulties encountered in various signal processing applications, such as data overlap with the target signal in time and frequency domains. The conventional filtering and windowing processes fail to promote better results in recovering the desired signal. The non-stationary signal with time-frequency representations is highly significant for certain valuable applications. An efficient signal separation and reconstruction method based on instantaneous frequency estimate is proposed to improve the non-stationary signal outcome. The proposed research includes speech signal data acquisition, signal component decomposition, instantaneous frequency estimation, overlapped signal separation, and reconstruction. Two datasets, Dacon Overlapped Speech and LJ Speech Dataset, are utilized to generate a new overlapped signal dataset. Initially, the generated speech signals are collected and decomposed into several monocomponents using Synchrosqueezing Wavelet Transform (SynWav), Renyi's quadratic entropy (RQuad), Narrow bandpass filtering (NBand) and single frequency filtering (SFreq). The instantaneous frequencies are estimated using the Hilbert-Huang transform (HilHuT) to generate a time-frequency representation of multi-component signals. The overlapped signals are separated and reconstructed to a desired signal using a Compressive sensing-based Discrete Cosine transform with amended intrinsic chirp separation (CDcT_AIChirS). The proposed model is simulated using PYTHON to examine the performances. In comparison, the mean square error is calculated to be 2.71, the root mean square error is calculated to be 1.64, and the signal to noise ratio is calculated to be 32dB.

Get by how much you pay: A novel data pricing scheme for data trading

As a crucial step in promoting data sharing, data trading can stimulate the development of the data economy. However, the current data trading market primarily focuses on satisfying data owners' interests, overlooking the demands of data requesters. Ignoring the demands of data requesters may lead to a loss of market competitiveness, customer loss, and missed business opportunities while damaging reputation and innovation capabilities. Therefore, in this paper, we introduce a novel pricing mechanism named Get By How Much You Pay (GHMP) based on compressed sensing technology and game theory to address pricing problems according to data requesters' demands. This scheme employs a dictionary matrix as the sparse basis matrix in compressed sensing. The quality of this matrix directly affects the precision with which the requester can reconstruct the data. If the requester requires higher-precision data, the corresponding payment will also increase accordingly so as to realize the pricing method based on the requester's demands. A game pricing method is proposed to address the final pricing and purchasing issues between the data requester and the data owner by utilizing an authorized smart contract as an intermediary. As an entity participating in the game, the smart contract can only receive a higher transaction fee if it successfully assists the data requester and data owner in completing the pricing. Therefore, it strives to establish more reasonable prices for both parties during the trading process to obtain profits. The experimental results demonstrate that this game-based approach assists the data requester and owner in achieving optimal data pricing, thereby satisfying the maximization of interests for both parties.

Bases for optimising stabiliser decompositions of quantum states

Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers. We introduce and study the vector space of linear dependencies of n-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in n. We construct elegant bases of linear dependencies of constant size three. Critically, our sparse bases can be computed without first compiling a dictionary of all n-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

Symmetry, gauge freedoms, and the interpretability of sequence-function relationships.

Quantitative models that describe how biological sequences encode functional activities are ubiquitous in modern biology. One important aspect of these models is that they commonly exhibit gauge freedoms, i.e., directions in parameter space that do not affect model predictions. In physics, gauge freedoms arise when physical theories are formulated in ways that respect fundamental symmetries. However, the connections that gauge freedoms in models of sequence-function relationships have to the symmetries of sequence space have yet to be systematically studied. Here we study the gauge freedoms of models that respect a specific symmetry of sequence space: the group of position-specific character permutations. We find that gauge freedoms arise when model parameters transform under redundant irreducible matrix representations of this group. Based on this finding, we describe an "embedding distillation" procedure that enables analytic calculation of the number of independent gauge freedoms, as well as efficient computation of a sparse basis for the space of gauge freedoms. We also study how parameter transformation behavior affects parameter interpretability. We find that in many (and possibly all) nontrivial models, the ability to interpret individual model parameters as quantifying intrinsic allelic effects requires that gauge freedoms be present. This finding establishes an incompatibility between two distinct notions of parameter interpretability. Our work thus advances the understanding of symmetries, gauge freedoms, and parameter interpretability in sequence-function relationships.

Surface velocity reconstruction of a vibrating structure based on dictionary learning and sparse sampling

The sparse regularization has been successfully applied to near-field acoustic holography to provide the reconstruction accuracy of sound field with limited number of measurements. However, most of the applications are concentrated on the reconstruction of the sound pressure and the corresponding sparse bases are designed for the sound pressure. In this study, dictionary learning is introduced and K-SVD is utilized to generate a sparse basis for the velocity. Then the reconstruction of surface velocity of a vibrating structure can be realized in a sparse framework to improve the reconstruction accuracy with limited number of measurements. In the process of data sample selection, the equivalent source method is used to generate the velocity samples according to the feature of the sound field and samples can be obtained by numerical simulations. The results of numerical simulations and experiment demonstrate the validity of the learned dictionary and the advantage of the proposed method.

Transient Interference Excision and Spectrum Reconstruction with Partial Samples Using Modified Alternating Direction Method of Multipliers-Net for the Over-the-Horizon Radar.

Transient interference often submerges the actual targets when employing over-the-horizon radar (OTHR) to detect targets. In addition, modern OTHR needs to carry out multi-target detection from sea to air, resulting in the sparse sampling of echo data. The sparse OTHR signal will raise serious grating lobes using conventional methods and thus degrade target detection performance. This article proposes a modified Alternating Direction Method of Multipliers (ADMM)-Net to reconstruct the target and clutter spectrum of sparse OTHR signals so that target detection can be performed normally. Firstly, transient interferences are identified based on the sparse basis representation and then excised. Therefore, the processed signal can be seen as a sparse OTHR signal. By solving the Doppler sparsity-constrained optimization with the trained network, the complete Doppler spectrum is reconstructed effectively for target detection. Compared with traditional sparse solution methods, the presented approach can balance the efficiency and accuracy of OTHR signal spectrum reconstruction. Both simulation and real-measured OTHR data proved the proposed approach's performance.

CARE: Large Precision Matrix Estimation for Compositional Data

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Digital Pathology Image Reconstruction with Alternating Direction Method of Multipliers using Wavelet, Contourlet and Shearlet Transforms

Digital pathology refers to image-based environment in which acquisition, extraction and interpretation of pathology information is supported by computational techniques. It has a huge potential to facilitate the diagnostic process, however, big data size and necessity of large storage areas are challenging. Therefore, in this research, Compressed Sensing (CS) scheme is studied with digital pathology images in order to reduce the amount of data for reconstruction. CS requires the sparsity of signals for a successful recovery which means that different sparsifying bases can alter the final performance. Wavelet, Contourlet and Shearlet Transforms are investigated to sparsify the digital pathology images, it is seen that Contourlet Transform is superior. Alternating Direction Method of Multipliers (ADMM) is chosen for reconstruction since it is a robust and fast convex optimization method. Despite the fact that digital pathology images are less sparse than classical images, CS reconstruction is satisfactory, which emphasizes the potential of CS for digital pathology. This study can be pioneering in the field of CS with digital pathology so it can encourage further studies of CS based imaging with different type of microscopes or at different wavelengths.

Sound field separation based on dictionary learning and sparse sampling

Sound field separation techniques are an advancing tool for extracting a target sound field from a mixed sound field. However, the methods bear a high measurement cost due to the restriction of the sampling theorem. In this study, a sound field separation method based on sparse sampling is established. The method initially utilizes dictionary learning to generate a sparse basis of the sound field. Then, a mixed sound field can be precisely recovered from sparse sampling of sound pressure and the target sound field can be extracted based on the recovered sound field by means of the theory of equivalent source method. The method is validated by numerical simulations. Compared to sound field separation based on the equivalent source method, the proposed method has advantage in terms of both the accuracy and the stability for sparse sampling.

Sparse basis covariance matrix estimation for high dimensional compositional data via hard thresholding

Motivated by the high-dimensional compositional data appearing in many fields, this paper addresses the problem of large covariance estimation for compositional data. Firstly, we introduce the hard thresholding estimator to approximate the sparse basis covariance matrix which is relevant with compositional data. Then the upper error bounds are measured by the general matrix lv,w-norm and the general entrywise Lv,w-norm respectively with v,w∈[1,∞] in terms of probability. Finally, numerical simulations and real datasets application demonstrate that our estimator is close to the oracle estimator and outperforms the COAT estimator proposed by Cao et al. (2019).

Generalized sparse radial basis function networks for multi-classification problems

Over the past decades, the radial basis function network (RBFN) has attracted extensive attention due to its simple network structure and powerful learning ability. Meanwhile, regularization methods have been intensively applied in RBFNs to enhance the performance of networks. A common regularization method is the ℓ2 regularization, which improves the stability and generalization ability but leads to dense networks. Another common regularization method is to employ the ℓ1 regularization that can successfully improve the sparsity of RBFN. The better strategy is to use the elastic-net regularization that combines both ℓ2 and ℓ1 regularization to improve stability and sparsity simultaneously. However, in multi-classification tasks, even the elastic-net regularization can only prune the redundant weights of nodes and cannot ensure the sparsity at the node level. In this paper, we propose a generalized sparse RBFN (GS-RBFN) based on the extended elastic-net regularization to handle multi-classification problems. By using the extended elastic-net regularization that integrates the Frobenius norm and L2,1 norm, we accomplish the stability and sparsity of RBFN for multi-classification problems, of which the binary classification problem is only a special case. In order to improve the training efficiency under large-scale tasks, we further propose the parallel GS-RBFN (PGS-RBFN) with the matrix inversion lemma to accelerate the intensive computation. The alternating direction method of multipliers (ADMM) and its consensus variant are applied to train our proposed models, and we demonstrate their convergence in solving corresponding optimization problems. Experimental results on multi-classification datasets illustrate the effectiveness and advantages of our algorithms in accuracy, sparsity and convergence.

Compressive Perception Image Reconstruction Technology for Basic Mixed Sparse Basis in Metal Surface Detection

<p>Applying Compressed Sensing (CS) technology to robot vision image transmission, an effective method for image reconstruction in robot imaging is proposed to improve the accuracy of reconstruction. Reconstructing images using a mixed sparse representation of DCT and circularly symmetric contour wave transform, the basic algorithm used is the Smoothed Projection Landweber (SPL) algorithm, which optimizes the coefficients under different sparse transformations by incorporating hard thresholding and binary thresholding methods for different sparse bases during iterations. The experiment shows that compared with single sparse base image reconstruction, the proposed reconstruction method has improved reconstruction accuracy.</p> <p> </p>

Kernel functions embed into the autoencoder to identify the sparse models of nonlinear dynamics

Numerous researches have shown that there are three main challenges in data-driven model identification methods: high-dimensional measurements, system complexity and unknown underlying dynamical properties. For most nonlinear dynamics, the feature space defined by the coefficients of their control equations is sparse. Therefore, sparse regression methods are used to learn the sparse coefficients of the control equations of nonlinear dynamics. However, this method strongly depends on the appropriate selection of the sparse basis vectors. In this essay, the autoencoder is combined with the sparse regression method to simultaneously identify the sparse coordinate and a parsimonious, interpretable and generalizable model of the specified system. It also integrates kernel functions to map the intractable measurements in the hidden space of the autoencoder into a linearly distinguishable kernel space, which kernelizes the candidate function library of the sparse identification of nonlinear dynamics (SINDy) model as the sparse dictionaries. Therefore, the flexible representation of neural networks, the simplicity of sparse regression methods and the implicit non-linear representation of kernel functions are consolidated in this article. To inspect the reliability of the proposed model in this paper, a set of nonlinear dynamics formulated by ordinary differential equations (ODEs), second-order trigonometric functions and partial differential equations (PDEs) are utilized as test cases. And the comparisons between the proposed model and other model identification methods illustrate that the performance of the former is the best.

Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations.

We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.

Qualitative exploration of the perceptions of exercise in patients with cancer initiated during chemotherapy: a meta-synthesis

ObjectiveTo synthesise qualitative literature on (1) the perceptions of patients with cancer of participating in an exercise intervention while undergoing chemotherapy and (2) to inform and guide professionals in oncology...

Novel dual compressive sensing method for solving the monostatic scattering problems of three-dimensional target

ABSTRACTAccording to the conventional dual compressive sensing method is limited to solving the electromagnetic scattering problems for two-dimensional targets, the Characteristic Basis Functions (CBFs) combined with the Compressive Sensing (CS) technique are proposed to solve the monostatic scattering problems for the three-dimensional (3D) target in this paper. The approach considered in this paper consists of successfully transforming the discrete surface-induced currents of Rao-Wilton-Glisson (RWG) basis functions using CBFs, which successfully enhance the sparsity of the induced currents. Then, the novel dual compressive sensing framework is obtained by applying the CBFs and discrete cosine transform matrices as sparse bases, respectively. The corresponding numerical calculations demonstrate that the proposed method can be used as an effective technical route to solve the monostatic scattering problem effectively.

Sound field recovery based on numerical data-driven and equivalent source method

Sparse representation has been applied to realize an accurate description of the sound field from limited set of measurements. The prerequisite of this application is that sound field can be sparsely represented in a specific basis. However, most of the sparse bases are constructed by using the physical models of sound field, and are only effective for a specific category of sound sources. In this paper, the data-driven dictionary learning approach is exploited to obtain a sparse basis of sound field. Meanwhile, to reduce the difficulty and workload of the collection of data sample, the equivalent source method is utilized to collect data samples by means of simulations and thus the data samples can be generated by taking advantage of sound field properties. The performance of the sound field recovery with sparse sampling based on learned dictionary is examined and is compared with those based on other sparse bases. The result indicates that numerical data-driven model is more flexible and is not limited to a specific category of sound sources. The advantage of the proposal is presented by the results of numerical simulation and experiment.

A New Basis for Sparse Principal Component Analysis

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a p × k matrix) is approximately sparse. We propose a method that presumes the p × k matrix becomes approximately sparse after a k × k rotation. The simplest version of the algorithm initializes with the leading k principal components. Then, the principal components are rotated with an k × k orthogonal rotation to make them approximately sparse. Finally, soft-thresholding is applied to the rotated principal components. This approach differs from prior approaches because it uses an orthogonal rotation to approximate a sparse basis. One consequence is that a sparse component need not to be a leading eigenvector, but rather a mixture of them. In this way, we propose a new (rotated) basis for sparse PCA. In addition, our approach avoids “deflation” and multiple tuning parameters required for that. Our sparse PCA framework is versatile; for example, it extends naturally to a two-way analysis of a data matrix for simultaneous dimensionality reduction of rows and columns. We provide evidence showing that for the same level of sparsity, the proposed sparse PCA method is more stable and can explain more variance compared to alternative methods. Through three applications—sparse coding of images, analysis of transcriptome sequencing data, and large-scale clustering of social networks, we demonstrate the modern usefulness of sparse PCA in exploring multivariate data. An R package, epca, and the supplementary materials for this article are available online.

Novel construction of measurement matrix and sparse basis to accelerate compressive sensing for solving wideband RCS of PEC objects

AbstractThis paper proposes a novel approach to enhance the computational efficiency and precision of the ultra‐wideband characteristic basis function method based on compressive sensing for calculating the wideband radar cross section (RCS) of objects, which involves the development of a new method for filling measurement matrix and constructing sparse basis. While randomly selecting rows from the original impedance matrix as the measurement matrix, the proposed method also avoids the double‐filling of equal elements in the measurement matrix. Furthermore, the Foldy–Lax equation is utilized to construct the merged ultra‐wideband characteristic basis functions (MUCBFs) at the highest frequency, and the sparse transform of the induced currents is performed using MUCBFs as the sparse basis. The numerical simulation results show that this method not only reduces the calculation effort of impedance matrix filling, but also effectively improves the calculation precision of the target wideband RCS.