•A parallel MRI reconstruction method called STDLR-SPIRiT to exploit both the low-rankness and self-consistency of k-space data.•Provides promising image quality for accelerated parallel magnetic ...resonance imaging.•Outperforms the state-of-the-art methods in terms of suppressing artifacts and achieving the lowest error.•Robust to auto-calibration signals.
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Parallel magnetic resonance imaging has served as an effective and widely adopted technique for accelerating data collection. The advent of sparse sampling offers aggressive acceleration, allowing flexible sampling and better reconstruction. Nevertheless, faithfully reconstructing the image from limited data still poses a challenging task. Recent low-rank reconstruction methods are superior in providing high-quality images. Nevertheless, none of them employ the routinely acquired calibration data to improve image quality in parallel magnetic resonance imaging. In this work, an image reconstruction approach named STDLR-SPIRiT is proposed to explore the simultaneous two-directional low-rankness (STDLR) in the k-space data and to mine the data correlation from multiple receiver coils with the iterative self-consistent parallel imaging reconstruction (SPIRiT). The reconstruction problem is then solved with a singular value decomposition-free numerical algorithm. Experimental results of phantom and brain imaging data show that the proposed method outperforms the state-of-the-art methods in terms of suppressing artifacts and achieving the lowest error. Moreover, the proposed method exhibits robust reconstruction even when the auto-calibration signals are limited in parallel imaging. Overall the proposed method can be exploited to achieve better image quality for accelerated parallel magnetic resonance imaging.
Although recent deep learning methods, especially generative models, have shown good performance in magnetic resonance imaging, there is still much room for improvement. Considering that the sample ...number and internal dimension in score-based generative model have key influence on estimating the gradients of data distribution, we present a new idea for parallel imaging reconstruction, named low-rank tensor assisted k-space generative model (LR-KGM). It means that we transform low-rank information into high-dimensional prior information for learning. More specifically, the multi-channel data is constructed into a large Hankel matrix to reduce the number of training samples, which is subsequently collapsed into a tensor for the stage of prior learning. In the testing phase, the low-rank rotation strategy is utilized to impose low-rank constraints on the output tensors of the generative network. Furthermore, we alternate the reconstruction between traditional generative iterations and low-rank high-dimensional tensor iterations. Experimental comparisons with the state-of-the-arts demonstrated that the proposed LR-KGM method achieved better performance.
Here we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it ...does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks.
Based on the traditional theory of singular value decomposition (SVD), singular values (SVs) and ratios of neighboring singular values (NSVRs) are introduced to the feature extraction of vibration ...signals. The proposed feature extraction method is called SV–NSVR. Combined with selected SV–NSVR features, continuous hidden Markov model (CHMM) is used to realize the automatic classification. Then the SV–NSVR and CHMM based method is applied in fault diagnosis and performance assessment of rolling element bearings. The simulation and experimental results show that this method has a higher accuracy for the bearing fault diagnosis compared with those using other SVD features, and it is effective for the performance assessment of rolling element bearings.
•A concept of neighboring singular value ratio (NSVR) is proposed.•The results of bearing fault diagnosis based on NSVRs and singular values (SVs) are different.•The method based on selected SV–NSVR and continuous hidden Markov model (CHMM) is proposed.•The proposed method is proved to be valid for bearing fault diagnosis and performance assessment.
In this paper we first construct a Lie group structure on n×n Hankel matrices over R+ by Hadamard product and then we find its Lie algebra structure and finally calculate dimension of this manifold ...over R+. Moreover, we discuss topological properties of this manifold using Frobenious norm. We pointed out the relation between Lie group and Lie algebra structures of these matrices by exponential map. It is also shown that the Hadamard product on Hankel matrices over R+ is not bounded by Frobenious norm. Lastly, we provide some applications of these manifolds.
The singular value decomposition (SVD) based on the Hankel matrix is commonly used in signal processing and fault diagnosis. The noise reduction performance of SVD based on the Hankel matrix is ...affected by three factors: the reconstruction component(s), the structure of the Hankel matrix, and the point number of the analysis data. In this article, the three influencing factors are systematically studied, and a method based on correlated SVD (C-SVD) is proposed and successfully applied to bearing fault diagnosis. First, perform SVD analysis on the collected original signal. Then, the reconstructed component(s) determination method of SVD based on the combination of singular value ratio (SVR) and correlation coefficient is proposed. Then, based on the SVR, using the envelope kurtosis as the indicator, the optimal structure of the Hankel matrix (number of rows and columns) is studied. Then, the number of data points of the analysis signal is discussed, and the constraint range is given. Finally, the envelope power spectrum analysis is performed on the reconstructed signal to extract the fault features. The proposed C-SVD method is compared with the existing typical methods and applied to the simulated signal and the actual bearing fault signal, and its superiority is verified.
Abstract
Intelligent fault diagnosis for mechanical condition monitoring has achieved a great deal of success in recent years, but most of the research is carried out in experimental environments. ...Vibration signals collected in real scenarios usually have strong noise interference, which significantly reduces fault classification capability and seriously affects the accuracy and robustness of classification. This paper proposes modified general normalized sparse filtering (MGNSF) with strong noise adaptability for rotating machinery fault diagnosis without any time-consuming denoising preprocessing, in which generalized normalization, weight and feature normalization, and the Hankel matrix. Diagnostic performance is studied with the change of normalization parameters and signal noise ratio. Weight and feature normalization can improve the distribution between features. The proposed algorithm is validated using two rolling bearing datasets. The experimental results show that MGNSF can extract the features of a faulty bearing under stronger noise interference and has strong noise adaptability.
Hankel matrices acting on Dirichlet spaces Bao, Guanlong; Wulan, Hasi
Journal of mathematical analysis and applications,
01/2014, Letnik:
409, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We give a connection between the Hankel matrix acting on Dirichlet spaces Dα, 0<α<2, and the Carleson measure supported on (−1,1). As an application, we prove that the generalized Hilbert operators ...Hβ are always bounded on Dirichlet spaces Dα for 0<α<2 and that the range (0,2) of α in our results is the best possible.
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(xj). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as ...normalized traces. This paper addresses global and constrained positivity of univariate trace polynomials on symmetric matrices of all finite sizes. A tracial analog of Artin's solution to Hilbert's 17th problem is given: a positive semidefinite univariate trace polynomial is a quotient of sums of products of squares and traces of squares of trace polynomials.
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