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On rank of block Hankel matrix for 2-D frequency detection and estimation

H. Hua Yang, Y. Hua
1996 IEEE Transactions on Signal Processing  
The authors are with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada. Publisher Item Identifier S 1053-587X(96)02273-6.  ...  Inst On Rank of Block Hankel Matrix for 2-D Frequency Detection and Estimation Howard Hua Yang and Yingbo Hua Abstract-For detection and estimation of 2-D frequencies from a 2-D array of data using  ...  Similarly, for detection and estimation of 2-D frequencies from a single 2-D array of data using a subspace decomposition method, one needs to form a block Hankel matrix where each block is a Hankel matrix  ... 
doi:10.1109/78.492568 fatcat:lf22ez22jngwhem4gz2trz2j3q

AN OPTIMISED PSEUDO-INVERSE ALGORITHM (OPIA) FOR MULTI-INPUT MULTI-OUTPUT MODAL PARAMETER IDENTIFICATION

F BAZAN
1996 Mechanical systems and signal processing  
A multi-input multi-output (MIMO) algorithm for modal parameter identification is developed based on linear prediction theory and its numerical efficiency compared to that of the well-known Eigensystem  ...  The problem of determining the correct system's order is analysed through perturbation theory of singular values of oversized Hankel-block matrices.  ...  For the purpose of deriving OPIA in the frequency domain, complex Hankel-like block matrices whose entries are shift versions of the frequency response matrix, must be used.  ... 
doi:10.1006/mssp.1996.0026 fatcat:6p35ywktgnc3bcvvniw7xxdev4

A Dynamic Mode Decomposition Approach With Hankel Blocks to Forecast Multi-Channel Temporal Series

Enio Vasconcelos Filho, Paulo Lopes dos Santos
2019 IEEE Control Systems Letters  
The Hankel block allows the estimation of hiddenoscillatory modes, by increasing the order of the underlying dynamical system.  ...  The Hankel block allows the estimation of hidden oscillatory modes, by increasing the order of the underlying dynamical system.  ...  ACKNOWLEDGMENTS Enio Vasconcelos Filho was supported by National Funds, through FCT/MCTES (Portuguese Foundation for Science and Technology), within the CISTER Research Unit, (UID/CEC/04234); Paulo Lopes  ... 
doi:10.1109/lcsys.2019.2917811 fatcat:ux4k4j5fa5ayxao3vqakbkuibm

Novel feature extraction technique based on ranks of Hankel matrices with application for ECG analysis

Mantas Landauskas, Ugnė Orinaitė
2021 Mathematical Models in Engineering  
The proof of concept for the technique to detect changes in the signal was explained and an effect of additive noise was tested.  ...  The H-rankgram is two-dimensional feature pattern which shows the change in algebraic complexity (measured using ranks of Hankel matrices) of a given signal at a different scale in time (estimated using  ...  An automated detection method for coronary artery disease based on a time-frequency representation (TFR) known as improved eigenvalue decomposition of Hankel matrix and Hilbert transform (IEVDHM-HT) using  ... 
doi:10.21595/mme.2021.22138 fatcat:zc7cjhg66zhr5gwdrfao6fjcia

Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

Elena Barton, Basad Al-Sarray, Stéphane Chrétien, Kavya Jagan
2018 Mathematics  
In this note, we present a component-wise algorithm combining several recent ideas from signal processing for simultaneous piecewise constants trend, seasonality, outliers, and noise decomposition of dynamical  ...  Our approach is entirely based on convex optimisation, and our decomposition is guaranteed to be a global optimiser.  ...  The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.  ... 
doi:10.3390/math6070124 fatcat:dqavn5ahjvbjxcwcc275dmvoge

A tensor decomposition approach to noninvasive atrial activity extraction in atrial fibrillation ECG

L. N. Ribeiro, A. R. Hidalgo-Munoz, G. Favier, J. C. M. Mota, A. L. F. de Almeida, V. Zarzoso
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
This work presents tensor decompositions as an alternative to classic blind source separation methods based on matrix decompositions due to their appealing uniqueness properties and considers in particular  ...  Analysis of the atrial activity (AA) signal contained in electrocardiograms during AF episodes is a noninvasive and inexpensive solution for obtaining useful information about AF.  ...  This decomposition will be unique up to permutation and scaling provided that the factors D (1) = D (1) 1 , D (1) 2 , . . . , D (1) R and D (2) = D (2) 1 , D (2) 2 , . . . , D (2) R are full-column rank  ... 
doi:10.1109/eusipco.2015.7362850 dblp:conf/eusipco/RibeiroHFMAZ15 fatcat:4cu4qxxbwjagfom56po6scp52y

Sparse + Low Rank Decomposition of Annihilating Filter-based Hankel Matrix for Impulse Noise Removal [article]

Kyong Hwan Jin, Jong Chul Ye
2015 arXiv   pre-print
Based on the observation that smoothness or textures within an image patch corresponds to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the  ...  associated rank-deficient Hankel matrices in the image domain to estimate the missing pixels.  ...  denotes the estimated rank of the Hankel matrix.  ... 
arXiv:1510.05559v1 fatcat:vtwcqvo72jbxrkqy5wtfdyx4am

Fast live cell imaging at nanometer scale using annihilating filter-based low-rank Hankel matrix approach

Junhong Min, Lina Carlini, Michael Unser, Suliana Manley, Jong Chul Ye, Manos Papadakis, Vivek K. Goyal, Dimitri Van De Ville
2015 Wavelets and Sparsity XVI  
Here, we proposed a new localization algorithm using annihilating filter-based low rank Hankel structured matrix approach (ALOHA).  ...  The results confirmed that it has the higher localization performances in both experiments in terms of accuracy and detection rate.  ...  Specifically, the estimation is done by minimizing Schatten-p norm of the Hankel matrix as follows: 1 2πσ 2 e − ρ 22 .  ... 
doi:10.1117/12.2187393 fatcat:lzwywgnu35aq7how56w4z5qmkq

Block term decomposition for modelling epileptic seizures

Borbála Hunyadi, Daan Camps, Laurent Sorber, Wim Van Paesschen, Maarten De Vos, Sabine Van Huffel, Lieven De Lathauwer
2014 EURASIP Journal on Advances in Signal Processing  
-1 tensor, i.e. by the combination of one particular temporal, spectral and spatial signature.  ...  Here, we present the application of a recently introduced technique, called block term decomposition (BTD) to separate EEG tensors into rank-(L r , L r , 1) terms, allowing to model more variability in  ...  . . . z J−1 1,r z J−1 2,r · · · z J−1 L r ,r ⎤ ⎥ ⎥ ⎥ ⎦ (12) For example, the Hankel matrix of a pure exponential is rank 1, while the one of a pure sinusoids or an exponentially damped sinusoid is rank  ... 
doi:10.1186/1687-6180-2014-139 fatcat:6s6ft3zd7va47ipekvaje5u74u

Subspace Identification of Linear Systems with Observation Outliers

Hideyuki TANAKA, Jaafar ALMUTAWA, Tohru KATAYAMA
2004 Transactions of the Institute of Systems Control and Information Engineers  
Based on detected outliers, a weighting matrix is generated automatically, and is incorporated in the weighted LQ decomposition to get an improved estimate of the system matrices.  ...  By using the median of residuals, outliers are detected by a simple scheme in robust statistics.  ...  Detection of Outliers Step 1 Define the following matrix from the output data Projecting y2T onto the row space of block Hankel matrix of the input data yields1 Step 2 Calculate the difference of th.e  ... 
doi:10.5687/iscie.17.89 fatcat:wp446hcalber5nbdeifqyb2sve

A Model-Agnostic Method for PMU Data Recovery Using Optimal Singular Value Thresholding [article]

Shuchismita Biswas, Virgilio A. Centeno
2021 arXiv   pre-print
The measurements are first transformed into a Page matrix, and the original signals are reconstructed using low-rank matrix estimation based on optimal singular value thresholding.  ...  Two variations of the recovery algorithm are shown- a) an offline block-processing method for imputing past measurements, and b) an online method for predicting future measurements.  ...  The alternative method used in literature for estimating matrix rank involves-a) selecting a threshold for rank approximation error, and b) choosing the lowest rank for which the approximate matrix does  ... 
arXiv:2108.03220v1 fatcat:ga63okx6pvajdmmywceb4xclay

The detection matrix as a model-agnostic tool to estimate the number of degrees of freedom in mechanical systems and engineering structures

Paolo Celli, Maurizio Porfiri
2022 Chaos  
From this estimation, we illustrate the possibility to identify damage. The detection matrix, recently introduced by Haehne et al. [Phys. Rev.  ...  Lett. 122, 158301 (2019)] in the context of network theory, is assembled from the transient response of a few nodes as a result of non-zero initial conditions: its rank offers an estimate of the number  ...  ACKNOWLEDGEMENTS PC acknowledges the support of the Research Foundation for the State University of New York.  ... 
doi:10.1063/5.0083767 pmid:35364822 fatcat:g4rgf66ujffljh2e3bglp32ejy

A Modified Sequential Multiplexed Method for Detecting Airborne and Sea Targets with Over-The-Horizon Radar

Zhaoyi Wang, Shengnan Shi, Ziyang Cheng, Zishu He
2020 IEEE Access  
To tackle it, a recovery algorithm based on the Hankel structured matrix is introduced, which recovers the slow-time domain signal of each range bin and thereby guarantees the detection performance of  ...  The proposed scheme seeks to improve the detection frequency of airborne target while ensuring the detection performance of two types of target.  ...  Xianxiang Yu from UESTC for discussions on this topic.  ... 
doi:10.1109/access.2020.2992129 fatcat:ceugcxwmlfgj7ozxts2cctncxi

Application of the Singular Spectrum Analysis on electroluminescence images of thin-film photovoltaic modules [article]

Evgenii Sovetkin, Bart E. Pieters
2021 arXiv   pre-print
We propose an EL image decomposition as a sum of three components: global intensity, cell, and aperiodic components.  ...  Furthermore, an explicit expression of the cell component signal is used to estimate the inverse characteristic length, a physical parameter related to the resistances in a PV module.  ...  Acknowledgements This work is supported by the Solar-era.net framework in the project "PEARL TF-PV" (Förderkennzeichen: 0324193A) and partly funded by the HGF project "Living Lab Energy Campus (LLEC)".  ... 
arXiv:2109.04048v1 fatcat:rzu7fdpipjbpvnsdl3tgot3e44

Review and Prospect: NMR Spectroscopy Denoising Reconstruction with Low Rank Hankel Matrices and Tensors [article]

Tianyu Qiu, Zi Wang, Huiting Liu, Di Guo, Xiaobo Qu
2020 arXiv   pre-print
In this review, we summarize the recent progress on low rank Hankel matrix and tensor methods, that exploit the exponential property of free induction decay signals, to enable effective denoising and spectra  ...  Nuclear Magnetic Resonance (NMR) spectroscopy is an important analytical tool in chemistry, biology, and life science, but it suffers from relatively low sensitivity and long acquisition time.  ...  During the visit, the low rank Hankel matrix property of exponential functions [31] came into his horizon and inspired him to complete a series of low rank Hankel reconstruction methods in NMR spectroscopy  ... 
arXiv:2007.12646v1 fatcat:wzy2qkaukjdgloo5k3aadc4qnu
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