Abstract
Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have developed a number of approaches to recover the original signals. Most of them rely on classical singular value decomposition, which are vulnerable to unexpected outliers. In this paper, to overcome this deficiency, we propose a new random-access HR model and develop robust algorithms combining \(L_1\)-Tucker decomposition methods of Hankel tensor and novel frequency recovery techniques to solve such HR problem. Simulations are designed to compare our proposed methods with some existing tensor-based algorithms for HR. The numerical results demonstrate the outlier-insensitivity of our methods.
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References
Agarwal K, Macháň R (2016) Multiple signal classification algorithm for super-resolution fluorescence microscopy. Nat Commun 7:1–9
Andersson CA, Bro R (1998) Improving the speed of multi-way algorithms: part I-Tucker3. Chemom Intell Lab 42:93–103
Brooks JP, Dulá J, Boone EL (2013) A pure \(L_1\)-norm principal component analysis. Comput Stat Data Anal 61:83–98
Chachlakis DG, Prater-Bennette A, Markopoulos PP (2019) \(L_1\)-norm Tucker tensor decomposition. IEEE Access 7:178454–178465
Chachlakis DG, Prater-Bennette A, Markopoulos PP (2020) \(L_1\)-norm higher-order orthogonal iterations for robust tensor analysis. 2020 International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, pp. 4826–4830
Chachlakis DG, Dhanaraj M, Prater-Bennette A, Markopoulos PP (2021) Dynamic \(L_1\)-norm Tucker tensor decomposition. IEEE J-STSP 15:587–602
De Lathauwert L, De Moort B, Vandewallet J (2000) On the best rank-1 and rank-\((R_1, R_2,\ldots , R_N)\) approximation of higher-order tensors. SIAM J Matrix Anal Appl 21:1324–1342
Dhanaraj M, Chachlakis DG, Markopoulos PP (2018) Incremental complex \(L_1\)-PCA for direction-of-arrival estimation. 2018 Western New York Image and Signal Processing Workshop (WNYISPW), IEEE, pp. 1–5
Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:498–520
Kapteyn A, Neudecker H, Wansbeek T (1986) An approach ton-mode components analysis. Psychometrika 31:269–275
Kokkinakis K, Loizou PC (2008) Using blind source separation techniques to improve speech recognition in bilateral cochlear implant patients. J Acoust Soc Am 123:2379–2390
Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51:455–500
Kumaresan R, Tufts D (2003) Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise. IEEE Trans Acoust Speech Signal Process 30:833–840
Kumaresan R, Scharf LL, Shaw AK (1986) An algorithm for pole-zero modeling and spectral analysis. IEEE Trans Acoust Speech Signal Process 34:637–640
Kung SY, Arun KS, Rao DVB (1983) State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem. J Opt Soc Am 73:1799–1811
Markopoulos PP, Dhanaraj M, Savakis A (2018) Adaptive \(L_1\)-norm principal-component analysis with online outlier rejection. IEEE J-STSP 12:1131–1143
Mozaffari M, Markopoulos PP, Prater-Bennette A (2021) Improved \(L_1\)- Tucker via \(L_1\)-fitting. 2021 29th European Signal Processing Conference (EUSIPCO), IEEE, pp. 1075–1079
Papadopoulos CK, Nikias CL (1990) Parameter estimation of exponentially damped sinusoids using higher order statistics. IEEE Trans Acoust Speech Signal Process 38:1424–1436
Papy JM, De Lathauwer L, Van Huffel S (2010) Exponential data fitting using multilinear algebra: the single-channel and multi-channel case. Numer Linear Algebra Appl 12:809–826
Qian C, Shi Y, Huang L, So HC (2018) Robust harmonic retrieval via block successive upper-bound minimization. IEEE Trans Signal Process 66:6310–6324
Roy R, Kailath T (1989) ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans Acoust Speech Signal Process 37:984–995
Sklivanitis G, Tountas K, Tsagkarakis N, Pados DA, Batalama SN (2020 Optimal joint channel estimation and data detection by \(L_1\)-norm PCA for Streetscape IoT. 2020 International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, pp. 9051–9054
Talwar S, Viberg M, Paulraj A (1996) Blind separation of synchronous co-channel digital signals using an antenna array-part 1: algorithms. IEEE Trans Signal Process 44:1184–1197
Tountas K, Chachlakis D, Markopoulos PP, Pados DA (2019) Iteratively reweighted \(L_1\)-norm PCA of tensor data. 2019 53rd Asilomar Conference on Signals, Systems, and Computers, IEEE, pp. 1658–1661
Tsagkarakis N, Tsagkarakis PP, Pados DA (2018) \(L_1\)-norm principal component analysis of complex data. IEEE Trans Signal Process 66:3256–3267
Tucker L (1966) Some mathematical notes on three-mode factor analysis. Psychometrika 31:279–311
Vorobyov SA, Yue R, Sidiropoulos ND, Gershman AB (2005) Robust iterative fitting of multilinear models. IEEE Trans Signal Process 53:2678–2689
Wen F, So HC (2015) Robust multi-dimensional harmonic retrieval using iteratively reweighted HOSVD. IEEE Signal Process Lett 22:2464–2468
Yokota T, Cichocki A (2014) Multilinear tensor rank estimation via sparse tucker decomposition. 2014 Joint 7th International Conference on Soft computing and Intelligent Systems (SCIS) and 15th International Symposium on Advanced Intelligent Systems (ISIS), IEEE, pp. 478–483
Zarzoso V, Nandi AK (2001) Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation. IEEE Trans Biomed Eng 48:12–18
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Communicated by Yimin Wei.
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This work was supported by the National Natural Science Foundation of China (Grant no. 12171271).
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Luan, Z., Ming, Z., Wu, Y. et al. Hankel tensor-based model and \(L_1\)-Tucker decomposition-based frequency recovery method for harmonic retrieval problem. Comp. Appl. Math. 42, 14 (2023). https://doi.org/10.1007/s40314-022-02151-3
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DOI: https://doi.org/10.1007/s40314-022-02151-3