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An Adaptive Constraint Method for Paraunitary Filter Banks with Applications to Spatiotemporal Subspace Tracking
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 080301 (2006)
This paper presents an adaptive method for maintaining paraunitary constraints on direct-form multichannel finite impulse response (FIR) filters. The technique is a spatiotemporal extension of a simple iterative procedure for imposing orthogonality constraints on nearly unitary matrices. A convergence analysis indicates that it has a large capture region, and its convergence rate is shown to be locally quadratic. Simulations of the method verify its capabilities in maintaining paraunitary constraints for gradient-based spatiotemporal principal and minor subspace tracking. Finally, as the technique is easily extended to multidimensional convolution forms, we illustrate such an extension for two-dimensional adaptive paraunitary filters using a simple image sequence encoding example.
Abreu E, Mitra SK, Marchesani R: Nonminimum phase channel equalization using noncausal filters. IEEE Transactions on Signal Processing 1997,45(1):1–13. 10.1109/78.552201
Bjorck A, Bowie C: An iterative algorithm for computing the best estimate of an orthogonal matrix. SIAM Journal on Numerical Analysis 1971,8(2):358–364. 10.1137/0708036
Chen T-P, Amari S-I, Lin Q: A unified algorithm for principal and minor components extraction. Neural Networks 1998,11(3):385–390. 10.1016/S0893-6080(98)00004-5
Chen T, Lin Q: Dynamic behavior of the whitening process. IEEE Signal Processing Letters 1998,5(1):25–26. 10.1109/97.654871
Douglas SC: Fast implementations of the filtered-X LMS and LMS algorithms for multichannel active noise control. IEEE Transactions on Speech and Audio Processing 1999,7(4):454–465. 10.1109/89.771315
Douglas SC, Amari S-I, Kung S-Y: On gradient adaptation with unit-norm constraints. IEEE Transactions on Signal Processing 2000,48(6):1843–1847. 10.1109/78.845952
Douglas SC, Amari S-I, Kung S-Y: Gradient adaptive paraunitary filter banks for spatio-temporal subspace analysis and multichannel blind deconvolution. Journal of VLSI Signal Processing 2004,37(2–3):247–261.
Douglas SC, Cichocki A: Neural networks for blind decorrelation of signals. IEEE Transactions on Signal Processing 1997,45(11):2829–2842. 10.1109/78.650109
Douglas SC, Kung S-Y, Amari S-I: A self-stabilized minor subspace rule. IEEE Signal Processing Letters 1998,5(12):328–330. 10.1109/97.735427
Douglas SC, Sawada H, Makino S: A spatio-temporal fastica algorithm for separating convolutive mixtures. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 5: 165–168.
Fan K, Hoffman AJ: Some metric inequalities in the space of matrices. Proceedings of the American Mathematical Society 1955,6(1):111–116. 10.1090/S0002-9939-1955-0067841-7
Farhang-Boroujeny B, Nooshfar S: Adaptive phase equalization using all-pass filters. Proceedings of IEEE International Conference on Communications (ICC '91), June 1991, Denver, Colo, USA 3: 1403–1407.
Hasan MA: Natural gradient for minor component extraction. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '05), May 2005, Kobe, Japan 5: 5138–5141.
Hua Y: Asymptotical orthonormalization of subspace matrices without square root. IEEE Signal Processing Magazine 2004,21(4):56–61. 10.1109/MSP.2004.1311143
Hyvarinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.
Kirac A, Vaidyanathan PP: Theory and design of optimum FIR compaction filters. IEEE Transactions on Signal Processing 1998,46(4):903–919. 10.1109/78.668545
Lim TJ, Macleod MD: Adaptive allpass filtering for nonminimum-phase system identification. IEE Proceedings–Vision, Image, and Signal Processing 1994,141(6):373–379. 10.1049/ip-vis:19941549
Loubaton P, Regalia PA: Blind deconvolution of multivariate signals by using adaptive FIR lossless filters. Proceedings of the European Signal Processing Conference (EUSIPCO '92), August 1992, Brussels, Belgium 1061–1064.
Manton JH: Optimization algorithms exploiting unitary constraints. IEEE Transactions on Signal Processing 2002,50(3):635–650. 10.1109/78.984753
Manton JH, Helmke U, Mareels IMY: A dual purpose principal and minor component flow. Systems and Control Letters 2005,54(8):759–769. 10.1016/j.sysconle.2004.11.015
McEwen PA, Kenney JG: Allpass forward equalizer for decision feedback equalization. IEEE Transactions on Magnetics 1995,31(6, part 1):3045–3047. 10.1109/20.490264
Moulin P, Mihcak MK: Theory and design of signal-adapted FIR paraunitary filter banks. IEEE Transactions on Signal Processing 1998,46(4):920–929. 10.1109/78.668546
Oja E, Karhunen J: On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Mathematical Analysis and Applications 1985,106(1):69–84. 10.1016/0022-247X(85)90131-3
Ottersten B, Kailath T: Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(2):317–327. 10.1109/29.103067
Porat B, Friedlander B: Estimation of spatial and spectral parameters of multiple sources. IEEE Transactions on Information Theory 1983,29(3):412–425. 10.1109/TIT.1983.1056670
Regalia PA, Loubaton P: Rational subspace estimation using adaptive lossless filters. IEEE Transactions on Signal Processing 1992,40(10):2392–2405. 10.1109/78.157284
Sun X, Douglas SC: Self-stabilized adaptive allpass filters for phase equalization and approximation. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 1: 444–447.
Tsatsanis MK, Giannakis GB: Principal component filter banks for optimal multiresolution analysis. IEEE Transactions on Signal Processing 1995,43(8):1766–1777. 10.1109/78.403336
Xuan B, Bamberger RI: FIR principal component filter banks. IEEE Transactions on Signal Processing 1998,46(4):930–940. 10.1109/78.668547
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Douglas, S.C. An Adaptive Constraint Method for Paraunitary Filter Banks with Applications to Spatiotemporal Subspace Tracking. EURASIP J. Adv. Signal Process. 2007, 080301 (2006). https://doi.org/10.1155/2007/80301
- Convergence Rate
- Quantum Information
- Image Sequence
- Iterative Procedure