Enhanced Gram-Schmidt Process for Improving the Stability in Signal and Image Processing
The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for signal and image processing applications.
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 S. Haykin, Neural Networks: A Comprehensive Foundation. New York: Macmillan, 1994.
 S. Haykin, Modern Filters. New York: Macmillan, 1990.
 S. Haykin, Adaptive Filter Theory. New Jersey: Prentice-Hall, 1991.
 H Lodhi and Y. Guo, “Gram-Schmidt kernels applied to structure activity analysis for drug design”, in Proc. of 2nd. Workshop on Datamining in Bioinformatics, Edmonton, Alberta, Canada, July 23rd. 2002, pp. 37-42.
 R. A. Mozingo and T. W. Miller, Introduction to Adaptive Arrays. New York: Wiley, 1980.
 R. T. Compton, Adaptive Antennas: Concepts and Performance. New Jersey: Prentice-Hall, 1988.
 G. W. Stewart, Introduction to Matrix Computations. Orlando: Academic Press, 1973.
 J. Makhoul, “A class of all-zero lattice digital filters: properties and applications,” IEEE Trans. Acoust. Speech and Signal Process., vol. ASSP-26, pp.304-314, 1978.
 N. Ahmed and D. H. Youn, “On a realization and related algorithm for adaptive prediction,” IEEE Trans. Acoust. Speech and Signal Process., vol. ASSP-28, pp.493-4974, 1980.
 K. A. Gallivan and C. E. Leiserson, “High-performance architectures for adaptive filtering based on the Gram-Schmidt algorithm,” SPIE, Real Time Signal Process. VII, vol.495, pp.30-36, 1984.
 M. Mastriani, “Self-Restorable Stochastic Neuro-Estimation using Forward-Propagation Training Algorithm,” in Proc. of INNS, Portland, OR, July 1993, vol. 1, pp. 404-411.
 M. Mastriani, “Self-Restorable Stochastic Neurocontrol using Back- Propagation and Forward-Propagation Training Algorithms,” in Proc. of ICSPAT, Santa Clara, CA, Sept. 1993, vol. 2, pp.1058-1071.
 M. Mastriani, “Pattern Recognition Using a Faster New Algorithm for Training Feed-Forward Neural Networks,” in Proc. of INNS, San Diego, CA, June 1994, vol. 3, pp. 601-606.
 M. Mastriani, “Predictor of Linear Output,” in Proc. IEEE Int. Symposium on Industrial Electronics, Santiago, Chile, May 1994, pp.269-274.
 M. Mastriani, “Predictor-Corrector Neural Network for doing Technical Analysis in the Capital Market,” in Proc. AAAI International Symposium on Artificial Intelligence, Monterrey, México, October 1994, pp. 49-58.
 N. Al-Dhahir and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: A unified approach," IEEE Trans. on Info. Theory, vol. 42, pp. 903-915, May 1996.
 P. J. W. Melsa, R. C. Younce, and C. E. Rhors, "Impulse response shortening for discrete multitone transceivers," IEEE Trans. on Communications, vol. 44, pp. 1662-1672, Dec. 1996.
 N. Al-Dhahir and J. M. Cioffi, "Optimum finite-length equalization for multicarrier transceivers," IEEE Trans. on Communications, vol. 44, pp. 56-63, Jan. 1996.
 B. Lu , L. D. Clark, G. Arslan, and B. L. Evans, "Divide-and-conquer and matrix pencil methods for discrete multitone equalization," IEEE Trans. on Signal Processing, in revision.
 G. Arslan , B. L. Evans, and S. Kiaei, "Equalization for Discrete Multitone Receivers To Maximize Bit Rate," IEEE Trans. on Signal Processing, vol. 49, no. 12, pp. 3123-3135, Dec. 2001.
 B. Farhang-Boroujeny and Ming Ding, "Design Methods for Time Domain Equalizer in DMT Transceivers", IEEE Trans. on Communications, vol. 49, pp. 554-562, March 2001.
 J. M. Cioffi, A Multicarrier Primer. Amati Communication Corporation and Stanford University, T1E1.4/97-157, Nov. 1991.
 M. Ding, A. J. Redfern, and B. L. Evans, "A Dual-path TEQ Structure For DMT-ADSL Systems", Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., May 13-17, 2002, Orlando, FL, accepted for publication.
 K. V. Acker, G. Leus, M. Moonen, O. van de Wiel, and T. Pollet, "Per tone equalization for DMT-based systems," IEEE Trans. on Communications, vol. 49, no. 1, pp. 109-119, Jan 2001.
 S. Trautmann, N.J. Fliege, “A new equalizer for multitone systems without guard time” IEEE Communications Letters, Vol.6, No. 1 pp. 34 -36, Jan 2002.
 M. Tuma and M. Benzi, “A robust preconditioning technique for large sparse least squares problems”, in Proc. of XV. Householder Symposium, Peebles, Scotland, June 17-21, 2002. pp.8
 H. J. Pedersen, “Random Quantum Billiards”, Master dissertation, K0benhavns Universitet, Copenhagen, Denmark, july 1997, pp.63
 G. H. Golub and C. F. van Loan, Matrix Computations, (3rd Edition) Johns Hopkins University Press, Baltimore, 1996.
 G. Hadley, Linear Algebra. Mass.: Wesley, 1961.
 G. Strang, Linear Algebra and Its Applications. New York: Academic Press, 1980.
 S. J. Leon, “Linear Algebra with Applications” Maxwell MacMillan, New York, 1990.