New version of Gram-Schmidt Process with inverse for Signal and Image Processing

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The process consists of taking each array and then subtracting the projections in common with the previous arrays. This paper introduces an enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for Digital Signal and Image Processing, among others applications.

[1]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[2]  Randy L. Haupt,et al.  Introduction to Adaptive Arrays , 1980 .

[3]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[4]  Marc Moonen,et al.  Per tone equalization for DMT-based systems , 2001, IEEE Trans. Commun..

[5]  G. Stewart.  Introduction to matrix computations , 1973 .

[6]  Charles E. Leiserson,et al.  High-Performance Architectures For Adaptive Filtering Based On The Gram-Schmidt Algorithm , 1984, Optics & Photonics.

[7]  J. Makhoul.  A class of all-zero lattice digital filters: Properties and applications , 1978 .

[8]  N. Al-Dhahir,et al.  Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach , 1996, IEEE Trans. Inf. Theory.

[9]  Andrew D. Jackson,et al.  Random Quantum Billiards , 1997 .

[10]  Behrouz Farhang-Boroujeny,et al.  Design methods for time-domain equalizers in DMT transceivers , 2001, IEEE Trans. Commun..

[11]  W. Greub.  Linear Algebra , 1981 .

[12]  Norbert J. Fliege,et al.  A new equalizer for multitone systems without guard time , 2002, IEEE Communications Letters.

[13]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[14]  Nasir Ahmed,et al.  On a realization and related algorithm for adaptive prediction , 1980 .

[15]  Yike Guo,et al.  Gram-Schmidt Kernels Applied to Structure Activity Analysis for Drug Design , 2002, BIOKDD.

[16]  Charles E. Rohrs,et al.  Impulse response shortening for discrete multitone transceivers , 1996, IEEE Trans. Commun..

[17]  Brian L. Evans,et al.  Equalization for discrete multitone transceivers to maximize bit rate , 2001, IEEE Trans. Signal Process..

[18]  R.C. Johnson,et al.  Introduction to adaptive arrays , 1982, Proceedings of the IEEE.

[19]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[20]  M. Mastriani.  Predictor of linear output , 1994, Proceedings of 1994 IEEE International Symposium on Industrial Electronics (ISIE'94).

[21]  Golub Gene H. Et.Al.  Matrix Computations, 3rd Edition , 2007 .

[22]  John W. Auer,et al.  Linear algebra with applications , 1996 .

[23]  S. Lambotharan,et al.  Robust Impulse Response Shortening for Discrete Multitone Transceivers , 2007, 2007 15th International Conference on Digital Signal Processing.

[24]  Ming Ding,et al.  A dual-path TEQ structure for DMT-ADSL systems , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  John M. Cioffi,et al.  Optimum finite-length equalization for multicarrier transceivers , 1996, IEEE Trans. Commun..

[26]  R. T. Compton.  Adaptive Antennas: Concepts and Performance , 1988 .