Single Value Decomposition and Signal Processing: v. 1

Compiled in this book is a selection of articles written by internationally recognized experts in the fields of matrix computation and signal processing. In almost all digital signal processing (DSR) problems, the available data is corrupted by (measurement) noise or is incomplete. Classical techniques are unable to separate ``signal'' spaces and ``noise'' spaces. However, the information hidden in the data can be made explicit through singular value decomposition (SVD). SVD based signal processing is making headway and will become feasible soon, thanks to the progress in parallel computations and VLSI implementation. The book is divided into six parts. Part one is a tutorial, beginning with an introduction, including (VLSI) parallel algorithms and some intriguing problems. It describes several applications of SVD in system identification and signal detection. It also deals with the fundamental harmonic retrieval problem and principal component analysis. Part two discusses details of model reduction, system identification and detection of multiple sinusoids in white noise, while part three is devoted to the total-least-squares and generalized singular value decomposition problems.

Table of Contents:
Parts: I. Tutorials. 1. Singular value decomposition: an introduction (P. Dewilde, E.F. Deprettere). 2. A variety of applications of singular value decomposition in identification and signal processing (J. Vandewalle, B. De Moor). 3. Eigen and singular value decomposition techniques for the solution of harmonic retrieval problems (M. Bouvet, H. Clergeot). 4. Advances in principal component signal processing (R.J. Vaccaro et al.). II: Model Reduction and Identification. 5. An overview of Hankel norm model reduction (A.C.M. Ran). 6. Identification of linear state space models with singular value decomposition using canonical correlation concepts (B. De Moor et al.). 7. Detection of multiple sinusoids in white noise: a signal enhancement approach (J.A. Cadzow et al.). III: Total Least Squares and GSVD. 8. The total least squares technique: computation, properties and applications (S. van Huffel, J. Vandewalle). 9. Oriented energy and oriented signal-to-signal ratio concepts in the analysis of vector sequences and time series (B. De Moor et al.). 10. ESPRIT - Estimation of signal parameters via rotational invariance techniques (R. Roy, T. Kailath). IV: Real-Time, Adaptive and Acceleration Algorithms. 11. On-line algorithm for signal separation based on SVD (D. Callaerts et al.). 12. A family of rank-one subspace updating methods (R.D. DeGroat, R.A. Roberts). 13. An array processing technique using the first principal component (P. Comon). 14. A novel method for reducing the computational load of SVD-based high discrimination algorithms (J.L. Mather). 15. Singular value decomposition of Frobenius Matrices for approximate and multi-objective signal processing tasks (E.A. Trachtenberg). V: Algorithms and Architectures. 16. On block Kogbetliantz methods for computation of the SVD (K.V. Fernando, S.J. Hammarling). 17. Reducing the number of sweeps in Hestenes' Method (P.C. Hansen). 18. Computational arrays for cyclic-by-rows Jacobi-algorithms (L. Thiele). 19. The symmetric tridiagonal eigenproblem on a custom linear array and hypercubes (E. de Doncker et al.). 20. Computing the singular value decomposition on the connection machine (L.M. Ewerbring, F.T. Luk). 21. Singular value decomposition on warp (M. Annaratone). 22. Execution of linear algebra operations on the SPRINT (A.J. De Groot et al.). VI. Resolution Limits, Enhancements and Questions. 23. An SVD analysis of resolution limits for harmonic retrieval problems (J.R. Casar, G. Cybenko). 24. A new application of SVD to harmonic retrieval (S. Mayrargue, J.P. Jouveau). 25. Retrieval of significant parameters from magnetic resonance signals via singular value decomposition (R. de Beer et al.).