SVD and Signal Processing, III (eBook)

Front Cover 1
SVD and Signal Processing, III: Algorithms, Architectures and Applications 4
Copyright Page 5
Preface 6
Contents 8
A short introduction to Beltrami's paper 14
On bilinear functions 18
PART 1: KEYNOTE PAPERS 32
Chapter 1. Implicitly restarted Arnoldi/Lanczos methods and large scale SVD applications 34
Chapter 2. Isospectral matrix flows for numerical analysis 46
Chapter 3. The Riemannian singular value decomposition 74
Chapter 4. Consistent signal reconstruction and convex coding 92
PART 2: ALGORITHMS AND THEORETICAL CONCEPTS 110
Chapter 5. The orthogonal qd-algorithm 112
Chapter 6. Accurate singular value computation with the Jacobi method 120
Chapter 7. Note on the accuracy of the eigensolution of matrices generated by finite elements 128
Chapter 8. Transpose-free Arnoldi iterations for approximating extremal singular values and vectors 136
Chapter 9. A Lanczos algorithm for computing the largest quotient singular values in regularization problems 144
Chapter 10. A QR-like SVD algorithm for a product/quotient of several matrices 152
Chapter 11. Approximating the PSVD and QSVD 162
Chapter 12. Bounds on singular values revealed by QR factorizations 170
Chapter 13. A stable algorithm for downdating the ULV decomposition 180
Chapter 14. The importance of a good condition estimator in the URV and ULV algorithms 188
Chapter 15. L-ULV(A), a low-rank revealing ULV algorithm 196
Chapter 16. Fast algorithms for signal subspace fitting with Toeplitz matrices and applications to exponential data modeling 204
Chapter 17. A block Toeplitz look-ahead Schur algorithm 212
Chapter 18. The set of 2-by-3 matrix pencils - Kronecker structures and their transitions under perturbations – And versal deformations of matrix pencils 220
Chapter 19. J-Unitary matrices for algebraic approximation and interpolation –The singular case 222
PART 3: ARCHITECTURES AND REAL TIME IMPLEMENTATION 238
Chapter 20. Sphericalized SVD Updating for Subspace Tracking 240
Chapter 21. Real-time architectures for sphericalized SVD Updating 248
Chapter 22. Systolic Arrays for SVD Downdating 256
Chapter 23. Subspace separation by discretizations of double bracket flows 264
Chapter 24. A continuous time approach to the analysis and design of parallel algorithms for subspace tracking 272
Chapter 25. Stable Jacobi SVD updating by factorization of the orthogonal matrix 280
Chapter 26. Transformational reasoning on time-adaptive Jacobi type algorithms 290
Chapter 27. Adaptive direction-of-arrival estimation based on rank and subspace tracking 300
Chapter 28. Multiple subspace ULV algorithm and LMS tracking 308
PART 4: APPLICATIONS 316
Chapter 29. SVD-based analysis of image boundary distortion 318
Chapter 30. The SVD in image restoration 328
Chapter 31. Two dimensional zero error modeling for image compression 336
Chapter 32. Robust image processing for remote sensing data 346
Chapter 33. SVD for linear inverse problems 354
Chapter 34. Fitting of circles and ellipses, least squares solution 362
Chapter 35. The use of SVD for the study of multivariate noise and vibration problems 370
Chapter 36. On applications of SVD and SEVD for NURBS identification 380
Chapter 37. A tetradic decomposition of 4th-order tensors : Application to the source separation problem 388
Chapter 38. The application of higher order singular value decomposition to independent component analysis 396
Chapter 39. Bandpass filtering for the HTLS estimation algorithm: design, evaluation and SVD analysis 404
Chapter 40. Structure preserving total least squares method and its application to parameter estimation 412
Chapter 41. Parameter estimation and order determination in the low-rank linear statistical model 420
Chapter 42. Adaptive detection using low rank approximation to a data matrix 428
Chapter 43. Realization of discrete-time periodic systems from input-output data 436
Chapter 44. Canonical correlation analysis of the deterministic realization problem 446
Chapter 45. An updating algorithm for on-line MIMO system identification 454
Chapter 46. Subspace techniques in blind mobile radio channel identification and equalization using fractional spacing and/or multiple antennas 462
Chapter 47. Reduction of general broad-band noise in speech by truncated QSVD: implementation aspects 472
Chapter 48. SVD-based modelling of medical NMR signals 480
Chapter 49. Inversion of bremsstrahlung spectra emitted by solar plasma 488
Authors Index 498