SVD and Signal Processing, III

Matrix Singular Value Decomposition (SVD) and its application to problems in signal processing is explored in this book. The papers discuss algorithms and implementation architectures for computing the SVD, as well as a variety of applications such as systems and signal modeling and detection. The publication presents a number of keynote papers, highlighting recent developments in the field, namely large scale SVD applications, isospectral matrix flows, Riemannian SVD and consistent signal reconstruction. It also features a translation of a historical paper by Eugenio Beltrami, containing one of the earliest published discussions of the SVD. With contributions sourced from internationally recognised scientists, the book will be of specific interest to all researchers and students involved in the SVD and signal processing field.

A short introduction to Beltrami's paper. On bilinear functions (E. Beltrami, 1873; English translation: D. Boley). Keynote Papers. Implicitly restarted Arnoldi/Lanczos methods and large scale SVD applications (D.C. Sorensen). Isospectral matrix flows for numerical analysis (U. Helmke). The Riemannian singular value decomposition (O.B.L.R. De Moor). Consistent signal reconstruction and convex coding (N.T. Thao, M. Vetterli). Algorithms and Theoretical Concepts. The orthogonal qd-algorithm. Accurate singular value computation with the Jacobi method. Note on the accuracy of the eigensolution of matrices generated by finite elements. Transpose-free Arnoldi iterations for approximating extremal singular values and vectors. A Lanczos algorithm for computing the largest quotient singular values in regularization problems. A QR-like SVD algorithm for a product/quotient of several matrices. Approximating the PSVD and QSVD. Bounds on singular values revealed by QR factorizations. A stable algorithm for downdating the ULV decomposition. The importance of a good condition estimator in the URV and ULV algorithms. L-ULV(A), a low-rank revealing ULV algorithm. Fast algorithms for signal subspace fitting with Toeplitz matrices and applications to exponential data modeling. A block Toeplitz look-ahead Schur algorithm. The set of 2-by-3 matrix pencils - Kronecker structures and their transitions under perturbations - and versal deformation of matrix pencils. J-Unitary matrices for algebraic approximation and interpolation - the singular case. Architectures and Real Time Implementation. Sphericalized SVD updating for subspace tracking. Real-time architectures for sphericalized SVD updating. Systolic arrays for SVD downdating. Subspace separation by discretizations of double bracket flows. A continuous time approach to the analysis and design of parallel algorithms for subspace tracking. Stable Jacobi SVD updating by factorization of the orthogonal matrix. Transformational reasoning on time-adaptive Jacobi type algorithms. Adaptive direction-of-arrival estimation based on rank and subspace tracking. Multiple subspace ULV algorithm and LMS tracking. Applications. SVD-based analysis of image boundary distortion. The SVD in image restoration. Two dimensional zero error modeling for image compression. Robust image processing for remote sensing data. SVD for linear inverse problems. Fitting of circles and ellipses, least squares solution. The use of SVD for the study of multivariate noise and vibration problems. On applications of SVD and SEVD for NURBS identification. A tetradic decomposition of 4th-order tensors: application to the source separation problem. The application of higher order singular value decomposition to independent conponent analysis. Bandpass filtering for the HTLS estimation algorithm: design, evaluation and SVD analysis. Structure preserving total least squares method and its application to parameter estimation. Parameter estimation and order determination in the low-rank linear statistical model. Adaptive detection using low rank approximation to a data matrix. Realization of discrete-time periodic systems from input-output data. Canonical correlation analysis of the deterministic realization problem. An updating algorithm for on-line MIMO system identification. Subspace techniques in blind mobile radio channel identification and equalization using fractional spacing and/or multiple antennas. Reduction of general broad-band noise in speech by truncated QSVD: implementation aspects. SVD-based modelling of medical NMR signals. Inversion of bremsstrahlung spectra emitted by solar plasma. Authors Index.