Modern Signal Processing

The mathematical basis of signal processing and its many areas of application is the subject of this book. Based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute, the volume emphasizes current challenges, new techniques adapted to new technologies, and certain recent advances in algorithms and theory.

Signal processing is everywhere in modern technology. Its mathematical basis and many areas of application are the subject of this book, based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory. The book covers two main areas: computational harmonic analysis, envisioned as a technology for efficiently analysing real data using inherent symmetries; and the challenges inherent in the acquisition, processing and analysis of images and sensing data in general [EMDASH] ranging from sonar on a submarine to a neuroscientist's fMRI study.

1. Introduction D. Rockmore and D. Healy; 2. Hyperbolic geometry, Nehari's theorem, electric circuits, and analog signal processing J. Allen and D. Healy; 3. Engineering applications of the motion-group Fourier transform G. Chirikjian and Y. Wang; 4. Fast x-ray and beamlet transforms for three-dimensional data D. Donoho and O. Levi; 5. Fourier analysis and phylogenetic trees S. Evans; 6. Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks A. Grunbaum; 7. An invitation to matrix-valued spherical functions A. Grunbaum, I. Pacharoni and J. Tirao; 8. Image registration for MRI P. Kostelec and S. Periaswamy; 9. The mathematics of JPEG 2000 Jin Li; 10. Integrated sensing and processing for statistical pattern recognition C. Priebe, D. Marchette and D. Healy; 11. Sampling of functions and sections for compact groups D. Maslen; 12. The Cooley-Tukey FFT and group theory D. Maslen and D. Rockmore; 13. Mathematical challenges for optical communications U. Osterberg; 14. The generalized spike process, sparsity and statistical independence N. Saito.

Covering the mathematical basis of signal processing and many areas of application, this 2004 book is based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory.