An Introduction to Finite Tight Frames

Description

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. The first book entirely devoted to finite frames, it features extensive exercises and MATLAB examples for classroom use, important examples, and numerous illustrations. The book provides an overview of the field of finite tight frames and discusses future research directions in the field. The book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing. Front Matter ....Pages i-xx Introduction (Shayne F. D. Waldron)....Pages 1-5 Tight frames (Shayne F. D. Waldron)....Pages 7-29 Frames (Shayne F. D. Waldron)....Pages 31-69 Canonical coordinates for vector spaces and affine spaces (Shayne F. D. Waldron)....Pages 71-98 Combining and decomposing frames (Shayne F. D. Waldron)....Pages 99-111 Variational characterisations of tight frames (Shayne F. D. Waldron)....Pages 113-149 The algebraic variety of tight frames (Shayne F. D. Waldron)....Pages 151-163 Projective unitary equivalence and fusion frames (Shayne F. D. Waldron)....Pages 165-187 Symmetries of tight frames (Shayne F. D. Waldron)....Pages 189-207 Group frames (Shayne F. D. Waldron)....Pages 209-243 Harmonic frames (Shayne F. D. Waldron)....Pages 245-264 Equiangular and Grassmannian frames (Shayne F. D. Waldron)....Pages 265-330 Tight frames generated by nonabelian groups (Shayne F. D. Waldron)....Pages 331-359 Weyl–Heisenberg SICs (Shayne F. D. Waldron)....Pages 361-427 Tight frames of orthogonal polynomials on the simplex (Shayne F. D. Waldron)....Pages 429-439 Continuous tight frames for finite dimensional spaces (Shayne F. D. Waldron)....Pages 441-470 Back Matter ....Pages 471-587