Quaternion and Clifford Fourier Transforms and Wavelets

Preface.- History of Quaternion and Clifford-Fourier Transforms and Wavelets.- Part I: Quaternions.- 1 Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis.- 2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations.- 3 Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals.- 4 Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions.- 5 Bochner’s Theorems in the Framework of Quaternion Analysis.- 6 Bochner-Minlos Theorem and Quaternion Fourier Transform.- Part II: Clifford Algebra.- 7 Square Roots of -1 in Real Clifford Algebras.- 8 A General Geometric Fourier Transform.- 9 Clifford-Fourier Transform and Spinor Representation of Images.- 10 Analytic Video (2D+t) Signals Using Clifford-Fourier Transforms in Multiquaternion Grassmann-Hamilton-Clifford Algebras.- 11 Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications.- 12 Color Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising.- 13 Seeing the Invisible and Maxwell’s Equations.- 14 A Generalized Windowed Fourier Transform in Real Clifford Algebra Cl_{0,n}.- 15 The Balian-Low theorem for the Windowed Clifford-Fourier Transform.- 16 Sparse Representation of Signals in Hardy Space.​- Index.