Wavelet Theory: An Elementary Approach with Applications
David K. Ruch, Patrick J. Van Fleet · 2009
Preface. Acknowledgments. 1 The Complex Plane and the Space L 2 (R). 1.1 Complex Numbers and Basic Operations. Problems. 1.2 The Space L 2 (R). Problems. 1.3 Inner Products. Problems. 1.4 Bases and Projections. Problems. 2 Fourier Series and Fourier Transformations. 2.1 Euler's Formula and the Complex Exponential Function. Problems. 2.2 Fourier Series. Problems. 2.3 The Fourier Transform. Problems. 2.4 Convolution and B-Splines. Problems. 3 Haar Spaces. 3.1 The Haar Space V 0 . Problems. 3.2 The General Haar Space V j . Problems. 3.3 The Haar Wavelet Space W 0 . Problems. 3.4 The General Haar Wavelet Space W j . Problems. 3.5 Decomposition and Reconstruction. Problems. 3.6 Summary. 4 The Discrete Haar Wavelet Transform and Applications. 4.1 The One-Dimensional Transformation. Problems. 4.2 The Two-Dimensional Transformation. Problems. 4.3 Edge Detection and Naive Image Compression. 5 Multiresolution Analysis. 5.1 Multiresolution Analysis. Problems. 5.2 The View from the Transform Domain. Problems. 5.3 Examples of Multiresolution Analyses. Problems. 5.4 Summary. 6 Daubechies Scaling Functions and Wavelets. 6.1 Constructing the Daubechies Scaling Functions. Problems. 6.2 The Cascade Algorithm. Problems. 6.3 Orthogonal Translates, Coding and Projections. Problems. 7 The Discrete Daubechies Transformation and Applications. 7.1 The Discrete Daubechies Wavelet Transform. Problems. 7.2 Projections and Signal and Image Compression. Problems. 7.3 Naive Image Segmentation. Problems. 8 Biorthogonal Scaling Functions and Wavelets. 8.1 A Biorthogonal Example and Duality. Problems. 8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces. Problems. 8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair. Problems. 8.4 Decomposition and Reconstruction. Problems. 8.5 The Discrete Biorthogonal Wavelet Transformation. Problems. 8.6 Riesz Basis Theory. Problems. 9 Wavelet Packets. 9.1 Constructing Wavelet Packet Functions. Problems. 9.2 Wavelet Packet Spaces. Problems. 9.3 The Discrete Packet Transform and Best Basis Algorithm. Problems. 9.4 The FBI Fingerprint Compression Standard. Appendix A: Huffman Coding. Problems. References. Topic Index. Author Index.