Title | Sampling, Wavelets, and Tomography [electronic resource] / edited by John J. Benedetto, Ahmed I. Zayed |
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Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8212-5 |
Descript | XXI, 344 p. online resource |
1 A Prelude to Sampling, Wavelets, and Tomography -- 1.1 Introduction -- 1.2 Sampling -- 1.3 Sampling and Frames -- 1.4 Wavelets and Multiresolution Analysis -- 1.5 Tomography, Spline Interpolation, and Medical Imaging -- References -- 2 Sampling Without Input Constraints: Consistent Reconstruction in Arbitrary Spaces -- 1 Introduction -- 2 Consistent Reconstruction -- 3 Reconstruction Scheme -- 4 Stability and Performance Analysis -- 5 Reconstruction from Nonredundant Measurements -- 6 Reconstruction from Redundant Measurements -- 7 Constructing Signals with Prescribed Properties -- References -- 3 An Introduction to Irregular Weyl-Heisenberg Frames -- 1 Introduction -- 2 Preliminaries -- 3 Density -- 4 Semi-Irregular WeylโHeisenberg Frames -- 5 General Irregular WeylโHeisenberg Frames -- 6 Concluding Remarks -- References -- 4 Robustness of Regular Sampling in Sobolev Algebras -- 1 Introduction -- 2 Wiener Amalgam Spaces W(B, LP) = W(B, ?P) -- 3 Generalities on Spline-type Spaces -- 4 Sobolev Spaces ?2S -- 5 LP-Theory -- 6 Changing the Smoothness Parameter -- 7 Changing the Sampling Lattice -- 8 Jitter Stability -- References -- 5 Sampling Theorems for Nonbandlimited Signals -- 1 Introduction -- 2 Signal Models -- 3 Biorthogonal Partners -- 4 Nonuniform Sampling -- 5 Derivative Sampling -- 6 Discrete-Time Case -- 7 Concluding Remarks -- References -- 6 Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets -- 1 Introduction -- 2 Status of Results in Multivariate Polynomial Matrix Factorization -- 3 Ladder Structure of Biorthogonal Multidimensional Multiband -- 4 Sampling in Wavelet Subspaces and Multiresolution Analysis -- 5 Wavelet Superresolution -- 6 Conclusions -- References -- 7 Function Spaces Based on Wavelet Expansions -- 1 Introduction -- 2 Wavelet expansions and sparseness -- 3 Robustness criteria -- 4 Distributions of wavelet coefficients -- 5 Spaces Ospsโ and contour-type functions -- References -- 8 Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces -- 1 Introduction and Preliminaries -- 2 Construction and Characterization of the Frame Multiwavelet Vector Sets Associated with a GFMRA -- 3 Examples of GFMRAs -- References -- 9 Sampling Theory and Parallel-Beam Tomography -- 1 Introduction -- 2 The Two-Dimensional Radon Transform -- 3 Sampling Lattices for the Radon Transform -- 4 The Support of (Rf) -- 5 Sampling Conditions -- 6 The Filtered Backprojection Algorithm -- 7 Analysis of the Effects of Undersampling -- 8 Further Developments -- References -- 10 Filtered Backprojection Algorithms for Spiral Cone Beam CT -- 1 Introduction -- 2 PI Line and PI Window -- 3 An Approximate Algorithm for Cone Beam CT -- 4 An Exact Algorithm for Cone Beam CT -- 5 Practical Implementation and Numerical Experiments -- 6 Selected Proofs -- References -- 11 Adaptive Irregular Sampling in Meshfree Flow Simulation -- 1 Introduction -- 2 Meshfree Particle Methods for Flow Simulation -- 3 Polyharmonic Splines -- 4 Adaptive Irregular Sampling -- 5 Meshfree Flow Simulation -- References -- 12 Thin-Plate Spline Interpolation -- 1 Introduction -- 2 A Brief Review of One-Dimensional Interpolation Techniques -- 3 Interpolating with Trigonometric Polynomials -- 4 Piecewise Linear Interpolation -- 5 Cubic Spline Interpolation -- 6 The Two-Dimensional Thin-Plate Spline Transformation -- References