Sampling, Wavelets, and Tomography

Couverture
Springer Science & Business Media, 2004 - 344 pages

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field.

This state-of-the-art book not only presents new results in these research areas, but it also demonstrates the role of sampling in both wavelet theory and tomography. Specific topics covered include:

* Robustness of Regular Sampling in Sobolev Algebras

* Irregular and Semi-Irregular Weyl-Heisenberg Frames

* Adaptive Irregular Sampling in Meshfree Flow Simulation

* Sampling Theorems for Non-Bandlimited Signals

* Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets

* Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces

* Sampling Theory and Parallel-Beam Tomography

* Thin-Plate Spline Interpolation in Medical Imaging

* Filtered Back-Projection Algorithms for Spiral Cone Computed Tomography

Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work.

Contributors: J.J. Benedetto, N.K. Bose, P.G. Casazza, Y.C. Eldar, H.G. Feichtinger, A. Faridani, A. Iske, S. Jaffard, A. Katsevich, S. Lertrattanapanich, G. Lauritsch, B. Mair, M. Papadakis, P.P. Vaidyanathan, T. Werther, D.C. Wilson, A.I. Zayed

 

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Table des matières

I
xv
II
xix
III
1
V
3
VI
6
VII
11
VIII
19
IX
23
LXXIX
149
LXXXI
152
LXXXII
153
LXXXIV
154
LXXXV
157
LXXXVI
158
LXXXVII
161
LXXXVIII
162

X
30
XI
33
XII
35
XIV
36
XV
38
XVI
40
XVIII
41
XIX
43
XXI
45
XXII
46
XXIII
47
XXV
49
XXVI
50
XXVII
51
XXVIII
52
XXIX
54
XXX
59
XXXI
61
XXXIV
64
XXXV
67
XXXVI
76
XXXVII
79
XXXIX
83
XL
84
XLI
90
XLII
93
XLIII
97
XLIV
100
XLV
103
XLVI
105
XLVII
110
XLVIII
115
XLIX
116
LI
119
LII
120
LIII
121
LIV
122
LV
124
LVI
126
LVII
129
LVIII
130
LIX
132
LXI
133
LXII
134
LXIII
135
LXV
137
LXIX
138
LXXI
140
LXXIII
141
LXXIV
142
LXXV
143
LXXVI
144
LXXVII
145
LXXVIII
148
LXXXIX
164
XC
165
XCI
168
XCII
172
XCIII
175
XCIV
179
XCVI
185
XCVII
205
XCVIII
210
C
216
CI
222
CII
225
CIV
226
CV
227
CVI
233
CVII
235
CVIII
237
CIX
243
CX
253
CXII
255
CXIII
259
CXIV
263
CXV
267
CXVI
272
CXVII
278
CXVIII
280
CXIX
283
CXX
284
CXXI
289
CXXII
291
CXXIII
292
CXXIV
294
CXXV
296
CXXVI
298
CXXVIII
299
CXXX
301
CXXXII
302
CXXXIII
307
CXXXIV
311
CXXXV
312
CXXXVI
314
CXXXVII
320
CXXXVIII
322
CXL
323
CXLI
325
CXLII
326
CXLIII
328
CXLIV
329
CXLVI
333
CXLVII
338
CXLVIII
339
CXLIX
341
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