The mojette transform: theory and applications
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
London
ISTE
2009
Hoboken, NJ Wiley |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XX, 274 S. |
| ISBN: | 9781848210806 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV035808517 | ||
| 003 | DE-604 | ||
| 005 | 20100922 | ||
| 007 | t | ||
| 008 | 091104s2009 xxu |||| 00||| eng d | ||
| 010 | |a 2008054465 | ||
| 020 | |a 9781848210806 |9 978-1-84821-080-6 | ||
| 035 | |a (OCoLC)298112175 | ||
| 035 | |a (DE-599)BVBBV035808517 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 | ||
| 050 | 0 | |a QA672 | |
| 082 | 0 | |a 515/.723 | |
| 082 | 0 | |a 516 | |
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 245 | 1 | 0 | |a The mojette transform |b theory and applications |c edited by Jeanpierre Guédon |
| 264 | 1 | |a London |b ISTE |c 2009 | |
| 264 | 1 | |a Hoboken, NJ |b Wiley | |
| 300 | |a XX, 274 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Radon transforms | |
| 650 | 4 | |a Geometric tomography | |
| 650 | 4 | |a Discrete geometry | |
| 650 | 0 | 7 | |a Radon-Transformation |0 (DE-588)4479199-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskrete Tomografie |0 (DE-588)4646495-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Radon-Transformation |0 (DE-588)4479199-9 |D s |
| 689 | 0 | 1 | |a Diskrete Tomografie |0 (DE-588)4646495-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Guédon, Jeanpierre |e Sonstige |4 oth | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0905/2008054465-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018667483 | ||
Datensatz im Suchindex
| _version_ | 1804140758627778560 |
|---|---|
| adam_text | Contents
Dedication
...................................... xiii
Preface
........................................ xv
Book Organization
................................ xix
First part. Mojette Theory
....................... 1
Chapter
1.
Discrete Geometry and Projections
.............. 3
David Coeurjolly, Nicolas
NORMAND
1.1.
Introduction
................................. 3
1.2.
Discrete pavings and discrete grids
................... 3
1.3.
Topological principles and discrete objects
.............. 5
1.4.
Arithmetic principles
........................... 7
1.4.1.
Preliminaries
............................. 7
1.4.2.
Lattices
................................ 8
1.4.3.
Farey series, rational angle and Stern-Brocot tree
...... 10
1.4.4.
Geometrical interpretations of arithmetic results
....... 10
1.5.
Discrete geometry elements
....................... 11
1.5.1.
Diophantine equations and discrete lines
............ 11
1.5.2.
Discrete projection along a rational angle
........... 14
1.5.3.
Convexity
............................... 16
1.5.4.
Pick s Theorem and related counting problems
........ 17
1.5.5.
Binary mathematical morphology and two-pixel structuring
elements
................................ 17
vi
The Mojette Transform
1.6.
Conclusion
.................................. 19
1.7.
Bibliography
................................ 19
Chapter
2.
Discrete Versions of the Radon Transform
......... 21
Imants Svalbe, Jeanpierre
GuÉDON
2.1.
Introduction
................................. 21
2.2.
General linear Radon transform
.................... 22
2.2.1.
The direct and inverse problems
................. 22
2.2.2.
The ill-posedness problem
.................... 23
2.2.3.
The summing paradigm and universal use for detectors
... 25
2.2.4.
Radon transform in geometry and dimension
......... 26
2.3.
Discrete versions of the Radon transform
............... 28
2.3.1.
The algebraic reconstruction technique (ART)
........ 28
2.3.2.
Matúš
and Flusser and the finite Radon transform (FRT)
. . 30
2.4.
Katz geometry
............................... 37
2.5.
Conclusion
.................................. 38
2.6.
Bibliography
................................ 38
Chapters. Direct Mojette Transform
.................... 41
Jeanpierre
GuÉDON,
Nicolas
Normand
3.1.
Introduction
................................. 41
3.2.
Computing Mojette projections
..................... 44
3.2.1.
General direct Mojette transform
................. 44
3.2.2.
Projections of shape characteristic function and mapping
function
................................ 47
3.2.3.
Alternative addition operators
.................. 48
3.3.
Properties
.................................. 49
3.3.1.
Linearity, central slice theorem
.................. 50
3.3.2.
Autocorrelation
........................... 52
3.3.3.
Angular sampling
.......................... 54
3.4.
Alternative pixel model
.......................... 54
3.4.1.
Spline pixel model
.......................... 55
3.4.1.1.
Spline
0
Mojette transform definition
........... 57
3.4.1.2.
Spline
n
Mojette transform definition
........... 60
3.4.1.3.
Spline
n
Mojette algorithms
................ 60
3.5.
Mojette transform in higher dimensions
................ 61
3.5.1. 3D
Mojette transform
........................ 61
3.5.2.
nD Mojette transform
........................ 63
Contents
vii
3.6.
Conclusion
.................................. 64
3.7.
Bibliography
................................ 64
Chapter
4.
Reconstructability with the
Inverse Mojette Transform
........................... 67
Jeanpierre
GuÉDON,
Nicolas
Normand
4.1.
Introduction
................................. 67
4.2.
The reconstructability of convex regions
............... 69
4.2.1.
Rectangular regions and the Katz criterion
........... 69
4.2.2.
General convex regions
....................... 70
4.3.
The choice of optimum angle sets
................... 71
4.3.1.
Red minimization from projections of a rectangular shape
. 72
4.3.2.
Redundancy minimization from a small overcomplete set
of projections
............................. 74
4.4.
Exact filtered backprojection reconstruction
............. 75
4.4.1.
Algorithm
............................... 75
4.5.
The notion of phantoms and partial reconstructability
....... 76
4.5.1.
Example
................................ 77
4.5.2.
Phantom definition
.*........................ 77
4.5.3.
Incomplete reconstruction theorem
............... 79
4.6.
Reconstructability in higher dimensions
................ 80
4.6.1.
Mojette reconstructability in
3D................. 80
4.6.2.
Mojette reconstructability in dimension
η
........... 81
4.7.
Conclusion
.................................. 81
4.8.
Bibliography
................................ 82
Chapter
5.
Inverse Mojette Transform Algorithms
........... 85
Nicolas
Normand, Imants
Svalbe, Pierre Evenou, Andrew Kingston
5.1.
Introduction
................................. 85
5.2.
Iterative local reconstruction (ILK)
................... 86
5.3.
Geometry-driven reconstruction (GDR)
................ 91
5.3.1.
The case where
g¿
= 1
for
і Є
Zq
................ 91
5.3.2.
The case where p,
=
m
for
і Є
Z¡
................ 94
5.3.3.
The case where pi
>
Pi-i and
# <
ft-i
............ 95
5.3.4.
The general case
........................... 95
5.3.5.
Discussion
............................... 96
5.4.
Global Mojette reconstruction
...................... 98
5.4.1.
Discrete exact reconstruction
................... 98
viii
The Mojette Transform
5.4.2.
The Farey backprojection
..................... 99
5.5.
Mojette inversion using the FRT
.................... 99
5.5.1.
The FRT, the Katz criterion, ghosts and information suffi¬
ciency
.................................. 101
5.5.2.
Ghosts, image redundancy and Mojette inversion
....... 103
5.5.3.
Untangling projections from ghost data using row or
column data
.............................. 104
5.5.4.
Untangling projections from ghost data using Latin squares
105
5.6.
Conclusion
..................................
Ill
5.7.
Bibliography
................................
Ill
Chapter
6.
Multiresolution Mojette Transform
.............. 115
Andrew Kingston,
Florent Autrusseau, Benoît Parrein
6.1.
Introduction
................................. 115
6.2.
Scalable Mojette projections
....................... 117
6.2.1.
Convolution property
........................ 118
6.2.2.
Downsampling property
...................... 119
6.2.3.
Scaling property
........................... 120
6.3.
Progressive reconstruction
........................ 121
6.3.1.
Projection schemes
......................... 121
6.3.2.
Reconstruction schemes
...................... 123
6.4.
Reconstruction of lossy or noisy scalable projections
....... 125
6.5.
Shear-stack Mojette projections
..................... 127
6.5.1.
Projection definition
......................... 127
6.5.2.
Reconstruction from shear-stack projections
.......... 132
6.5.2.1.
A review of slant-stack reconstruction procedure
. . . . 133
6.5.2.2.
Extension to blockwise reconstruction for shear-stacks
133
6.6.
Multiresolutional shear-stack Mojette projections
.......... 134
6.6.1.
The shear-stack downsampling property
............ 136
6.6.2.
The shear-stack convolution property
.............. 136
6.6.3.
The shear-stack scaling property
................. 137
6.6.4.
Projection description
........................ 138
6.7.
Reconstruction from multiresolution projections
.......... 141
6.7.1.
Quantization consideration
.................... 143
6.7.2.
Multiple description coding
.................... 144
6.8.
Conclusion
................................ 145
6.9.
Bibliography
............................. 146
Contents ix
Second part. Applications
........................ 149
Chapter
7.
Communication, Networks and Storage
........... 151
Benoît Parrein,
Fadi BouLOS, Nicolas
Normand,
Pierre Evenou
7.1.
Introduction
................................. 151
7.2.
Mojette coding: a geometric channel coding
............. 153
7.2.1.
A redundant representation
.................... 153
7.2.2.
Geometric buffers
.......................... 155
7.2.3.
Reconstruction with missing projections
............ 156
7.2.4.
Performances
............................. 157
7.2.4.1.
Overhead
............................ 158
7.2.4.2.
Complexity
........................... 160
7.2.4.3.
Functionalities
......................... 161
7.3.
Applications in communication and storage
............. 161
7.3.1.
Network coding
........................... 161
7.3.1.1.
Network coding process
................... 163
7.3.1.2.
The Mojette transform for network coding
....... 164
7.3.1.3.
Performance examples
.................... 165
7.3.2.
Self-organized networks
...................... 167
7.3.2.1.
MP-OLSR specifications
.................. 167
7.3.2.2.
Simulation results
....................... 168
7.3.3.
Distributed storage
......................... 171
7.4.
Priority encoding transmission
..................... 174
7.4.1.
Mojette priority encoding
..................... 174
7.4.1.1.
Separated geometric buffer
................. 174
7.4.1.2.
Concatenated geometric buffer
............... 175
7.4.2.
Optimal redundancy allocation
.................. 176
7.4.3.
Application to image transmission
................ 177
7.5.
Conclusion
.................................. 180
7.6.
Bibliography
................................ 180
Chapter
8.
Mojette Discrete Tomography
................. 183
Myriam
ServiÈres,
Jeanpierre
GuÉDON,
Nicolas
Normand, Yves
Bizais
8.1.
Introduction
................................. 183
8.2.
Operators
.................................. 184
χ
The Mojette Transform
8.2.1.
Mojette operator with general pixel model and spline
specialization
............................. 184
8.2.2.
Mojette backprojector M*
..................... 189
8.2.3.
Properties of
M¿MS
........................ 190
8.2.3.1.
M¡MS
expression
....................... 191
8.2.3.2.
M¡
Мб,
a Toeplitz-Block-Toeplitz matrix
........ 192
8.3.
Mojette operators in classic tomography algorithms
........ 193
8.3.1.
Test images and
Poisson
noise
.................. 194
8.3.2.
Mojette FBP vs classic FBP
.................... 195
8.3.2.1.
FBP algorithm
......................... 195
8.3.2.2.
Ko
filter
............................. 195
8.3.2.3.
Mojette FBP
.......................... 197
8.3.2.4.
Classical projection interpolations
............. 198
8.3.3.
Conjugate gradient Mojette reconstruction
........... 201
8.3.3.1.
Conjugate gradient Mojette algorithm
.......... 201
8.3.3.2.
Reconstruction without noise
................ 204
8.3.3.3.
Conditioning of
M¿M¿
................... 204
8.3.3.4.
Conjugate gradient Mojette reconstruction vs Mojette
FBP reconstruction
....................... 205
8.3.4.
Discrete exact Mojette tomographic reconstruction
..... 206
8.3.4.1.
Discrete exact Mojette tomographic reconstruction
algorithm
............................. 206
8.3.4.2.
Reconstructions with a reduced number of angles
. . . 207
8.3.4.3.
Interpolation between projections
............. 208
8.4.
Discussion
.................................. 211
8.5.
Conclusion
.................................. 213
8.6.
Bibliography
................................ 213
Chapter
9.
Lossless Compression
....................... 215
Andrew Kingston,
Florent Autrusseau
9.1.
Introduction
................................. 215
9.2.
A review of the preliminary study
................... 217
9.3.
Projection compression using multichannel audio techniques
.. 220
9.4.
Projection compression using multiband image techniques
.... 224
9.4.1.
Intra-projection compression
................... 224
9.4.2.
Inter-projection compression
................... 227
9.5.
Conclusions
................................. 232
9.6.
Bibliography
................................ 235
Contents xi
Chapter
10.
Mojette-based Security
..................... 239
Andrew Kingston,
Florent Autrusseau,
Eric Grall, Thierry
Hamon,
Benoît
Parrein
10.1.
Introduction
................................ 239
10.2.
Digital watermarking
.......................... 241
10.3.
Shared secret
............................... 244
10.4.
Encryption
................................. 246
10.4.1.
Encryption by reconstruction inconsistency
......... 246
10.4.2.
Symmetric block algorithm
................... 252
10.4.2.1.
Mojette round
........................ 252
10.4.2.2.
Mojette substitution
..................... 253
10.4.2.3.
Symmetric Mojette cipher
................. 256
10.4.3.
Selective encryption
........................ 258
10.4.3.1.
Joint compression and encryption
............ 260
10.4.3.2.
Cascaded Radon projections
............... 260
10.4.3.3.
Experimental results
.................... 263
10.5.
Conclusion
................................ 265
10.6.
Bibliography
................................ 266
List of Authors
................................... 269
Index
......................................... 271
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV035808517 |
| callnumber-first | Q - Science |
| callnumber-label | QA672 |
| callnumber-raw | QA672 |
| callnumber-search | QA672 |
| callnumber-sort | QA 3672 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)298112175 (DE-599)BVBBV035808517 |
| dewey-full | 515/.723 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 516 - Geometry |
| dewey-raw | 515/.723 516 |
| dewey-search | 515/.723 516 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01719nam a2200469zc 4500</leader><controlfield tag="001">BV035808517</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100922 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">091104s2009 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2008054465</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848210806</subfield><subfield code="9">978-1-84821-080-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)298112175</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035808517</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA672</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.723</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The mojette transform</subfield><subfield code="b">theory and applications</subfield><subfield code="c">edited by Jeanpierre Guédon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">ISTE</subfield><subfield code="c">2009</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, NJ</subfield><subfield code="b">Wiley</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 274 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Radon transforms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric tomography</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete geometry</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Radon-Transformation</subfield><subfield code="0">(DE-588)4479199-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diskrete Tomografie</subfield><subfield code="0">(DE-588)4646495-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Radon-Transformation</subfield><subfield code="0">(DE-588)4479199-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Diskrete Tomografie</subfield><subfield code="0">(DE-588)4646495-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Guédon, Jeanpierre</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0905/2008054465-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018667483</subfield></datafield></record></collection> |
| id | DE-604.BV035808517 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:05:04Z |
| institution | BVB |
| isbn | 9781848210806 |
| language | English |
| lccn | 2008054465 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018667483 |
| oclc_num | 298112175 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XX, 274 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | ISTE Wiley |
| record_format | marc |
| spelling | The mojette transform theory and applications edited by Jeanpierre Guédon London ISTE 2009 Hoboken, NJ Wiley XX, 274 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Radon transforms Geometric tomography Discrete geometry Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Diskrete Tomografie (DE-588)4646495-5 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 s Diskrete Tomografie (DE-588)4646495-5 s DE-604 Guédon, Jeanpierre Sonstige oth http://www.loc.gov/catdir/enhancements/fy0905/2008054465-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The mojette transform theory and applications Radon transforms Geometric tomography Discrete geometry Radon-Transformation (DE-588)4479199-9 gnd Diskrete Tomografie (DE-588)4646495-5 gnd |
| subject_GND | (DE-588)4479199-9 (DE-588)4646495-5 |
| title | The mojette transform theory and applications |
| title_auth | The mojette transform theory and applications |
| title_exact_search | The mojette transform theory and applications |
| title_full | The mojette transform theory and applications edited by Jeanpierre Guédon |
| title_fullStr | The mojette transform theory and applications edited by Jeanpierre Guédon |
| title_full_unstemmed | The mojette transform theory and applications edited by Jeanpierre Guédon |
| title_short | The mojette transform |
| title_sort | the mojette transform theory and applications |
| title_sub | theory and applications |
| topic | Radon transforms Geometric tomography Discrete geometry Radon-Transformation (DE-588)4479199-9 gnd Diskrete Tomografie (DE-588)4646495-5 gnd |
| topic_facet | Radon transforms Geometric tomography Discrete geometry Radon-Transformation Diskrete Tomografie |
| url | http://www.loc.gov/catdir/enhancements/fy0905/2008054465-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT guedonjeanpierre themojettetransformtheoryandapplications |