Computed tomography: from photon statistics to modern cone-beam CT ; with 10 tables
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 521 S. Illustrationen, Diagramme |
| ISBN: | 9783642072574 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV039594996 | ||
| 003 | DE-604 | ||
| 005 | 20230202 | ||
| 007 | t | ||
| 008 | 110922s2010 gw a||| |||| 00||| eng d | ||
| 020 | |a 9783642072574 |9 978-3-642-07257-4 | ||
| 035 | |a (OCoLC)756352132 | ||
| 035 | |a (DE-599)BVBBV039594996 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-1043 |a DE-29T |a DE-29 |a DE-19 |a DE-739 | ||
| 084 | |a YR 2520 |0 (DE-625)154095: |2 rvk | ||
| 084 | |a UH 5420 |0 (DE-625)145661: |2 rvk | ||
| 100 | 1 | |a Buzug, Thorsten M. |d 1963- |e Verfasser |0 (DE-588)129309559 |4 aut | |
| 245 | 1 | 0 | |a Computed tomography |b from photon statistics to modern cone-beam CT ; with 10 tables |c Thorsten M. Buzug |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIII, 521 S. |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Computertomografie |0 (DE-588)4113240-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Computertomografie |0 (DE-588)4113240-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024446007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024446007 | ||
Datensatz im Suchindex
| _version_ | 1804148431873114112 |
|---|---|
| adam_text | Contents 1 Introduction........................................................................................................ 1.1 Computed Tomography ֊ State of the Art.............................................. 1.2 Inverse Problems ..................................................................................... 1.3 Historical Perspective .............................................................................. 1.4 Some Examples......................................................................................... 1.5 Structure of the Book................................................................................ 1 1 2 4 7 11 2 Fundamentals of X-ray Physics.......................................................................... 2.1 Introduction............................................................................................. 2.2 X-ray Generation..................................................................................... 2.2.1 X-ray Cathode............................................................................. 2.2.2 Electron-Matter Interaction...................................................... 2.2.3 Temperature Load....................................................................... 2.2.4 X-ray Focus and Beam Quality.................................................. 2.2.5 Beam Filtering............................................................................. 2.2.6 Special Tube Designs................................................................. 2.3 Photon-Matter
Interaction...................................................................... 2.3.1 Lambert-Beer’s Law................................................................... 2.3.2 Mechanisms of Attenuation ...................................................... 2.4 Problems with Lambert-Beer’s Law....................................................... 2.5 X-ray Detection ....................................................................................... 2.5.1 Gas Detectors.............................................................................. 2.5.2 Solid-State Scintillator Detectors............................................... 2.5.3 Solid-State Flat-Panel Detectors................................................ 2.6 X-ray Photon Statistics ............................................................................ 2.6.1 Statistical Properties of the X-ray Source................................. 2.6.2 Statistical Properties of the X-ray Detector .............................. 2.6.3 Statistical Law of Attenuation.................................................... 2.6.4 Moments of the Poisson Distribution....................................... 2.6.5 Distribution for a High Number of X-ray Quanta .................. 2.6.6 Non-Poisson Statistics............................................................... 15 15 15 16 19 23 24 28 30 31 32 34 46 48 48 50 52 59 60 64 66 68 70 72
x Contents 3 4 Milestones of Computed Tomography............................................................. 75 3.1 Introduction............................................................................................ 75 3.2 Tomosynthesis ........................................................................................ 76 3.3 Rotation-Translation of a Pencil Beam (First Generation).................. 79 3.4 Rotation-Translation of a Narrow Fan Beam (Second Generation) ... 83 3.5 Rotation of a Wide Aperture Fan Beam (Third Generation).......... . . 84 3.6 Rotation-Fix with Closed Detector Ring (Fourth Generation)........... 87 3.7 Electron Beam Computerized Tomography......................................... 89 3.8 Rotation in Spiral Path............................................................................. 90 3.9 Rotation in Cone-Beam Geometry........................................................ 91 3.10 Micro-CT.................................................................................................. 93 3.11 PET-CT Combined Scanners................................................................. 96 3.12 Optical Reconstruction Techniques............................... 98 ï Fundamentals of Signal Processing............................................. 101 4.1 Introduction.............................................................................................. 102 4.2 Signals......................................................................................................... 102 4.3 Fundamental
Signals................................................................................ 102 4.4 Systems....................................................................................................... 104 4.4.1 Linearity......................................................................................... 104 4.4.2 Position or Translation Invariance............................................... 105 4.4.3 Isotropy and Rotation Invariance................................................. 105 4.4.4 Causality......................................................................................... 106 4.4.5 Stability........................................................................................... 106 4.5 Signal Transmission.................................................................................. 106 4.6 Dirac’s Delta Distribution......................................................................... 109 4.7 Dirac Comb................................................................................................ 112 4.8 Impulse Response...................................................................................... 115 4.9 Transfer Function...................................................................................... 116 4.10 Fourier Transform.................................................................................... 118 4.11 Convolution Theorem.............................................................................. 124 4.12 Rayleigh’s
Theorem.................................................................................... 125 4.13 Power Theorem.......................................................................................... 125 4.14 Filtering in the Frequency Domain.......................................................... 126 4.15 Hankel Transform .................................................................................... 128 4.16 Abel Transform.......................................................................................... 132 4.17 Hilbert Transform .................................................................................... 133 4.18 Sampling Theorem and Nyquist Criterion...............................................135 4.19 Wiener-Khintchine Theorem................................................................... 141 4.20 Fourier Transform of Discrete Signals.................................................... 144 4.21 Finite Discrete Fourier Transform............................................................ 145 4.22 z-Transform............................................................................................... 147 4.23 Chirp z-Transform.................................................................................... 148
Contents 5 Two-Dimensional Fourier-Based Reconstruction Methods............................. 151 5.1 Introduction ............................................................................................... 151 5.2 Radon Transformation ..............................................................................153 5.3 Inverse Radon Transformation and Fourier Slice Theorem.................... 163 5.4 Implementation of the Direct Inverse Radon Transform........................ 167 5.5 Linogram Method ...................................................................................... 170 5.6 Simple Backprojection................................................................................ 175 5.7 Filtered Backprojection.............................................................................. 179 5.8 Comparison Between Backprojection and Filtered Backprojection ... 183 5.9 Filtered Layergram: Deconvolution of the Simple Backprojection .... 187 5.10 Filtered Backprojection and Radons Solution...........................................191 5.11 Cormack Transform.................................................................................... 194 6 Algebraic and Statistical Reconstruction Methods............................................ 201 6.1 Introduction............................................................................................... 201 6.2 Solution with Singular Value Decomposition.......................................... 207 6.3 Iterative Reconstruction with ART........................................................... 211 6.4 Pixel Basis
Functions and Calculation of the System Matrix................ 218 6.4.1 Discretization of the Image: Pixels and Blobs............................ 219 6.4.2 Approximation of the System Matrix in the Case of Pixels .... 221 6.4.3 Approximation of the System Matrix in the Case of Blobs .... 222 6.5 Maximum Likelihood Method.................................................................. 223 6.5.1 Maximum Likelihood Method for Emission Tomography .... 224 6.5.2 Maximum Likelihood Method for Transmission CT............... 230 6.5.3 Regularization of the Inverse Problem ........................................ 235 6.5.4 Approximation Through Weighted Least Squares....................... 238 7 Technical Implementation................................................................................... 241 7.1 Introduction ............................................................................................... 241 7.2 Reconstruction with Real Signals............................................................. 242 7.2.1 Frequency Domain Windowing................................................... 244 7.2.2 Convolution in the Spatial Domain............................................. 247 7.2.3 Discretization of the Kernels.........................................................252 7.3 Practical Implementation of the Filtered Backprojection....................... 255 7.3.1 Filtering of the Projection Signal................................................. 255 7.3.2 Implementation of the Backprojection........................................ 258 7.4 Minimum Number of
Detector Elements................................................258 7.5 Minimum Number of Projections............................................................. 259 7.6 Geometry of the Fan-Beam System........................................................... 261 7.7 Image Reconstruction for Fan-Beam Geometry...................................... 262 7.7.1 Rebinning of the Fan Beams......................................................... 265 7.7.2 Complementary Rebinning........................................................... 270 Xï
XII Contents 7.8 7.7.3 Filtered Backprojection for Curved Detector Arrays............... 272 7.7.4 Filtered Backprojection for Linear Detector Arrays................... 280 7.7.5 Discretization of Backprojection for Fan-Beam Geometry .... 286 Quarter-Detector Offset and Sampling Theorem.................................... 293 8 Three-Dimensional Fourier-Based Reconstruction Methods...........................303 8.1 Introduction................................................................................................303 8.2 Secondary Reconstruction Based on 2D Stacks of Tomographic Slices 304 8.3 Spiral CT..................................................................................................... 309 8.4 Exact 3D Reconstruction in Parallel-Beam Geometry............................321 8.4.1 3D Radon Transform and the Fourier Slice Theorem............... 321 8.4.2 Three-Dimensional Filtered Backprojection .............................. 326 8.4.3 Filtered Backprojection and Radon’s Solution............................ 327 8.4.4 Central Section Theorem................................... 329 8.4.5 Orlov’s Sufficiency Condition............................. ......................... 335 8.5 Exact 3D Reconstruction in Cone-Beam Geometry............................... 336 8.5.1 Key Problem of Cone-Beam Geometry ...................................... 339 8.5.2 Method of Grangeat...................................................................... 341 8.5.3 Computation of the First Derivative on the Detector............... 347 8.5.4 Reconstruction with the Derivative
of the Radon Transform .. 348 8.5.5 Central Section Theorem and Grangeat’s Solution..................... 350 8.5.6 Direct 3D Fourier Reconstruction with the Cone-Beam Geometry.......................................................................... 354 8.5.7 Exact Reconstruction using Filtered Backprojection............... 357 8.6 Approximate 3D Reconstructions in Cone-Beam Geometry............... 366 8.6.1 Missing Data in the 3D Radon Space ..........................................366 8.6.2 FDK Cone-Beam Reconstruction for Planar Detectors........... 371 8.6.3 FDK Cone-Beam Reconstruction for Cylindrical Detectors... 388 8.6.4 Variations of the FDK Cone-Beam Reconstruction................... 390 8.7 Helical Cone-Beam Reconstruction Methods...........................................394 9 Image Quality and Artifacts............................................................................... 403 9.1 Introduction ............................................................................................... 403 9.2 Modulation Transfer Function of the Imaging Process........................... 404 9.3 Modulation Transfer Function and Point Spread Function................... 410 9.4 Modulation Transfer Function in Computed Tomography................... 412 9.5 SNR, DQE, and ROC.................................................................................. 421 9.6 2D Artifacts................................................................................................. 423 9.6.1 Partial Volume Artifacts ............................................................. 423
9.6.2 Beam-Hardening Artifacts..........................................................425 9.6.3 Motion Artifacts.......................................................................... 432 9.6.4 Sampling Artifacts ....................................................................... 435 9.6.5 Electronic Artifacts....................................................................... 435 9.6.6 Detector Afterglow....................................................................... 437 9.6.7 Metal Artifacts.............................................................................. 438
Contents 9.6.8 Scattered Radiation Artifacts ........................................................ 443 9.7 3D Artifacts................................................................................................. 445 9.7.1 Partial Volume Artifacts ............................................................... 446 9.7.2 Staircasing in Slice Stacks ............................................................. 448 9.7.3 Motion Artifacts............................................................................ 450 9.7.4 Shearing in Slice Stacks Due to Gantry Tilt................................. 451 9.7.5 Sampling Artifacts in Secondary Reconstruction........................ 454 9.7.6 Metal Artifacts in Slice Stacks........................................................ 455 9.7.7 Spiral CT Artifacts .........................................................................456 9.7.8 Cone-Beam Artifacts..................................................................... 458 9.7.9 Segmentation and Triangulation Inaccuracies............................. 459 9.8 Noise in Reconstructed Images.................................................................462 9.8.1 Variance of the Radon Transform ................................................ 462 9.8.2 Variance of the Reconstruction ................................................... 464 9.8.3 Dose, Contrast, and Variance....................................................... 467 10 Practical Aspects of Computed Tomography......................................................471 10.1 Introduction
............................................................................................. 471 10.2 Scan Planning........................................................................................... 471 10.3 Data Representation................................................................................. 475 10.3.1 Hounsfield Units........................................................................... 475 10.3.2 Window Width and Window Level............................................. 476 10.3.3 Three-Dimensional Representation ........................................... 479 10.4 Some Applications in Medicine............................................................... 482 11 Dose....................................................................................................................... 485 11.1 Introduction ............................................................................................. 485 11.2 Energy Dose, Equivalent Dose, and Effective Dose...............................486 11.3 Definition of Specific CT Dose Measures................................................487 11.4 Device-Related Measures for Dose Reduction........................................ 493 11.5 User-Related Measures for Dose Reduction .......................................... 499 References.................................................................................................................... 503 Subject Index.............................................................................................................. 511 XIII
|
| any_adam_object | 1 |
| author | Buzug, Thorsten M. 1963- |
| author_GND | (DE-588)129309559 |
| author_facet | Buzug, Thorsten M. 1963- |
| author_role | aut |
| author_sort | Buzug, Thorsten M. 1963- |
| author_variant | t m b tm tmb |
| building | Verbundindex |
| bvnumber | BV039594996 |
| classification_rvk | YR 2520 UH 5420 |
| ctrlnum | (OCoLC)756352132 (DE-599)BVBBV039594996 |
| discipline | Physik Medizin |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01387nam a2200337 c 4500</leader><controlfield tag="001">BV039594996</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110922s2010 gw a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642072574</subfield><subfield code="9">978-3-642-07257-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)756352132</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV039594996</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1043</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">YR 2520</subfield><subfield code="0">(DE-625)154095:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UH 5420</subfield><subfield code="0">(DE-625)145661:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Buzug, Thorsten M.</subfield><subfield code="d">1963-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)129309559</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computed tomography</subfield><subfield code="b">from photon statistics to modern cone-beam CT ; with 10 tables</subfield><subfield code="c">Thorsten M. Buzug</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 521 S.</subfield><subfield code="b">Illustrationen, Diagramme</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="650" ind1="0" ind2="7"><subfield code="a">Computertomografie</subfield><subfield code="0">(DE-588)4113240-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Computertomografie</subfield><subfield code="0">(DE-588)4113240-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</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=024446007&sequence=000001&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:BVB01-024446007</subfield></datafield></record></collection> |
| id | DE-604.BV039594996 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:07:02Z |
| institution | BVB |
| isbn | 9783642072574 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024446007 |
| oclc_num | 756352132 |
| open_access_boolean | |
| owner | DE-1043 DE-29T DE-29 DE-19 DE-BY-UBM DE-739 |
| owner_facet | DE-1043 DE-29T DE-29 DE-19 DE-BY-UBM DE-739 |
| physical | XIII, 521 S. Illustrationen, Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Buzug, Thorsten M. 1963- Verfasser (DE-588)129309559 aut Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables Thorsten M. Buzug Berlin [u.a.] Springer 2010 XIII, 521 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Computertomografie (DE-588)4113240-3 gnd rswk-swf Computertomografie (DE-588)4113240-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024446007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buzug, Thorsten M. 1963- Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables Computertomografie (DE-588)4113240-3 gnd |
| subject_GND | (DE-588)4113240-3 |
| title | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables |
| title_auth | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables |
| title_exact_search | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables |
| title_full | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables Thorsten M. Buzug |
| title_fullStr | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables Thorsten M. Buzug |
| title_full_unstemmed | Computed tomography from photon statistics to modern cone-beam CT ; with 10 tables Thorsten M. Buzug |
| title_short | Computed tomography |
| title_sort | computed tomography from photon statistics to modern cone beam ct with 10 tables |
| title_sub | from photon statistics to modern cone-beam CT ; with 10 tables |
| topic | Computertomografie (DE-588)4113240-3 gnd |
| topic_facet | Computertomografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024446007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT buzugthorstenm computedtomographyfromphotonstatisticstomodernconebeamctwith10tables |