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Erschienen in: Journal of Digital Imaging 6/2011

01.12.2011

Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets

verfasst von: Francisco Gómez, Cristina Santa Marta, Eduardo Romero

Erschienen in: Journal of Imaging Informatics in Medicine | Ausgabe 6/2011

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Abstract

This paper presents a novel method which reconstructs any desired 3D image resolution from raw cone-beam CT data. X-ray attenuation through the object is approximated using ridgelet basis functions which allow us to have multiresolution representation levels. Since the Radon data have preferential orientations by nature, a spherical wavelet transform is used to compute the ridgelet coefficients from the Radon shell data. The whole method uses the classical Grangeat’s relation for computing derivatives of the Radon data which are then integrated and projected to a spherical wavelet representation and back-reconstructed using a modified version of the well known back-projection algorithm. Unlike previous reconstruction methods, this proposal uses a multiscale representation of the Radon data and therefore allows fast display of low-resolution data level.
Literatur
1.
Zurück zum Zitat ISO/IEC FCD 14495-1: Information technology-lossless and near-lossless compression of continuous tone still images-part 1: baseline [JTC 1/SC 29/WG 1 N 575], in: ISO/IEC JTC 1/SC 29, 1997 ISO/IEC FCD 14495-1: Information technology-lossless and near-lossless compression of continuous tone still images-part 1: baseline [JTC 1/SC 29/WG 1 N 575], in: ISO/IEC JTC 1/SC 29, 1997
2.
Zurück zum Zitat Antoranz JC, Desco M, Molins A, Vaquero JJ: Design and development of a CT imaging system for small animals. Mol Imaging Biol 5(3):118, 2003 Antoranz JC, Desco M, Molins A, Vaquero JJ: Design and development of a CT imaging system for small animals. Mol Imaging Biol 5(3):118, 2003
3.
Zurück zum Zitat Bae KT, Whiting BR: CT data storage reduction by means of compressing projection data instead of images: feasibility study. Radiology 219:850–855, 2001PubMed Bae KT, Whiting BR: CT data storage reduction by means of compressing projection data instead of images: feasibility study. Radiology 219:850–855, 2001PubMed
4.
Zurück zum Zitat Whiting BR, Bae KT: Method and apparatus for compressing computed tomography raw projection data. United States Patent 20030228041, November 2003 Whiting BR, Bae KT: Method and apparatus for compressing computed tomography raw projection data. United States Patent 20030228041, November 2003
5.
Zurück zum Zitat Beylkin G: Discrete Radon transform. IEEE Trans Acoust Speech Signal Process 35(2):162–172, 1987CrossRef Beylkin G: Discrete Radon transform. IEEE Trans Acoust Speech Signal Process 35(2):162–172, 1987CrossRef
6.
Zurück zum Zitat Bogdanova I, Vandergheynst P, Antoine J, Jacques L, Morvidone M: Stereographic wavelet frames on the sphere. Appl Comput Harmon Anal 19(2):223–252, 2005CrossRef Bogdanova I, Vandergheynst P, Antoine J, Jacques L, Morvidone M: Stereographic wavelet frames on the sphere. Appl Comput Harmon Anal 19(2):223–252, 2005CrossRef
7.
Zurück zum Zitat Cachier P, Mangin J, Pennec X, Rivire D, Papadopoulos-Oranos D, Rgis J, Ayache N: Multisubject non-rigid registration of brain MRI using intensity and geometric features. In Proc. of MICCAI'01. in, pages 734–742, 2001. Cachier P, Mangin J, Pennec X, Rivire D, Papadopoulos-Oranos D, Rgis J, Ayache N: Multisubject non-rigid registration of brain MRI using intensity and geometric features. In Proc. of MICCAI'01. in, pages 734–742, 2001.
8.
Zurück zum Zitat Candes E: Ridgelets: Theory and Applications. PhD thesis, Stanford University, Department of Statistics, 1998 Candes E: Ridgelets: Theory and Applications. PhD thesis, Stanford University, Department of Statistics, 1998
9.
Zurück zum Zitat Carre P, Helbert D, Andres E: 3D fast ridgelet transform. In Image Processing, 2003. ICIP 2003. Proceedings. 2003 International Conference on, volume 1, pp 1021–1024 vol.1, Sept. 2003 Carre P, Helbert D, Andres E: 3D fast ridgelet transform. In Image Processing, 2003. ICIP 2003. Proceedings. 2003 International Conference on, volume 1, pp 1021–1024 vol.1, Sept. 2003
10.
Zurück zum Zitat Chen Z, Feng D: Compression of dynamic PET based on principal component analysis and JPEG 2000 in sinogram domain. In DICTA, pp 811–820, 2003 Chen Z, Feng D: Compression of dynamic PET based on principal component analysis and JPEG 2000 in sinogram domain. In DICTA, pp 811–820, 2003
11.
Zurück zum Zitat Taubman D, Marcellin MW: JPEG2000 image compression, fundamentals, standards and practice. Kluwer Academic Publishers, Norwell, 2002CrossRef Taubman D, Marcellin MW: JPEG2000 image compression, fundamentals, standards and practice. Kluwer Academic Publishers, Norwell, 2002CrossRef
12.
Zurück zum Zitat Ebrahimi T, Santa-Cruz D: A study of JPEG2000 still image coding versus other standards. In Proceeding of the X European Signal Processing Conference (EUSIPCO), vol. 2, pp 673–676, 2000 Ebrahimi T, Santa-Cruz D: A study of JPEG2000 still image coding versus other standards. In Proceeding of the X European Signal Processing Conference (EUSIPCO), vol. 2, pp 673–676, 2000
13.
Zurück zum Zitat de Crevoisier R, Tucker S, Dong L, Mohan R, Cheung R, Cox J, Kuban D: Increased risk of biochemical and local failure in patients with distended rectum on the planning CT for prostate cancer radiotherapy. Int J Radiat Oncol Biol Phys 62(4):965–973, 2005PubMedCrossRef de Crevoisier R, Tucker S, Dong L, Mohan R, Cheung R, Cox J, Kuban D: Increased risk of biochemical and local failure in patients with distended rectum on the planning CT for prostate cancer radiotherapy. Int J Radiat Oncol Biol Phys 62(4):965–973, 2005PubMedCrossRef
14.
Zurück zum Zitat Grangeat P: Mathematical framework of cone beam 3d reconstruction via the first derivative of the radon transform. in mathematical methods in tomography. In: Herman GT, Louis AK, Natterer F Eds. Lecture notes in mathematics,vol. 1497. Springer, New York, 1991, pp 66–97 Grangeat P: Mathematical framework of cone beam 3d reconstruction via the first derivative of the radon transform. in mathematical methods in tomography. In: Herman GT, Louis AK, Natterer F Eds. Lecture notes in mathematics,vol. 1497. Springer, New York, 1991, pp 66–97
15.
Zurück zum Zitat Hoffman E, Reinhardt J, Sonka M, Simon B, Guo J, Saba O, Chon D, Samrah S, Shikata H, Tschirren J, Palagyi K, Beck K, McLennan G: Characterization of the interstitial lung diseases via density-based and texture-based analysis of computed tomography images of lung structure and function. Acad Radiol 10(10):1104–1118, 2003PubMedCrossRef Hoffman E, Reinhardt J, Sonka M, Simon B, Guo J, Saba O, Chon D, Samrah S, Shikata H, Tschirren J, Palagyi K, Beck K, McLennan G: Characterization of the interstitial lung diseases via density-based and texture-based analysis of computed tomography images of lung structure and function. Acad Radiol 10(10):1104–1118, 2003PubMedCrossRef
16.
Zurück zum Zitat Hsieh J: Computed tomography: Principles, design, artifacts, and recent advances, volume PM114 of SPIE press monograph. SPIE Publications, Bellingham, 2003 Hsieh J: Computed tomography: Principles, design, artifacts, and recent advances, volume PM114 of SPIE press monograph. SPIE Publications, Bellingham, 2003
17.
Zurück zum Zitat Sánches I, Ribeiro E: Lossless image compression of computerized tomography projections. In SIBGRAPI'01: Proceedings of the XIV Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'01), page 385, 2001 Sánches I, Ribeiro E: Lossless image compression of computerized tomography projections. In SIBGRAPI'01: Proceedings of the XIV Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'01), page 385, 2001
18.
Zurück zum Zitat Benedetto J, Zayed A, Zayed A: Sampling, wavelets, and tomography. Kluwer Academic Publishers, Boston, 2003 Benedetto J, Zayed A, Zayed A: Sampling, wavelets, and tomography. Kluwer Academic Publishers, Boston, 2003
19.
Zurück zum Zitat Letourneau D, Martinez A, Lockman D, Yan D, Vargas C, Ivaldi G, Wong J: Assessment of residual error for online cone-beam ct-guided treatment of prostate cancer patients. Int J Radiat Oncol Biol Phys 62(4):1239–1246, 2005PubMedCrossRef Letourneau D, Martinez A, Lockman D, Yan D, Vargas C, Ivaldi G, Wong J: Assessment of residual error for online cone-beam ct-guided treatment of prostate cancer patients. Int J Radiat Oncol Biol Phys 62(4):1239–1246, 2005PubMedCrossRef
20.
Zurück zum Zitat Lu Y, Do MN: Multidimensional directional filter banks and surfacelets. IEEE Trans Image Process 16(4):918–931, 2007PubMedCrossRef Lu Y, Do MN: Multidimensional directional filter banks and surfacelets. IEEE Trans Image Process 16(4):918–931, 2007PubMedCrossRef
21.
Zurück zum Zitat Georgy S, Hejazi M, Yo-Sung H: Modified discrete radon transforms and their application to rotation-invariant image analysis. In International Workshop on Multimedia Signal Processing (MMSP), pages 429–434, 2006 Georgy S, Hejazi M, Yo-Sung H: Modified discrete radon transforms and their application to rotation-invariant image analysis. In International Workshop on Multimedia Signal Processing (MMSP), pages 429–434, 2006
22.
Zurück zum Zitat Muller-Merbach J: Simulation of X-ray projections for experimental 3D tomography. Technical report, Image Processing Laboratory Department of Electrical Engineering - Linkoping University, 1996 Muller-Merbach J: Simulation of X-ray projections for experimental 3D tomography. Technical report, Image Processing Laboratory Department of Electrical Engineering - Linkoping University, 1996
23.
Zurück zum Zitat Knauf A, Louis K, Oeckl S, Schön T: 3D-computerized tomography and its application to NDT. In Proceedings European Conference on Nondestructive Testing 2006, 2006 Knauf A, Louis K, Oeckl S, Schön T: 3D-computerized tomography and its application to NDT. In Proceedings European Conference on Nondestructive Testing 2006, 2006
24.
Zurück zum Zitat Paquin D, Levy D, Xing L: Multiscale registration of planning ct and daily cone beam CT images for adaptive radiation therapy. Med Phys 36(1):4–11, 2009PubMedCrossRef Paquin D, Levy D, Xing L: Multiscale registration of planning ct and daily cone beam CT images for adaptive radiation therapy. Med Phys 36(1):4–11, 2009PubMedCrossRef
25.
Zurück zum Zitat Siddiqui K, Siegel E, Reiner B, Crave O, Johnson J, Wu Z, Dagher J, Bilgin A, Marcellin M, Nadar M: Improved compressibility of multislice CT datasets using 3D JPEG2000 compression. In CARS 2004 - Computer Assisted Radiology and Surgery. pp 57–62, 2004 Siddiqui K, Siegel E, Reiner B, Crave O, Johnson J, Wu Z, Dagher J, Bilgin A, Marcellin M, Nadar M: Improved compressibility of multislice CT datasets using 3D JPEG2000 compression. In CARS 2004 - Computer Assisted Radiology and Surgery. pp 57–62, 2004
26.
Zurück zum Zitat Varela J, Tahoces P, Souto M, Vidal J: A compression and transmission scheme of computer tomography images for telemedicine based on JPEG2000. IEEE Trans Consum Electron 46(4):1103–1127, 2000CrossRef Varela J, Tahoces P, Souto M, Vidal J: A compression and transmission scheme of computer tomography images for telemedicine based on JPEG2000. IEEE Trans Consum Electron 46(4):1103–1127, 2000CrossRef
27.
Zurück zum Zitat Welland G: Beyond wavelets. Academic, San Diego, 2003 Welland G: Beyond wavelets. Academic, San Diego, 2003
28.
Zurück zum Zitat Pan X, Zou Y, Sidky E: Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan. Phys Med Biol 50:13–27, 2005PubMedCrossRef Pan X, Zou Y, Sidky E: Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan. Phys Med Biol 50:13–27, 2005PubMedCrossRef
Metadaten
Titel
Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets
verfasst von
Francisco Gómez
Cristina Santa Marta
Eduardo Romero
Publikationsdatum
01.12.2011
Verlag
Springer-Verlag
Erschienen in
Journal of Imaging Informatics in Medicine / Ausgabe 6/2011
Print ISSN: 2948-2925
Elektronische ISSN: 2948-2933
DOI
https://doi.org/10.1007/s10278-011-9369-y

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