Abstract

A fast, powerful and stable filter based on combined wavelet and Fourier analysis for the elimination of horizontal or vertical stripes in images is presented and compared with other types of destriping filters. Strict separation between artifacts and original features allowing both, suppression of the unwanted structures and high degree of preservation of the original image information is endeavoured. The results are validated by visual assessments, as well as by quantitative estimation of the image energy loss. The capabilities and the performance of the filter are tested on a number of case studies related to applications in tomographic imaging. The case studies include (i) suppression of waterfall artifacts in electron microscopy images based on focussed ion beam nanotomography, (ii) removal of different types of ring artifacts in synchrotron based X-ray microtomography and (iii) suppression of horizontal stripe artifacts from phase projections in grating interferometry.

© 2009 Optical Society of America

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2008 (1)

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

2007 (4)

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

P. Rakwatin, W. Takeuchi, and Y. Yasuoka, "Stripe Noise Reduction in MODIS Data by Combining Histogram Matching with Facet Filter," IEEE Trans. Geosci. Remote Sens. 45, 1844-1856 (2007).
[CrossRef]

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

2006 (3)

M. Boin and A. Haibel, "Compensation of Ring Artefacts in Synchrotron Tomographic Images," Opt. Express 14, 12071-12075 (2006).
[CrossRef] [PubMed]

J. G. Liu and G. L. K. Morgan, "FFT Selective and Adaptive Filtering for Removal of Systematic Noise in ETM+ Imageodesy Images," IEEE Trans. Geosci. Remote Sens. 44, 3716-3724 (2006).
[CrossRef]

J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

2005 (1)

2004 (2)

J. Sijbers and A. Postnov, "Reduction of Ring Artefacts in High Resolution Micro-CT Reconstructions," Phys.Med. Biol. 49, N247-N253 (2004).
[CrossRef] [PubMed]

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Albani and B. Klinkenberg, "A Spatial Filter for the Removal of Striping Artifacts in Digital Elevation Models," Photogramm. Engineering & Remote Sens. 69, 755-765 (2003).

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

2001 (2)

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

J. Torres and S. O. Infante, "Wavelet Analysis for the Elimination of Striping Noise in Satellite Images," Opt. Eng. 40, 1309-1314 (2001).
[CrossRef]

2000 (1)

C. Christopoulos and T. Ebrahimi, "The JPEG2000 Still Image Coding System: An Overview," IEEE Trans. Consumer Electron. 47, 1103-1127 (2000).
[CrossRef]

1998 (1)

C. Raven, "Numerical Removal of Ring Artifacts in Microtomography," Rev. Sci. Instrum. 69, 2978-2980 (1998).
[CrossRef]

1989 (1)

S. G. Mallat, "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Trans. Pattern Anal. Machine Intelligence 11, 674-693 (1989).
[CrossRef]

1978 (1)

G. Kowalski, "Suppression of Ring Artefacts in CT Fan-Beam Scanners," IEEE Trans. Nucl. Sci. NS-25, 1111-1116 (1978).
[CrossRef]

Abela, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Albani, M.

M. Albani and B. Klinkenberg, "A Spatial Filter for the Removal of Striping Artifacts in Digital Elevation Models," Photogramm. Engineering & Remote Sens. 69, 755-765 (2003).

Arrell, K.

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

Betemps, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Boin, M.

Chen, J.

J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

Chen, Q.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Christopoulos, C.

C. Christopoulos and T. Ebrahimi, "The JPEG2000 Still Image Coding System: An Overview," IEEE Trans. Consumer Electron. 47, 1103-1127 (2000).
[CrossRef]

Cloetens, P.

Conover, D.

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

David, C.

Diaz, A.

Donoghue, D.

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

Ebrahimi, T.

C. Christopoulos and T. Ebrahimi, "The JPEG2000 Still Image Coding System: An Overview," IEEE Trans. Consumer Electron. 47, 1103-1127 (2000).
[CrossRef]

Gasser, P.

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

Gasser, Ph.

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

Groso, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Guo, H.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

Haibel, A.

Henein, S.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Holzer, L.

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

Indutnyi, F.

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

Infante, S. O.

J. Torres and S. O. Infante, "Wavelet Analysis for the Elimination of Striping Noise in Satellite Images," Opt. Eng. 40, 1309-1314 (2001).
[CrossRef]

Isenegger, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Kaech, A.

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

Klinkenberg, B.

M. Albani and B. Klinkenberg, "A Spatial Filter for the Removal of Striping Artifacts in Digital Elevation Models," Photogramm. Engineering & Remote Sens. 69, 755-765 (2003).

Kowalski, G.

G. Kowalski, "Suppression of Ring Artefacts in CT Fan-Beam Scanners," IEEE Trans. Nucl. Sci. NS-25, 1111-1116 (1978).
[CrossRef]

Lange, M.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Lin, H.

J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

Liu, J. G.

J. G. Liu and G. L. K. Morgan, "FFT Selective and Adaptive Filtering for Removal of Systematic Noise in ETM+ Imageodesy Images," IEEE Trans. Geosci. Remote Sens. 44, 3716-3724 (2006).
[CrossRef]

Mallat, S. G.

S. G. Mallat, "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Trans. Pattern Anal. Machine Intelligence 11, 674-693 (1989).
[CrossRef]

Meister, D.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Mikuljan, G.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

Morgan, G. L. K.

J. G. Liu and G. L. K. Morgan, "FFT Selective and Adaptive Filtering for Removal of Systematic Noise in ETM+ Imageodesy Images," IEEE Trans. Geosci. Remote Sens. 44, 3716-3724 (2006).
[CrossRef]

Münch, B.

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

Ning, R.

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

Pfeiffer, F.

Postnov, A.

J. Sijbers and A. Postnov, "Reduction of Ring Artefacts in High Resolution Micro-CT Reconstructions," Phys.Med. Biol. 49, N247-N253 (2004).
[CrossRef] [PubMed]

Rakwatin, P.

P. Rakwatin, W. Takeuchi, and Y. Yasuoka, "Stripe Noise Reduction in MODIS Data by Combining Histogram Matching with Facet Filter," IEEE Trans. Geosci. Remote Sens. 45, 1844-1856 (2007).
[CrossRef]

Raven, C.

C. Raven, "Numerical Removal of Ring Artifacts in Microtomography," Rev. Sci. Instrum. 69, 2978-2980 (1998).
[CrossRef]

Shao, Y.

J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

Sijbers, J.

J. Sijbers and A. Postnov, "Reduction of Ring Artefacts in High Resolution Micro-CT Reconstructions," Phys.Med. Biol. 49, N247-N253 (2004).
[CrossRef] [PubMed]

Stampanoni, M.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, D. Meister, M. Lange, R. Betemps, S. Henein, and R. Abela, "TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs.," Synchrotron Radiation Instrumentation 879, 848-851 (2007).

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "Quantitative X-ray phase imaging with a grating interferometer," Opt. Express 13, 6296-6304 (2005).
[CrossRef] [PubMed]

Takeuchi, W.

P. Rakwatin, W. Takeuchi, and Y. Yasuoka, "Stripe Noise Reduction in MODIS Data by Combining Histogram Matching with Facet Filter," IEEE Trans. Geosci. Remote Sens. 45, 1844-1856 (2007).
[CrossRef]

Tang, X.

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

Torres, J.

J. Torres and S. O. Infante, "Wavelet Analysis for the Elimination of Striping Noise in Satellite Images," Opt. Eng. 40, 1309-1314 (2001).
[CrossRef]

Wang, W.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

Wegmann, M.

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

Weitkamp, T.

Wepf, R.

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

Winnefeld, F.

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

Wise, S.

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

Wood, J.

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

Yang, L.

J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

Yasuoka, Y.

P. Rakwatin, W. Takeuchi, and Y. Yasuoka, "Stripe Noise Reduction in MODIS Data by Combining Histogram Matching with Facet Filter," IEEE Trans. Geosci. Remote Sens. 45, 1844-1856 (2007).
[CrossRef]

Yu, R.

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

Zhu, B.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

Ziegler, E.

Zingg, A.

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

Cement and Concrete Research (1)

A. Zingg, L. Holzer, A. Kaech, and F. Winnefeld, "TheMicrostructure of Dispersed and Non-dispersed Fresh Cement Pastes - New In-sight by Cryo-Microscopy," Cement and Concrete Research 38, 522-529 (2008).
[CrossRef]

Earth Surface Processes and Landforms (1)

K. Arrell, S. Wise, J. Wood, and D. Donoghue, "Spectral Filtering as a Method of Visualising and Removing Striped Artefacts in Digital Elevation Data," Earth Surface Processes and Landforms 33, 943-961 (2007).
[CrossRef]

IEEE Trans. Consumer Electron. (1)

C. Christopoulos and T. Ebrahimi, "The JPEG2000 Still Image Coding System: An Overview," IEEE Trans. Consumer Electron. 47, 1103-1127 (2000).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

P. Rakwatin, W. Takeuchi, and Y. Yasuoka, "Stripe Noise Reduction in MODIS Data by Combining Histogram Matching with Facet Filter," IEEE Trans. Geosci. Remote Sens. 45, 1844-1856 (2007).
[CrossRef]

J. G. Liu and G. L. K. Morgan, "FFT Selective and Adaptive Filtering for Removal of Systematic Noise in ETM+ Imageodesy Images," IEEE Trans. Geosci. Remote Sens. 44, 3716-3724 (2006).
[CrossRef]

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, "Destriping CMODIS Data by Power Filtering," IEEE Trans. Geosci. Remote Sens. 41, 2119-2124 (2003).
[CrossRef]

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J. Chen, H. Lin, Y. Shao, and L. Yang, "Oblique Striping Removal in Remote Sensing Imagery Based on Wavelet Transform," Int. J. Remote Sens. 27, 1717-1723 (2006).
[CrossRef]

J. Microsc. (2)

L. Holzer, F. Indutnyi, P. Gasser, B. Münch, and M. Wegmann, "Three-Dimensional Analysis of Porous BaTiO3 Ceramics Using FIB Nanotomography," J. Microsc. 216, 84-95 (2004).
[CrossRef] [PubMed]

L. Holzer, Ph. Gasser, A. Kaech, M. Wegmann, A. Zingg, R. Wepf, and B. Münch, "Cryo-FIB-nanotomography for Quantitative Analysis of Particle Structures in Cement Suspensions," J. Microsc. 227, 216-228 (2007).
[CrossRef] [PubMed]

Med. Phys. (1)

X. Tang, R. Ning, R. Yu, and D. Conover, "Cone Beam Volume CT Image Artifacts Caused by Defective Cells in X-Ray Flat Panel Imagers and the Artifact Removal Using a Wavelet-Analysis-Based Algorithm," Med. Phys. 28, 812-825 (2001).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. Torres and S. O. Infante, "Wavelet Analysis for the Elimination of Striping Noise in Satellite Images," Opt. Eng. 40, 1309-1314 (2001).
[CrossRef]

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Photogramm. Engineering & Remote Sens. (1)

M. Albani and B. Klinkenberg, "A Spatial Filter for the Removal of Striping Artifacts in Digital Elevation Models," Photogramm. Engineering & Remote Sens. 69, 755-765 (2003).

Phys.Med. Biol. (1)

J. Sijbers and A. Postnov, "Reduction of Ring Artefacts in High Resolution Micro-CT Reconstructions," Phys.Med. Biol. 49, N247-N253 (2004).
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D. Prêt, F. Villiéras, I. Bihannic, S. Sammartino, L. Michot, M. Pelletier, and M. Stampanoni "Influence of hydration on montmorillonite organization: a multiscale study based on synchrotron X-ray tomography, diffraction and small angle scattering of neutrons," in prep. for Langmuir.

A.C. Kak and M. Slaney, "Principles of computerized tomographic imaging," Society for Industrial and Applied Mathematics, Philadelphia, PA (2001).

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I. Daubechies, Ten lectures on Wavelets (SIAM, Philadelphia, PA 1992).

Z. Zhang, Z. Shi, W. Guo, and S. Huang, "Adaptively Image De-striping through Frequency Filtering," ICO20: Opt. Inf. Proc. Proc. SPIE 6027, 60273V (2006).
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Z. Wang and Y. Fu, "Frequency-domain Regularized Deconvolution for Images with Stripe Noise," ICIG Proc. 4th Intl Conf. Image and Graphics, 110-115 (2007).

A. Lyckegaard, G. Johnson, and P. Tafforeau, "Correction of Ring Artefacts in X-ray Tomographic Images," 3D IMS, 1st Conf. 3D-Imaging on Materials and Systems, sept.8-12, Carans-Maubuisson, 101 (2008).

M. Axelsson, S. Svensson, and G. Borgefors, "Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images," Pattern. Recog. 4174, 61-70 (2006).
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S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, Second Edition, ISBN: 978-0-12-466606-1,1-end 1999).

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E. J. Candés and D. L. Donoho, "Curvelets - a surprisingly effective nonadaptive representation for objects with edges," in Curves and Surfaces, L. L. Schumaker et al. (eds), (Vanderbilt University Press, Nashville, TN, 1-10, 1999).

S. Foucher, V. Gouaillier, and L. Gagnon, "Global semantic classification of scenes using ridgelet transform," IS&T/SPIE Symposium on Electronic Imaging: SPIE Human Vision 5292, San Jose, 402-413 (2004).

F. Tsai, S. Lin, J. Rau, L. Chen, and G. Liu, "Destriping Hyperion Imagery Using Spline Interpolation," Proc. 26th Asian Conf. Remote Sensing, November, Hanoi, Vietnam (2005).

Z. Cai, "Ringing Artefact Reduction Using Adaptive Averaging Filtering," Proc. ISCE, UK, June, 156-159 (2004).

M. J. Oimoen, "An Effective Filter for Removal of Production Artifacts in U.S. Geological Survey 7.5-Minute Digital Elevation Models," Proc. 14th Intl Conf. Appl. Geol. Remote Sens., November, Las Vegas, N USAV, 311-319 (2000).

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Figures (22)

Fig. 1.
Fig. 1.

Scaling (blue) and wavelet (red) functions of four different types of wavelets: Haar (DB1), DB2, DB4 and DB42.

Fig. 2.
Fig. 2.

A multiscale wavelet decomposition is the successive fragmentation of the previous low frequency band signal into its high and low frequency bands by using a high pass (a) and a low pass function (b), and successive downsampling (c) of the coefficients on each band by a factor of 2, in order to preserve the total number of coefficients, which is 1024 for this example.

Fig. 3.
Fig. 3.

Original Lena image impaired by two vertical stripe offsets (left). The wavelet decomposition up to the level 4 is visualized in the centre. The low pass coefficients cl are displayed at the upper left, the horizontal details coefficients ch for each decomposition level are displayed in the vertical row to the left (3), the diagonal detail coefficients cd in the diagonal row (2). The striping noise is condensed to the vertical details coefficients cv in the horizontal row at the top (1). The details bands that are affected by the vertical striping noise are enframed with red boxes (only as qualitative markers). After applying the 2D Fourier transforms to those bands (right), the information of the striping noise will be completely condensed to the abscissa. The transforms have been applied to each R, G, B channel separately and overlayed to color wavelet coefficients.

Fig. 4.
Fig. 4.

Stripes elimination from the original Lena image (Fig.3, left) by using different strategies. The left image displays the result after removing the relevant vertical details bands [1] (wavelet: DB42), the centre image shows the result of damping the horizontal frequencies in x̂ for ŷ close to zero, and the right image displays the results of the combined method proposed in this work.

Fig. 5.
Fig. 5.

Matlab code for combined wavelet-FFT stripe filtering.

Fig. 6.
Fig. 6.

Image consisting of vertical stripes only (left), its wavelet multiscale decomposition with L = 4 obtained using the Haar wavelet (centre), and the subsequent FFT transform of the vertical details coefficients cv (right), illustrating that by applying this transformation chain, the entire image information is condensed into narrow frequency bands and the remaining low pass coefficients cl only.

Fig. 7.
Fig. 7.

Four artificial images created by randomly selecting complex coefficients ĉ v l,m,n=�� at �� = 0 (left image), �� = ±1, �� = ±2, and �� = ±3 (right image), while setting all remaining coefficients to zero.

Fig. 8.
Fig. 8.

This figure demonstrates the high structural preservation capability of the proposed wavelet-FFT filter. For this purpose, the original Lena (1) was scaled by a factor of ≈ 1/50 and subsequently has been corrupted with a pattern of heavy horizontal and vertical stripes (2). The resulting image (3) has then been treated with the wavelet-FFT filter and rescaled (4). The difference between the original Lena (1) and the filtered image (4) is displayed in (5).

Fig. 9.
Fig. 9.

The Lena image ravaged by seven stripes of different colors and sizes (24, 16, 12, 8, 4, 2, 1 pixels, (Fig.3, top left) was filtered with the DB15 wavelet at σ → 0 by assuming different highest decomposition levels L = 0,⋯,7. The bottom rightmost image is the original Lena.

Fig. 10.
Fig. 10.

Three images (Lena, cement, sinogram), which have been filtered with Daubechies wavelets at different size (DB1 to DB43). The damping coefficients are σ = 1.5 (Lena), σ = 7.0 (cement), σ = 1.5 (sinogram), and the highest decomposition levels was L = 4, L = 8, L = 4, respectively.

Fig. 11.
Fig. 11.

Destriping of a single section from a 3D volume of unhydrated particles of cement paste accessed by FIB-nt. The original image to the top left is severely affected by the waterfall effect. The top right image is the result of wavelet, the bottom left the result of FFT, and the bottom right the result of wavelet-FFT destriping procedure. The original picture was taken from Holzer et al. [30].

Fig. 12.
Fig. 12.

Destriping of a single section from a 3D volume accessed by FIB-nt (see Fig.11, top left) by using different damping coefficients σ= 1,2,4,8 (from left to right), as well as different highest decomposition levels L = 2,4,6,8 (from top to bottom).

Fig. 13.
Fig. 13.

Removal of sharp marked ring artifact from a reconstructed slice with the wavelet-FFT filter (DB25 wavelet) by damping of the 1-5 components with σ = 2.4 - (a) Original sinogram and (c) reconstruction, (b) Filtered sinogram and (d) reconstruction. Sample: 530 million-year-old fossilized embryo of an animal closely related to modern marine worms (priapulids), pixel size: 0.375 μm. Sample courtesy: S. Bengtson, Swedish Museum of Natural History, Stockholm, Sweden. Image acquired at the TOMCAT beamline [34], at the SLS-PSI, Villligen, Switzerland.

Fig. 14.
Fig. 14.

Magnified portion of Fig.13(c) and (d) around the image center - (a) Original image, (b) Artifacts removed with a DB25 wavelet and by filtering the 1–5 components with σ = 2.4. Features hidden in (a) by the rings are clearly revealed in (b) after artifact removal (e.g. arrows).

Fig. 15.
Fig. 15.

Horizontal (a) and vertical (b) line profile through the center of the reconstructed slices in Fig.13(c) and (d).

Fig. 16.
Fig. 16.

Removal of a wide strong ring artifact from a reconstructed slice with the wavelet-FFT filter (DB30 wavelet) - (a) Original image, (b) Artifact removed by filtering the 1-5 components with σ = 2.4 (c) Artifact removed by filtering the 0-6 components with σ = 2.4. Sample: compacted purified smectite, pixel size: 0.74 μm. Sample courtesy: D. Prêt, Poitiers University, Poitiers, France [35]. Image acquired at the TOMCAT beamline [34], at the SLS-PSI, Villligen, Switzerland.

Fig. 17.
Fig. 17.

Magnified portion of Fig.16 around the ring artifact - (a) Original image, (b) Artifact removed with a DB30 wavelet and by filtering the 1-5 components with σ = 2.4 (c) Artifact removed with a DB30 wavelet and by filtering the 0-6 components with σ = 2.4.

Fig. 18.
Fig. 18.

Magnified portion of Fig.16 around the image center - (a) Original image, (b) Artifact removed with a DB30 wavelet and by filtering the 1–5 components with σ= 2.4 (c) Artifact removed with a DB30 wavelet and by filtering the 0–6 components with σ= 2.4.

Fig. 19.
Fig. 19.

Horizontal (a) and vertical (b) line profile through the center of the reconstructed slices in Fig.16.

Fig. 20.
Fig. 20.

Removal of wide and faint ring artifacts from a reconstructed slice with the wavelet-FFT filter (DB15 wavelet) by damping of the 0-4 components with σ = 2.4 - (a) Original and (b) Filtered reconstructed slice. Sample: 28μm cylinder of hardened cement paste, impregnated with epoxy resin, pixel size: 100 nm. Image acquired at the TOMCAT beamline [34], at the SLS-PSI, Villligen, Switzerland.

Fig. 21.
Fig. 21.

Horizontal (a) and vertical (b) line profile through the center of the reconstructed slices in Fig.20.

Fig. 22.
Fig. 22.

Removal of horizontal stripes from a phase projection generated through integration of a DPC radiograph obtained with the Differential Phase Contrast (DPC) technique [36] based on a grating interferometer and a phase stepping approach - (a) Original and (b) Filtered projection (DB30, L = 3 and σ = 3). Sample: BaTiO 3 sphere, pixel size: 100 nm. Image acquired at the TOMCAT beamline [34], at the SLS-PSI, Villligen, Switzerland.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

f(t)nan·Γn(t)
Γn(t),Γm(t)=nΓn(t)·Γm(t)={1,n=m0,nm
an=f(t),Γn(t)
f(t)=nCL,n·ΦL,n(t)+l=1Lndl,n·Ψl,n(t)
Ψl,n(t)=2l/2·Ψ0(t2l·n2l)
f(x,y)=mnClL,m,n·ΦL,m,n(x,y)+l=1Lmnchl,m,n·Ψhl,m,n(x,y)
+l=1Lmncvl,m,n·Ψvl,m,n(x,y)+l=1Lmncdl,m,n·Ψdl,m,n(x,y)
f(x,y)W={clL,m,n,chl,m,n,cvl,m,n,cdl,m,n},l{1,,L}
a(x,y)={A,x[xa,,xe]0,otherwise
g(x̂,ŷ)=1eŷ22·σ2
εs1Nx=0N1sx2
εr=sosf2so2

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