Abstract

We present a new approach, based on the curvelet transform, for the fusion of magnetic resonance and computed tomography images. The objective of this fusion process is to obtain images, with as much detail as possible, for medical diagnosis. This approach is based on the application of the additive wavelet transform on both images and the segmentation of their detail planes into small overlapping tiles. The ridgelet transform is then applied on each of these tiles, and the fusion process is performed on the ridgelet transforms of the tiles. To maximize the benefit of the fused images, inverse interpolation techniques are used to obtain high resolution images from the low resolution fused images. Three inverse interpolation techniques are presented and compared. Simulation results show the superiority of the proposed curvelet fusion approach to the traditional discrete wavelet transform fusion technique. Results also reveal that inverse interpolation techniques have succeeded in obtaining high resolution images from the fused images with better quality than that of the traditional cubic spline interpolation technique.

© 2010 Optical Society of America

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  1. H. Moustafa and S. Rehan, “Applying image fusion techniques for the detection of hepatic lesions and acute intra-cerebral hemorrhage,” in ITI 4th International Conference on Information and Communications Technology 2006 (IEEE, 2006).
    [CrossRef]
  2. A. Wang, H. J. Sun, and Y. Y. Guan, “The application of wavelet transform to multi-modality medical image fusion,” in IEEE International Conference on Networking, Sensing and Control (IEEE, 2006), pp. 270-274.
    [CrossRef]
  3. C. Pohl and J. L. van Genderen, “Multisensor image fusion in remote sensing: concepts, methods and application,” Int. J. Remote Sens. 19, 823-854 (1998).
    [CrossRef]
  4. A. A. Goshtasby and S. Nikolov, “Image fusion: advances in the state of the art,” Inf. Fusion 8, 114-118 (2007).
    [CrossRef]
  5. M. Ouendeno, “Image fusion for improved perception,” Ph.D. dissertation (Florida Institute of Technology, 2007).
  6. M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
    [CrossRef]
  7. M. Choi, R. Y. Kim, and M.-G. Kim, “The curvelet transform for image fusion,” in ISPRS Congress Istanbul 2004, Proceedings of the Youth Forum, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2004), Vol. 35-B8, pp. 59-64.
  8. S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
    [CrossRef]
  9. S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.
  10. Y. Zhang and G. Hong, “An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images,” Inf. Fusion 6, 225-234 (2005).
    [CrossRef]
  11. S. Udomhunsakul and P. Wongsita, “Feature extraction in medical MRI images,” in Proceeding of 2004 IEEE Conference on Cybernetics and Intelligent Systems (IEEE, 2004), Vol. 1, pp. 340-344.
  12. L. Hui., “Multi-sensor imager registration and fusion,” Ph.D. dissertation (University of California, 1993).
  13. E. Canga, “Image fusion,” M.S. thesis (University of Bath, 2002).
  14. A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.
  15. Y. Shen, J. C. Ma, and L. Y. Ma, “An adaptive pixel weighted image fusion algorithm based on local priority for CT and MRI images,” in IEEE Instrumentation and Measurement Technology Conference (IEEE, 2006), pp. 420-422.
    [CrossRef]
  16. J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
    [CrossRef]
  17. G. Y. Chen and B. Kegl, “Image denoising with complex ridgelets,” Pattern Recogn. 578-585 (2007).
    [CrossRef]
  18. J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
    [CrossRef]
  19. F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
    [CrossRef]
  20. C. Chao and J. Tao, “Study of image magnification based on curvelet transformation,” in ISPRS Congress Beijing 2008, Proceedings of Commission II, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2008), Vol. 37-B2, pp. 289-292
  21. J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
    [CrossRef]
  22. B. B. Saevarsson, J. R. Sveinsson, and J. A. Benediktsson, “Combined wavelet and curvelet denoising of SAR images,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2004), Vol. 6, pp. 4235-4238.
  23. S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
    [CrossRef]
  24. S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
    [CrossRef]
  25. G. Piella, “New quality measures for image fusion,” in Proceedings of the Seventh International Conference on Information Fusion (Swedish Defence Research Agency, 2004), pp. 542-546.
  26. G. Piella and H. Heijmans, “A new quality metric for image fusion,” in Proceedings of International Conference on Image Processing (IEEE, 2003), Vol. 3, pp. 173-176.
  27. Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptual quality assessment of JPEG compressed images,” in Proceedings of IEEE 2002 International Conference on Image Processing (IEEE, 2002), pp. 477-480.
    [CrossRef]
  28. S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.
  29. T. Kratochvil and P. Simicek, “Utilization of MATLAB for picture quality evaluation” ( Institute of Radio Electronics, Brno University of Technology, 2005).

2008 (1)

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

2007 (2)

G. Y. Chen and B. Kegl, “Image denoising with complex ridgelets,” Pattern Recogn. 578-585 (2007).
[CrossRef]

A. A. Goshtasby and S. Nikolov, “Image fusion: advances in the state of the art,” Inf. Fusion 8, 114-118 (2007).
[CrossRef]

2006 (2)

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

2005 (3)

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

Y. Zhang and G. Hong, “An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images,” Inf. Fusion 6, 225-234 (2005).
[CrossRef]

2002 (2)

J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
[CrossRef]

S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
[CrossRef]

1999 (1)

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

1998 (1)

C. Pohl and J. L. van Genderen, “Multisensor image fusion in remote sensing: concepts, methods and application,” Int. J. Remote Sens. 19, 823-854 (1998).
[CrossRef]

Abd El-Samie, F. E.

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.

Abrial, P.

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

Ali, F. E.

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

Ali, M. A. M.

S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.

Arbiol, R.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

ben Hamza, A.

A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.

Benediktsson, J. A.

B. B. Saevarsson, J. R. Sveinsson, and J. A. Benediktsson, “Combined wavelet and curvelet denoising of SAR images,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2004), Vol. 6, pp. 4235-4238.

Bovik, A. C.

Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptual quality assessment of JPEG compressed images,” in Proceedings of IEEE 2002 International Conference on Image Processing (IEEE, 2002), pp. 477-480.
[CrossRef]

Candes, E.

J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
[CrossRef]

Canga, E.

E. Canga, “Image fusion,” M.S. thesis (University of Bath, 2002).

Chao, C.

C. Chao and J. Tao, “Study of image magnification based on curvelet transformation,” in ISPRS Congress Beijing 2008, Proceedings of Commission II, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2008), Vol. 37-B2, pp. 289-292

Chen, G. Y.

G. Y. Chen and B. Kegl, “Image denoising with complex ridgelets,” Pattern Recogn. 578-585 (2007).
[CrossRef]

Choi, M.

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

M. Choi, R. Y. Kim, and M.-G. Kim, “The curvelet transform for image fusion,” in ISPRS Congress Istanbul 2004, Proceedings of the Youth Forum, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2004), Vol. 35-B8, pp. 59-64.

Dessouky, M. I.

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

Donoho, D. L.

J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
[CrossRef]

El-Dokany, I. M.

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

Elkaffas, S. M.

S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.

El-Khamy, S. E.

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

El-Tobely, T. A.

S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.

Fors, O.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

Ghrare, S. E.

S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.

Goshtasby, A. A.

A. A. Goshtasby and S. Nikolov, “Image fusion: advances in the state of the art,” Inf. Fusion 8, 114-118 (2007).
[CrossRef]

Guan, Y. Y.

A. Wang, H. J. Sun, and Y. Y. Guan, “The application of wavelet transform to multi-modality medical image fusion,” in IEEE International Conference on Networking, Sensing and Control (IEEE, 2006), pp. 270-274.
[CrossRef]

Hadhoud, M. M.

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

He, Y.

A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.

Heijmans, H.

G. Piella and H. Heijmans, “A new quality metric for image fusion,” in Proceedings of International Conference on Image Processing (IEEE, 2003), Vol. 3, pp. 173-176.

Hong, G.

Y. Zhang and G. Hong, “An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images,” Inf. Fusion 6, 225-234 (2005).
[CrossRef]

Hui., L.

L. Hui., “Multi-sensor imager registration and fusion,” Ph.D. dissertation (University of California, 1993).

Ismail, M.

S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.

Jumari, K.

S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.

Kegl, B.

G. Y. Chen and B. Kegl, “Image denoising with complex ridgelets,” Pattern Recogn. 578-585 (2007).
[CrossRef]

Kim, H. O.

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

Kim, M.-G.

M. Choi, R. Y. Kim, and M.-G. Kim, “The curvelet transform for image fusion,” in ISPRS Congress Istanbul 2004, Proceedings of the Youth Forum, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2004), Vol. 35-B8, pp. 59-64.

Kim, R. Y.

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

M. Choi, R. Y. Kim, and M.-G. Kim, “The curvelet transform for image fusion,” in ISPRS Congress Istanbul 2004, Proceedings of the Youth Forum, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2004), Vol. 35-B8, pp. 59-64.

Kratochvil, T.

T. Kratochvil and P. Simicek, “Utilization of MATLAB for picture quality evaluation” ( Institute of Radio Electronics, Brno University of Technology, 2005).

Krim, H.

A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.

Kwok, J. T.

S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
[CrossRef]

Li, S.

S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
[CrossRef]

Ma, J. C.

Y. Shen, J. C. Ma, and L. Y. Ma, “An adaptive pixel weighted image fusion algorithm based on local priority for CT and MRI images,” in IEEE Instrumentation and Measurement Technology Conference (IEEE, 2006), pp. 420-422.
[CrossRef]

Ma, L. Y.

Y. Shen, J. C. Ma, and L. Y. Ma, “An adaptive pixel weighted image fusion algorithm based on local priority for CT and MRI images,” in IEEE Instrumentation and Measurement Technology Conference (IEEE, 2006), pp. 420-422.
[CrossRef]

Moudden, Y.

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

Moustafa, H.

H. Moustafa and S. Rehan, “Applying image fusion techniques for the detection of hepatic lesions and acute intra-cerebral hemorrhage,” in ITI 4th International Conference on Information and Communications Technology 2006 (IEEE, 2006).
[CrossRef]

Nam, M.-R.

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

Nguyen, M. K.

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

Nikolov, S.

A. A. Goshtasby and S. Nikolov, “Image fusion: advances in the state of the art,” Inf. Fusion 8, 114-118 (2007).
[CrossRef]

Nunez, J.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

Otazu, X.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

Ouendeno, M.

M. Ouendeno, “Image fusion for improved perception,” Ph.D. dissertation (Florida Institute of Technology, 2007).

Pala, V.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

Piella, G.

G. Piella, “New quality measures for image fusion,” in Proceedings of the Seventh International Conference on Information Fusion (Swedish Defence Research Agency, 2004), pp. 542-546.

G. Piella and H. Heijmans, “A new quality metric for image fusion,” in Proceedings of International Conference on Image Processing (IEEE, 2003), Vol. 3, pp. 173-176.

Pohl, C.

C. Pohl and J. L. van Genderen, “Multisensor image fusion in remote sensing: concepts, methods and application,” Int. J. Remote Sens. 19, 823-854 (1998).
[CrossRef]

Prades, A.

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

Ragheb, A. M.

S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.

Rehan, S.

H. Moustafa and S. Rehan, “Applying image fusion techniques for the detection of hepatic lesions and acute intra-cerebral hemorrhage,” in ITI 4th International Conference on Information and Communications Technology 2006 (IEEE, 2006).
[CrossRef]

Saad, A. A.

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

Saevarsson, B. B.

B. B. Saevarsson, J. R. Sveinsson, and J. A. Benediktsson, “Combined wavelet and curvelet denoising of SAR images,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2004), Vol. 6, pp. 4235-4238.

Salam, B. M.

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

Sallam, B. M.

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

Sheikh, H. R.

Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptual quality assessment of JPEG compressed images,” in Proceedings of IEEE 2002 International Conference on Image Processing (IEEE, 2002), pp. 477-480.
[CrossRef]

Shen, Y.

Y. Shen, J. C. Ma, and L. Y. Ma, “An adaptive pixel weighted image fusion algorithm based on local priority for CT and MRI images,” in IEEE Instrumentation and Measurement Technology Conference (IEEE, 2006), pp. 420-422.
[CrossRef]

Simicek, P.

T. Kratochvil and P. Simicek, “Utilization of MATLAB for picture quality evaluation” ( Institute of Radio Electronics, Brno University of Technology, 2005).

Starck, J. L.

J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
[CrossRef]

Starck, J.-L.

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

Sun, H. J.

A. Wang, H. J. Sun, and Y. Y. Guan, “The application of wavelet transform to multi-modality medical image fusion,” in IEEE International Conference on Networking, Sensing and Control (IEEE, 2006), pp. 270-274.
[CrossRef]

Sveinsson, J. R.

B. B. Saevarsson, J. R. Sveinsson, and J. A. Benediktsson, “Combined wavelet and curvelet denoising of SAR images,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2004), Vol. 6, pp. 4235-4238.

Tao, J.

C. Chao and J. Tao, “Study of image magnification based on curvelet transformation,” in ISPRS Congress Beijing 2008, Proceedings of Commission II, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2008), Vol. 37-B2, pp. 289-292

Udomhunsakul, S.

S. Udomhunsakul and P. Wongsita, “Feature extraction in medical MRI images,” in Proceeding of 2004 IEEE Conference on Cybernetics and Intelligent Systems (IEEE, 2004), Vol. 1, pp. 340-344.

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C. Pohl and J. L. van Genderen, “Multisensor image fusion in remote sensing: concepts, methods and application,” Int. J. Remote Sens. 19, 823-854 (1998).
[CrossRef]

Wang, A.

A. Wang, H. J. Sun, and Y. Y. Guan, “The application of wavelet transform to multi-modality medical image fusion,” in IEEE International Conference on Networking, Sensing and Control (IEEE, 2006), pp. 270-274.
[CrossRef]

Wang, Y.

S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
[CrossRef]

Wang, Z.

Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptual quality assessment of JPEG compressed images,” in Proceedings of IEEE 2002 International Conference on Image Processing (IEEE, 2002), pp. 477-480.
[CrossRef]

Willsky, A.

A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.

Wongsita, P.

S. Udomhunsakul and P. Wongsita, “Feature extraction in medical MRI images,” in Proceeding of 2004 IEEE Conference on Cybernetics and Intelligent Systems (IEEE, 2004), Vol. 1, pp. 340-344.

Zhang, Y.

Y. Zhang and G. Hong, “An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images,” Inf. Fusion 6, 225-234 (2005).
[CrossRef]

Astron. Astrophys. (1)

J.-L. Starck, P. Abrial, Y. Moudden, and M. K. Nguyen, “Wavelets, ridgelets and curvelets on the sphere,” Astron. Astrophys. 446, 1191-1204 (2006).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

M. Choi, R. Y. Kim, M.-R. Nam, and H. O. Kim, “Fusion of multispectral and panchromatic satellite images using the curvelet transform,” IEEE Geosci. Remote Sens. Lett. 2, 136-140 (2005).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

J. Nunez, X. Otazu, O. Fors, A. Prades, V. Pala, and R. Arbiol, “Multiresolution-based image fusion with additive wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 37, 1204-1211 (1999).
[CrossRef]

IEEE Trans. Image Process. (1)

J. L. Starck, E. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process. 11, 670-684 (2002).
[CrossRef]

Inf. Fusion (3)

Y. Zhang and G. Hong, “An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images,” Inf. Fusion 6, 225-234 (2005).
[CrossRef]

S. Li, J. T. Kwok, and Y. Wang, “Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images,” Inf. Fusion 3, 17-23 (2002).
[CrossRef]

A. A. Goshtasby and S. Nikolov, “Image fusion: advances in the state of the art,” Inf. Fusion 8, 114-118 (2007).
[CrossRef]

Infosystems (1)

S. E. Ghrare, M. A. M. Ali, M. Ismail, and K. Jumari, “Diagnostic quality evaluation of compressed medical images for telemedicine applications,” Infosystems , March 2008, pp. 15-19.

Int. J. Inf. Acquisition (1)

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, “A new approach for adaptive polynomial based image interpolation,” Int. J. Inf. Acquisition 3, 139-159 (2006).
[CrossRef]

Int. J. Remote Sens. (1)

C. Pohl and J. L. van Genderen, “Multisensor image fusion in remote sensing: concepts, methods and application,” Int. J. Remote Sens. 19, 823-854 (1998).
[CrossRef]

J. Digital Signal Process. (1)

S. E. El-Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie, “Efficient implementation of image interpolation as an inverse problem,” J. Digital Signal Process. 15(2), 137-152 (2005).
[CrossRef]

Pattern Recogn. (1)

G. Y. Chen and B. Kegl, “Image denoising with complex ridgelets,” Pattern Recogn. 578-585 (2007).
[CrossRef]

Prog. Electromagn. Res. C (1)

F. E. Ali, I. M. El-Dokany, A. A. Saad, and F. E. Abd El-Samie, “Curvelet fusion of MR and CT images,” Prog. Electromagn. Res. C 3, 215-224 (2008).
[CrossRef]

Other (16)

C. Chao and J. Tao, “Study of image magnification based on curvelet transformation,” in ISPRS Congress Beijing 2008, Proceedings of Commission II, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2008), Vol. 37-B2, pp. 289-292

S. Udomhunsakul and P. Wongsita, “Feature extraction in medical MRI images,” in Proceeding of 2004 IEEE Conference on Cybernetics and Intelligent Systems (IEEE, 2004), Vol. 1, pp. 340-344.

L. Hui., “Multi-sensor imager registration and fusion,” Ph.D. dissertation (University of California, 1993).

E. Canga, “Image fusion,” M.S. thesis (University of Bath, 2002).

A. ben Hamza, Y. He, H. Krim, and A. Willsky, “A multiscale approach to pixel-level image fusion,” in Integrated Computer-Aided Engineering (IOS Press, 2005), Vol. 12, pp. 135-146.

Y. Shen, J. C. Ma, and L. Y. Ma, “An adaptive pixel weighted image fusion algorithm based on local priority for CT and MRI images,” in IEEE Instrumentation and Measurement Technology Conference (IEEE, 2006), pp. 420-422.
[CrossRef]

M. Ouendeno, “Image fusion for improved perception,” Ph.D. dissertation (Florida Institute of Technology, 2007).

H. Moustafa and S. Rehan, “Applying image fusion techniques for the detection of hepatic lesions and acute intra-cerebral hemorrhage,” in ITI 4th International Conference on Information and Communications Technology 2006 (IEEE, 2006).
[CrossRef]

A. Wang, H. J. Sun, and Y. Y. Guan, “The application of wavelet transform to multi-modality medical image fusion,” in IEEE International Conference on Networking, Sensing and Control (IEEE, 2006), pp. 270-274.
[CrossRef]

S. M. Elkaffas, T. A. El-Tobely, A. M. Ragheb, and F. E. Abd El-Samie, “An integrated IHS and DWFT fusion technique for improving the spectral quality of remote sensing images,” in Proceedings of the 2nd International Computer Engineering Conference (ICENCO)(IEEE, 2006), pp. 54-61.

M. Choi, R. Y. Kim, and M.-G. Kim, “The curvelet transform for image fusion,” in ISPRS Congress Istanbul 2004, Proceedings of the Youth Forum, The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences (International Society for Photogrammetry and Remote Sensing, 2004), Vol. 35-B8, pp. 59-64.

G. Piella, “New quality measures for image fusion,” in Proceedings of the Seventh International Conference on Information Fusion (Swedish Defence Research Agency, 2004), pp. 542-546.

G. Piella and H. Heijmans, “A new quality metric for image fusion,” in Proceedings of International Conference on Image Processing (IEEE, 2003), Vol. 3, pp. 173-176.

Z. Wang, H. R. Sheikh, and A. C. Bovik, “No-reference perceptual quality assessment of JPEG compressed images,” in Proceedings of IEEE 2002 International Conference on Image Processing (IEEE, 2002), pp. 477-480.
[CrossRef]

T. Kratochvil and P. Simicek, “Utilization of MATLAB for picture quality evaluation” ( Institute of Radio Electronics, Brno University of Technology, 2005).

B. B. Saevarsson, J. R. Sveinsson, and J. A. Benediktsson, “Combined wavelet and curvelet denoising of SAR images,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2004), Vol. 6, pp. 4235-4238.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the discrete curvelet transform.

Fig. 2
Fig. 2

Decomposition in the AWT.

Fig. 3
Fig. 3

Reconstruction in the AWT.

Fig. 4
Fig. 4

Illustration of the pseudopolar grid in the frequency domain for an n × n image ( n = 8 ).

Fig. 5
Fig. 5

Flow graph of the discrete ridgelet transform.

Fig. 6
Fig. 6

1D signal interpolation. The pixel at position x is estimated using its neighborhood pixels and the distance s.

Fig. 7
Fig. 7

Original images for case (1): (a) MR image ( 256 × 256 ) and (b) CT image ( 256 × 256 ).

Fig. 8
Fig. 8

DWT of the images of case (1): (a) MR image and (b) CT image.

Fig. 9
Fig. 9

AWT approximation planes of the MR and CT images for case (1) after successive convolutions with the low-pass kernel: (a)  P 1 of MR image, (b)  P 2 of MR image, (c)  P 3 of MR image, (d)  P 1 of CT image, (e)  P 2 of CT image, and (f)  P 3 of CT image.

Fig. 10
Fig. 10

Fused images for case (1): (a) DWT fusion, (b) curvelet fusion, and (c) postprocessing of the curvelet fused image.

Fig. 11
Fig. 11

Fusion of decimated images of case (1): (a) wavelet fusion and (b) curvelet fusion.

Fig. 12
Fig. 12

Interpolation of the fused images of case (1) using inverse techniques: (on left) Interpolation of wavelet results, (on right) interpolation of curvelet results; (a) LMMSE interpolation, (b) LMMSE interpolation, (c) maximum entropy interpolation, (d) maximum entropy interpolation, (e) regularized interpolation, and (f) regularized interpolation.

Tables (6)

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Table 1 PSNR Results for the Wavelet and Curvelet Fusion of the Original MR and CT Images

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Table 2 Similarity Results for the Wavelet and Curvelet Fusion of the Original MR and CT Images

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Table 3 PSNR Results for the Wavelet and Curvelet Fusion of the Decimated MR and CT Images

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Table 4 Similarity Results for the Wavelet and Curvelet Fusion of the Decimated MR and CT Images

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Table 5 PSNR Results for Interpolation of the Fused Images

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Table 6 Similarity Results for Interpolation of the Fused Images

Equations (40)

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

I ( n 1 , n 2 ) = W 1 ( ϕ ( W ( I 1 ( n 1 , n 2 ) ) , W ( I 2 ( n 1 , n 2 ) ) ) ) ,
f 1 ( P ) = P 1 , f 2 ( P 1 ) = P 2 , f 3 ( P 2 ) = P 3 , , f n ( P n 1 ) = P n ,
H = 1 256 [ 1 4 6 4 1 4 16 24 16 4 6 24 36 24 6 4 16 24 16 4 1 4 6 4 1 ] .
Δ l = P l 1 P l ( l = 1 , 2 , , n ) .
P = l = 1 n Δ l + P n ,
ψ a , b , θ = a 1 / 2 ψ ( ( x 1 cos θ + x 2 sin θ b ) a )
R f ( a , b , θ ) = ψ a , b , θ ( x 1 , x 2 ) f ( x 1 , x 2 ) d x 1 d x 2 .
f ( x 1 , x 2 ) = 0 2 π 0 R f ( a , b , θ ) ψ a , b , θ ( x 1 , x 2 ) d a a 3 d b d θ 4 π .
R f ( θ , t ) = f ( x 1 , x 2 ) δ ( x 1 cos θ + x 2 sin θ t ) d x 1 d x 2 .
R f ( a , b , θ ) = R f ( θ , t ) a 1 / 2 ψ ( ( t b ) a ) d t .
f ^ ( x ) = k = c ( x k ) β ( x x k ) ,
β 3 ( x ) = { 2 3 | x | 2 + | x | 3 2 0 | x | < 1 ( 2 | x | ) 3 6 1 | x | < 2 0 2 | x | .
f ^ ( x ) = c ( x k 1 ) [ ( 3 + s ) 3 4 ( 2 + s ) 3 + 6 ( 1 + s ) 3 4 s 3 ] / 6 + c ( x k ) [ ( 2 + s ) 3 4 ( 1 + s ) 3 + 6 s 3 ] / 6 + c ( x k + 1 ) [ ( 1 + s ) 3 4 s 3 ] / 6 + c ( x k + 2 ) s 3 / 6
g = Df + v ,
D = D 1 D 1 ,
D 1 = 1 2 [ 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 ] .
min f ^ E [ ε t ε ] = E [ T r ( ε ε t ) ] ,
f ^ = Tg ,
min f ^ E [ T r ( ε ε t ) ] = E [ T r { ( f Tg ) ( f Tg ) t } ] = E [ T r { ff t T ( Dff t + vf t ) ( ff t D t + fv t ) T t + T ( Dff t D t + vf t D t + Dfv t + vv t ) T t } ] .
E [ fv t ] = [ 0 ] .
E [ ff t ] = R f , E [ vv t ] = R v .
min f ^ E [ T r ( ε ε t ) ] = T r { R f 2 TDR f + TDR f D t T t + TR v T t } .
T = R f D t ( DR f D t + R v ) 1 .
f ^ = R f D t ( DR f D t + R v ) 1 g .
R f = [ R 0 , 0 R 0 , 1 R 0 , N 1 R 1 , 0 R 1 , 1 R N - 1 , 0 R N 1 , N 1 ] ,
R i , j = E [ f i f j t ] .
R f = [ R 0 , 0 0 0 0 R 1 , 1 0 0 R N 1 , N 1 ] .
R f ( n 1 , n 2 ) 1 w 2 k = 1 w l = 1 w f ( k , l ) f ( n 1 + k , n 2 + l ) .
H e = i = 1 N 2 f i log 2 ( f i ) ,
H e = f t log 2 ( f ) .
Ψ ( f ) = f t log 2 ( f ) λ [ g Df 2 v 2 ] .
ln ( f ^ ) = 1 λ ln ( 2 ) [ 2 D t ( g D f ^ ) ] .
f ^ = exp [ 1 λ ln ( 2 ) [ 2 D t ( g D f ^ ) ] ] .
f ^ λ ln ( 2 ) [ 2 D t ( g D f ^ ) ] .
f ^ ( D t D + η I ) 1 D t g ,
Ψ ( f ^ ) = g D f ^ 2 + λ Q f ^ 2 ,
f ^ = ( D t D + λ Q t Q ) - 1 D t g .
f ^ i , j = ( D t D + λ Q t Q ) 1 D t g i , j ,
MSE = n 1 = 0 N 1 1 n 2 = 0 N 2 1 [ R ( n 1 , n 2 ) F ( n 1 , n 2 ) ] N 1 × N 2 ,
PSNR = 10 log ( f max 2 MSE ) ,

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