Abstract

Traditional mammography can be positively complemented by phase contrast and scattering x-ray imaging, because they can detect subtle differences in the electron density of a material and measure the local small-angle scattering power generated by the microscopic density fluctuations in the specimen, respectively. The grating-based x-ray interferometry technique can produce absorption, differential phase contrast (DPC) and scattering signals of the sample, in parallel, and works well with conventional X-ray sources; thus, it constitutes a promising method for more reliable breast cancer screening and diagnosis. Recently, our team proved that this novel technology can provide images superior to conventional mammography. This new technology was used to image whole native breast samples directly after mastectomy. The images acquired show high potential, but the noise level associated to the DPC and scattering signals is significant, so it is necessary to remove it in order to improve image quality and visualization. The noise models of the three signals have been investigated and the noise variance can be computed. In this work, a wavelet-based denoising algorithm using these noise models is proposed. It was evaluated with both simulated and experimental mammography data. The outcomes demonstrated that our method offers a good denoising quality, while simultaneously preserving the edges and important structural features. Therefore, it can help improve diagnosis and implement further post-processing techniques such as fusion of the three signals acquired.

© 2013 OSA

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    [CrossRef] [PubMed]
  2. M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
    [CrossRef] [PubMed]
  3. E. Jerhotova, J. Svihlik, and A. Prochazka, “Biomedical image volumes denoising via the wavelet transform,” in Applied Biomedical Engineering, G.D. Gargiulo and A. McEwan, eds. (Intech, 2011), pp 435–458 (2009).
  4. S. Rangarajan, R. Venkataramanan, and R. Shah, “Image denoising using wavelets,” (technical report, 2002).
  5. D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika81(3), 425–455 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. P. Kisilev, D. Shaked, and S. H. Lim, “Noise and signal activity maps for better imaging algorithms,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2007), pp.117–120.
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    [CrossRef]
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    [CrossRef] [PubMed]

2011 (2)

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

S. K. Mohideen, S. A. Perumal, and M. M Sathik, “Image denoising using discrete wavelet transform,” J. Comput. Sci.8(1), 8–11 (2011).

2010 (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

2009 (3)

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika81(3), 425–455 (2009).
[CrossRef]

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Z. Wang and A. C. Bovik, “Mean-square error : Love it or leave it?,” IEEE Signal Process Mag.26(1), 98–117 (2009).
[CrossRef]

2006 (1)

J.F. Aujol and G. Gilboa, “Constrained and SNR-based solutions for TV-Hilbert space image denoising,” J. Math. Imaging Vision26,217–237 (2006).
[CrossRef]

2003 (1)

P. Sakellaropoulos, L. Costaridou, and G. Panayiotakis, “A wavelet-based spatially adaptive method for mammographic contrast enhancement,” Phys. Med. Biol.48(6), 787–803 (2003).
[CrossRef] [PubMed]

2002 (1)

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

2000 (2)

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process.9(9), 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef]

1965 (1)

B.M. Priestley, “Evolutionary spectra and non-stationary processes,” J. R. Stat. Soc. Series B27(2), 204–237 (1965).

Angelini, E.

Y. Jin, E. Angelini, and A. Laine, “Wavelets in medical image processing: denoising, segmentation and registration,” in Handbook of Biomedical Image Analysis, Volume 1: Segmentation models, Part A, J. S. Suri, D.L. Wilson, and S. Laxminarayan, eds. (Kluwer Academic/Plenum Publishers, 2005), pp. 305–358.
[CrossRef]

Aujol, J.F.

J.F. Aujol and G. Gilboa, “Constrained and SNR-based solutions for TV-Hilbert space image denoising,” J. Math. Imaging Vision26,217–237 (2006).
[CrossRef]

Bovik, A. C.

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Z. Wang and A. C. Bovik, “Mean-square error : Love it or leave it?,” IEEE Signal Process Mag.26(1), 98–117 (2009).
[CrossRef]

Bui, T. D.

G. Y. Chen, T. D. Bui, and A. Krzyzak, “Image denoising using neighbouring wavelet coefficients,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 917–920.

Chang, S. G.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process.9(9), 1522–1531 (2000).
[CrossRef]

Chen, G. Y.

G. Y. Chen, T. D. Bui, and A. Krzyzak, “Image denoising using neighbouring wavelet coefficients,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 917–920.

Costaridou, L.

P. Sakellaropoulos, L. Costaridou, and G. Panayiotakis, “A wavelet-based spatially adaptive method for mammographic contrast enhancement,” Phys. Med. Biol.48(6), 787–803 (2003).
[CrossRef] [PubMed]

David, C.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Donoho, D. L.

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika81(3), 425–455 (2009).
[CrossRef]

Eberhard, W.

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Galbo, C. E.

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Gilboa, G.

J.F. Aujol and G. Gilboa, “Constrained and SNR-based solutions for TV-Hilbert space image denoising,” J. Math. Imaging Vision26,217–237 (2006).
[CrossRef]

Goossens, B.

B. Goossens, A. Pizurica, and W. Philips, “Em-based estimation of spatially variant correlated image noise,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2008), pp. 1744–1747.

Gupta, S.

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Hauser, N.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Hohl, M. K.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Jerhotova, E.

E. Jerhotova, J. Svihlik, and A. Prochazka, “Biomedical image volumes denoising via the wavelet transform,” in Applied Biomedical Engineering, G.D. Gargiulo and A. McEwan, eds. (Intech, 2011), pp 435–458 (2009).

Jin, Y.

Y. Jin, E. Angelini, and A. Laine, “Wavelets in medical image processing: denoising, segmentation and registration,” in Handbook of Biomedical Image Analysis, Volume 1: Segmentation models, Part A, J. S. Suri, D.L. Wilson, and S. Laxminarayan, eds. (Kluwer Academic/Plenum Publishers, 2005), pp. 305–358.
[CrossRef]

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika81(3), 425–455 (2009).
[CrossRef]

Kaufhold, J.

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Kenterlis, P.

P. Kenterlis and D. Salonikidis, “Evaluation of wavelet domain methods for image denoising,” (technical report).

Kisilev, P.

P. Kisilev, D. Shaked, and S. H. Lim, “Noise and signal activity maps for better imaging algorithms,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2007), pp.117–120.

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Krzyzak, A.

G. Y. Chen, T. D. Bui, and A. Krzyzak, “Image denoising using neighbouring wavelet coefficients,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 917–920.

Kubik-Huch, R.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Laine, A.

Y. Jin, E. Angelini, and A. Laine, “Wavelets in medical image processing: denoising, segmentation and registration,” in Handbook of Biomedical Image Analysis, Volume 1: Segmentation models, Part A, J. S. Suri, D.L. Wilson, and S. Laxminarayan, eds. (Kluwer Academic/Plenum Publishers, 2005), pp. 305–358.
[CrossRef]

Lim, S. H.

P. Kisilev, D. Shaked, and S. H. Lim, “Noise and signal activity maps for better imaging algorithms,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2007), pp.117–120.

Markey, M. K.

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Mohideen, S. K.

S. K. Mohideen, S. A. Perumal, and M. M Sathik, “Image denoising using discrete wavelet transform,” J. Comput. Sci.8(1), 8–11 (2011).

Panayiotakis, G.

P. Sakellaropoulos, L. Costaridou, and G. Panayiotakis, “A wavelet-based spatially adaptive method for mammographic contrast enhancement,” Phys. Med. Biol.48(6), 787–803 (2003).
[CrossRef] [PubMed]

Perumal, S. A.

S. K. Mohideen, S. A. Perumal, and M. M Sathik, “Image denoising using discrete wavelet transform,” J. Comput. Sci.8(1), 8–11 (2011).

Philips, W.

B. Goossens, A. Pizurica, and W. Philips, “Em-based estimation of spatially variant correlated image noise,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2008), pp. 1744–1747.

Pizurica, A.

B. Goossens, A. Pizurica, and W. Philips, “Em-based estimation of spatially variant correlated image noise,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2008), pp. 1744–1747.

Priestley, B.M.

B.M. Priestley, “Evolutionary spectra and non-stationary processes,” J. R. Stat. Soc. Series B27(2), 204–237 (1965).

Prochazka, A.

E. Jerhotova, J. Svihlik, and A. Prochazka, “Biomedical image volumes denoising via the wavelet transform,” in Applied Biomedical Engineering, G.D. Gargiulo and A. McEwan, eds. (Intech, 2011), pp 435–458 (2009).

Rangarajan, S.

S. Rangarajan, R. Venkataramanan, and R. Shah, “Image denoising using wavelets,” (technical report, 2002).

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Roessl, E.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Sakellaropoulos, P.

P. Sakellaropoulos, L. Costaridou, and G. Panayiotakis, “A wavelet-based spatially adaptive method for mammographic contrast enhancement,” Phys. Med. Biol.48(6), 787–803 (2003).
[CrossRef] [PubMed]

Salonikidis, D.

P. Kenterlis and D. Salonikidis, “Evaluation of wavelet domain methods for image denoising,” (technical report).

Sampat, M. P.

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Sathik, M. M

S. K. Mohideen, S. A. Perumal, and M. M Sathik, “Image denoising using discrete wavelet transform,” J. Comput. Sci.8(1), 8–11 (2011).

Shah, R.

S. Rangarajan, R. Venkataramanan, and R. Shah, “Image denoising using wavelets,” (technical report, 2002).

Shaked, D.

P. Kisilev, D. Shaked, and S. H. Lim, “Noise and signal activity maps for better imaging algorithms,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2007), pp.117–120.

Singer, G.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Stampanoni, M.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Svihlik, J.

E. Jerhotova, J. Svihlik, and A. Prochazka, “Biomedical image volumes denoising via the wavelet transform,” in Applied Biomedical Engineering, G.D. Gargiulo and A. McEwan, eds. (Intech, 2011), pp 435–458 (2009).

Thomas, J. A.

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Thring, T.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Trippel, M.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

Trotter, D. E.

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Venkataramanan, R.

S. Rangarajan, R. Venkataramanan, and R. Shah, “Image denoising using wavelets,” (technical report, 2002).

Vetterli, M.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process.9(9), 1522–1531 (2000).
[CrossRef]

Wang, Z.

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Z. Wang and A. C. Bovik, “Mean-square error : Love it or leave it?,” IEEE Signal Process Mag.26(1), 98–117 (2009).
[CrossRef]

Yu, B.

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process.9(9), 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef]

Biometrika (1)

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika81(3), 425–455 (2009).
[CrossRef]

IEEE Signal Process Mag. (1)

Z. Wang and A. C. Bovik, “Mean-square error : Love it or leave it?,” IEEE Signal Process Mag.26(1), 98–117 (2009).
[CrossRef]

IEEE Trans. Image Process. (3)

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process.9(9), 1522–1531 (2000).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef]

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, “Complex wavelet structural similarity: a new image similarity index,” IEEE Trans. Image Process.18(11), 2385–2401 (2009).
[CrossRef] [PubMed]

Invest. Radiol. (1)

M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mmmography,” Invest. Radiol.46(12), 801–806 (2011).
[CrossRef] [PubMed]

J. Comput. Sci. (1)

S. K. Mohideen, S. A. Perumal, and M. M Sathik, “Image denoising using discrete wavelet transform,” J. Comput. Sci.8(1), 8–11 (2011).

J. Math. Imaging Vision (1)

J.F. Aujol and G. Gilboa, “Constrained and SNR-based solutions for TV-Hilbert space image denoising,” J. Math. Imaging Vision26,217–237 (2006).
[CrossRef]

J. R. Stat. Soc. Series B (1)

B.M. Priestley, “Evolutionary spectra and non-stationary processes,” J. R. Stat. Soc. Series B27(2), 204–237 (1965).

Med. Phys. (1)

J. Kaufhold, J. A. Thomas, W. Eberhard, C. E. Galbo, and D. E. Trotter, “A calibration approach to glandular tissue composition estimation in digital mammography,” Med. Phys.29,1867–1880 (2002).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

P. Sakellaropoulos, L. Costaridou, and G. Panayiotakis, “A wavelet-based spatially adaptive method for mammographic contrast enhancement,” Phys. Med. Biol.48(6), 787–803 (2003).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81,073709 (2010).
[CrossRef] [PubMed]

Other (8)

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B. Goossens, A. Pizurica, and W. Philips, “Em-based estimation of spatially variant correlated image noise,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2008), pp. 1744–1747.

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G. Y. Chen, T. D. Bui, and A. Krzyzak, “Image denoising using neighbouring wavelet coefficients,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 917–920.

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[CrossRef]

E. Jerhotova, J. Svihlik, and A. Prochazka, “Biomedical image volumes denoising via the wavelet transform,” in Applied Biomedical Engineering, G.D. Gargiulo and A. McEwan, eds. (Intech, 2011), pp 435–458 (2009).

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Figures (7)

Fig. 1
Fig. 1

a. Noiseless DPC image, b. Noiseless DCI image

Fig. 2
Fig. 2

a. Noisy DPC image, b. Denoised using VisuShrink, c. Denoised by BayesShrink, d. Denoised by NeighShrink, e. Denoised using the median filter, f. Denoised by Signal-activity-maps, g. Denoised using the Wiener filter and h. Denoised by WND.

Fig. 3
Fig. 3

a. Noisy DCI image, b. Denoised using VisuShrink, c. Denoised by BayesShrink, d. Denoised by NeighShrink, e. Denoised using the median filter, f. Denoised by Signal-activity-maps, g. Denoised using the Wiener filter and h. Denoised by WND.

Fig. 4
Fig. 4

a. Noisy DPC image, b. Denoised using VisuShrink, c. Denoised by BayesShrink, d. Denoised by NeighShrink, e. Denoised using the median filter, f. Denoised by Signal-activity-maps, g. Denoised using the Wiener filter and h. Denoised by WND. The red line marks the position of the row profile plotted in Fig. 5.

Fig. 5
Fig. 5

a. Noisy DCI image, b. Denoised using VisuShrink, c. Denoised by BayesShrink, d. Denoised by NeighShrink, e. Denoised using the median filter, f. Denoised by Signal-activity-maps, g. Denoised using the Wiener filter and h. Denoised by WND. The red line marks the position of the row profile plotted in Fig. 6.

Fig. 6
Fig. 6

Mammography DPC image row intensity profile showing the denoising effects of the methods implemented. The row selected traverses the tumor and the big spike corresponds to a salient edge. Blue and red represent noisy and denoised respectively. a. Denoised using VisuShrink, b. Denoised by BayesShrink, c. Denoised by NeighShrink, d. Denoised using the median filter, e. Denoised by Signal-activity-maps, f. Denoised using the Wiener filter and g. Denoised by WND.

Fig. 7
Fig. 7

Mammography DCI image row intensity profile showing the denoising effects of the methods implemented. The row selected traverses the tumor and the big spike corresponds to a salient edge. Blue and red represent noisy and denoised respectively. a. Denoised using VisuShrink, b. Denoised by BayesShrink, c. Denoised by NeighShrink, d. Denoised using the median filter, e. Denoised by Signal-activity-maps, f. Denoised using the Wiener filter and g. Denoised by WND.

Tables (5)

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Table 1 MSE values for each denoising method and all the simulated noise levels for the DPC images. The different noise leveles were generated by changing the value of a 0 r.

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Table 2 CWSSIM for each denoising method and all the simulated noise levels for the DPC images

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Table 3 MSE values for each denoising method and all the simulated noise levels for the DCI images

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Table 4 CWSSIM values for each denoising method and all the simulated noise levels for the DCI images

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Table 5 SNR for the DPC and DCI mammograms calculated in a background ROI

Equations (25)

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σ I , det 2 = f 1 I
σ T , det 2 T 2 = f 1 r N p s a 0 r ( 1 + f 1 s T f 1 r )
σ D P C , det 2 = f 1 r 2 π 2 v r 2 N p s a 0 r ( 1 + f 1 s T f 1 r V 2 )
σ V , det 2 V 2 = f 1 r v r 2 N p s a 0 r [ v r 2 ( 1 + f 1 s T f 1 r ) + 2 ( 1 + f 1 s T f 1 r V 2 ) ]
n ( t ) = σ s ( t ) ε ( t ) ,
σ s ( t ) = 1 2 π π π A ( ω ) e j ω t d ω ,
n ( t ) = 1 2 π π π A ( ω ) e j ω t d F ( ω ) ,
σ s 2 ( t ) = E [ n ( t ) n ( t ) ]
= 1 ( 2 π ) 2 π π π π E [ d F ( ω 1 ) d F ( ω 2 ) ] A ( ω 1 ) A ( ω 2 ) e ( j ω 1 t ) e ( j ω 2 t ) .
σ s 2 ( t ) = 1 ( 2 π ) 2 π π π π E [ d F ( ω 1 ) d F ( ω 2 ) ] A * ( ω 1 ) A ( ω 2 ) e ( j ω 1 t ) e ( j ω 2 t ) .
E [ d F ( ω 1 ) d F ( ω 2 ) ] = 2 π δ ( ω 1 ω 2 ) d ω 1 d ω 2 ,
σ s 2 ( t ) = 1 2 π π π A * ( ω ) A ( ω ) e ( j ω t ) d ω .
[ σ wavelet ( s , o ) ( t ) ] 2 = 1 2 π π π H ( s , o ) ( ω ) H * ( s , o ) ( ω ) A * ( ω ) A ( ω ) e ( j ω t ) d ω .
T ( σ x ) = σ wavelet 2 ( t ) σ x ( t )
Z [ t ] = w T u t
w L S = ( U T U ) 1 U T | Y | ,
σ ^ x 2 [ t ] = max ( 1 2 L + 1 [ k ] B t Y [ k ] 2 σ wavelet 2 ( t ) , 0 ) ,
D P C noisy ( t ) = D P C ( t ) + σ D P C , det × r a n d n ( t )
V noisy ( t ) = V ( t ) + σ V , det × r a n d n ( t ) ,
M S E ( x , y ) = 1 M i = 1 M ( x i y i ) 2 ,
S S I M ( x , y ) = ( 2 μ x μ y + C 1 ) ( 2 σ x y + C 2 ) ( μ x 2 + μ y 2 + C 1 ) ( σ x 2 + σ y 2 + C 2 ) ,
σ x y = 1 M i = 1 M ( x i μ x ) ( y i μ y )
C W S S I M ( c x , c y ) = 2 | i = 1 N c x , i c y , i * | + K i = 1 N | c x , i | 2 + i = 1 N | c y , i | 2 + K ,
C W S S I M ( c x , c y ) = 2 i = 1 N | c x , i | | c y , i | + K i = 1 N | c x , i | 2 + i = 1 N | c y , i | 2 + K 2 | i = 1 N c x , i c y , i * | + K 2 i = 1 N | c x , i c y , i * | + K .
S N R = μ σ ,

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