Abstract

An automated method is presented for analyzing signal-dependent noise. Signal-dependent noise is present in many types of data-acquisition processes and has been investigated by other researchers with various methods. Regardless of the noise analysis methods, often the starting point is based on a particular signal-dependent noise model, which also forms the basis for our study. The approach determines whether the estimated noise variance is dependent on the signal by approximating the functional relation within the constraints of the assumed signal-noise model. The method relies on the Fourier attributes of the signal and noise and uses the wavelet expansion for separating these components. The technique does not rely on the underlying noise and signal probability distributions. Two-dimensional simulations as well as mammography data are used to illustrate the merits of the approach.

© 2006 Optical Society of America

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  1. T. R. Oenning and J. Moon, "Modeling the Lorentzian magnetic recording channel with transition noise," IEEE Trans. Magn. 37, 583-591 (2001).
  2. B. Dierickx, "Electronic image sensors vs. film: beyond the state-of-the-art," presented at the Proceedings of the OEEPE Workshop on Automation in Digital Photogrammetric Production, Paris, France, 22-24 June 1999.
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  8. S. I. Sadhar and A. N. Rajagopalan, "Image estimation in film-grain noise," IEEE Signal Process. Lett. 12, 238-241 (2005).
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  12. K. Krissian, K. Vosburgh, R. Kikinis, and C. F. Westin, "Anisotropic diffusion of ultrasound constrained by speckle noise model," Tech. Rep. 0004 (Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Laboratory of Mathematics in Imaging, 2004).
  13. A. Achim, A. Bezerianos, and P. Tsakalides, "Novel Bayesian multiscale method for speckle removal in medical ultrasound images," IEEE Trans. Med. Imaging 20, 772-783 (2001).
  14. B. Sklar, "Rayleigh fading channels in mobile digital communication systems. Part I: Characterization," IEEE Commun. Mag. 35, 90-100 (1997).
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  16. N. Karssemeijer, "Adaptive noise equalization and recognition of microcalcification clusters in mammograms," Int. J. Pattern Recognit. Artif. Intell. 7, 1357-1376 (1993).
  17. W. Veldkamp and N. Karssemeijer, "Improved correction for signal dependent noise applied to automatic detection of microcalcifications," in Digital Mammography (Kluwer Academic, 1998), pp. 169-176.
  18. S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).
  19. K. J. McLoughlin, P. J. Bones, and N. Karssemeijer, "Noise equalization for detection of microcalcification clusters in direct digital mammogram images," IEEE Trans. Med. Imaging 23, 313-320 (2004).
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  22. J. J. Heine, S. R. Deans, R. P. Velthuizen, and L. P. Clarke, "On the statistical nature of mammograms," Med. Phys. 26, 2254-2265 (1999).
  23. A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
  24. J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).
  25. M. Behera, "Characterization of preliminary breast tomosynthesis data: noise and power spectra analysis," M.S. thesis (Biomedical Engineering Program, University of South Florida, 2004).
  26. D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).
  27. M. B. Williams, P. A. Mangiafico, and P. U. Simoni, "Noise power spectra of images from digital mammography detectors," Med. Phys. 26, 1279-1293 (1999).
  28. J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).
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  30. J. J. Heine, S. R. Deans, and L. P. Clarke, "Multiresolution probability analysis of random fields," J. Opt. Soc. Am. A 16, 6-16 (1999).
  31. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).
  32. I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics (Society for Industrial and Applied Mathematics, 1992).

2005

S. I. Sadhar and A. N. Rajagopalan, "Image estimation in film-grain noise," IEEE Signal Process. Lett. 12, 238-241 (2005).

2004

M. Dai, C. Peng, A. Chan, and D. Loguinov, "Bayesian wavelet shrinkage with edge detection for SAR image despeckling," IEEE Trans. Geosci. Remote Sens. 42, 1642-1648 (2004).

K. J. McLoughlin, P. J. Bones, and N. Karssemeijer, "Noise equalization for detection of microcalcification clusters in direct digital mammogram images," IEEE Trans. Med. Imaging 23, 313-320 (2004).

A. E. Burgess, "On the noise variance of a digital mammography system," Med. Phys. 31, 1987-1995 (2004).

2002

J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).

2001

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).

A. Achim, A. Bezerianos, and P. Tsakalides, "Novel Bayesian multiscale method for speckle removal in medical ultrasound images," IEEE Trans. Med. Imaging 20, 772-783 (2001).

T. R. Oenning and J. Moon, "Modeling the Lorentzian magnetic recording channel with transition noise," IEEE Trans. Magn. 37, 583-591 (2001).

2000

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

1999

J. J. Heine, S. R. Deans, D. Gangadharan, and L. P. Clarke, "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Opt. Eng. (Bellingham) 38, 1505-1516 (1999).

J. J. Heine, S. R. Deans, R. P. Velthuizen, and L. P. Clarke, "On the statistical nature of mammograms," Med. Phys. 26, 2254-2265 (1999).

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

M. B. Williams, P. A. Mangiafico, and P. U. Simoni, "Noise power spectra of images from digital mammography detectors," Med. Phys. 26, 1279-1293 (1999).

J. J. Heine, S. R. Deans, and L. P. Clarke, "Multiresolution probability analysis of random fields," J. Opt. Soc. Am. A 16, 6-16 (1999).

1998

1997

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

B. Sklar, "Rayleigh fading channels in mobile digital communication systems. Part I: Characterization," IEEE Commun. Mag. 35, 90-100 (1997).

1994

D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).

1993

N. Karssemeijer, "Adaptive noise equalization and recognition of microcalcification clusters in mammograms," Int. J. Pattern Recognit. Artif. Intell. 7, 1357-1376 (1993).

1984

R. Kasturi, J. F. Walkup, and T. F. Krile, "Image restoration in signal-dependent noise using a Markovian covariance model," Comput. Vis. Graph. Image Process. 28, 363-376 (1984).

1983

1982

G. T. Barnes, "Radiographic mottle: a comprehensive theory," Med. Phys. 9, 656-667 (1982).

1981

Achim, A.

A. Achim, A. Bezerianos, and P. Tsakalides, "Novel Bayesian multiscale method for speckle removal in medical ultrasound images," IEEE Trans. Med. Imaging 20, 772-783 (2001).

Aiazzi, B.

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

L. Alparone, F. Argenti, B. Aiazzi, and S. Baronti, "Multiresolution approaches to adaptive speckle reduction in synthetic aperture radar images," presented at the International Conference on Image Processing, Barcelona, Spain, September 14-17, 2003.

Albagli, D.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Alparone, L.

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

L. Alparone, F. Argenti, B. Aiazzi, and S. Baronti, "Multiresolution approaches to adaptive speckle reduction in synthetic aperture radar images," presented at the International Conference on Image Processing, Barcelona, Spain, September 14-17, 2003.

Argenti, F.

L. Alparone, F. Argenti, B. Aiazzi, and S. Baronti, "Multiresolution approaches to adaptive speckle reduction in synthetic aperture radar images," presented at the International Conference on Image Processing, Barcelona, Spain, September 14-17, 2003.

Barducci, A.

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

Barnes, G. T.

G. T. Barnes, "Radiographic mottle: a comprehensive theory," Med. Phys. 9, 656-667 (1982).

Baronti, S.

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

L. Alparone, F. Argenti, B. Aiazzi, and S. Baronti, "Multiresolution approaches to adaptive speckle reduction in synthetic aperture radar images," presented at the International Conference on Image Processing, Barcelona, Spain, September 14-17, 2003.

Behera, M.

M. Behera, "Characterization of preliminary breast tomosynthesis data: noise and power spectra analysis," M.S. thesis (Biomedical Engineering Program, University of South Florida, 2004).

Bezerianos, A.

A. Achim, A. Bezerianos, and P. Tsakalides, "Novel Bayesian multiscale method for speckle removal in medical ultrasound images," IEEE Trans. Med. Imaging 20, 772-783 (2001).

Bialek, W.

D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).

Bones, P. J.

K. J. McLoughlin, P. J. Bones, and N. Karssemeijer, "Noise equalization for detection of microcalcification clusters in direct digital mammogram images," IEEE Trans. Med. Imaging 23, 313-320 (2004).

Burgess, A. E.

A. E. Burgess, "On the noise variance of a digital mammography system," Med. Phys. 31, 1987-1995 (2004).

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).

Chan, A.

M. Dai, C. Peng, A. Chan, and D. Loguinov, "Bayesian wavelet shrinkage with edge detection for SAR image despeckling," IEEE Trans. Geosci. Remote Sens. 42, 1642-1648 (2004).

Clarke, L. P.

J. J. Heine, S. R. Deans, D. Gangadharan, and L. P. Clarke, "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Opt. Eng. (Bellingham) 38, 1505-1516 (1999).

J. J. Heine, S. R. Deans, R. P. Velthuizen, and L. P. Clarke, "On the statistical nature of mammograms," Med. Phys. 26, 2254-2265 (1999).

J. J. Heine, S. R. Deans, and L. P. Clarke, "Multiresolution probability analysis of random fields," J. Opt. Soc. Am. A 16, 6-16 (1999).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution probability analysis of gray scaled images," J. Opt. Soc. Am. A 15, 1048-1058 (1998).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

Cullers, D. K.

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution probability analysis of gray scaled images," J. Opt. Soc. Am. A 15, 1048-1058 (1998).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

Dai, M.

M. Dai, C. Peng, A. Chan, and D. Loguinov, "Bayesian wavelet shrinkage with edge detection for SAR image despeckling," IEEE Trans. Geosci. Remote Sens. 42, 1642-1648 (2004).

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics (Society for Industrial and Applied Mathematics, 1992).

Deans, S. R.

J. J. Heine, S. R. Deans, D. Gangadharan, and L. P. Clarke, "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Opt. Eng. (Bellingham) 38, 1505-1516 (1999).

J. J. Heine, S. R. Deans, and L. P. Clarke, "Multiresolution probability analysis of random fields," J. Opt. Soc. Am. A 16, 6-16 (1999).

J. J. Heine, S. R. Deans, R. P. Velthuizen, and L. P. Clarke, "On the statistical nature of mammograms," Med. Phys. 26, 2254-2265 (1999).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution probability analysis of gray scaled images," J. Opt. Soc. Am. A 15, 1048-1058 (1998).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

Dierickx, B.

B. Dierickx, "Electronic image sensors vs. film: beyond the state-of-the-art," presented at the Proceedings of the OEEPE Workshop on Automation in Digital Photogrammetric Production, Paris, France, 22-24 June 1999.

D'Orsi, C. J.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Froehlich, G. K.

Gangadharan, D.

J. J. Heine, S. R. Deans, D. Gangadharan, and L. P. Clarke, "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Opt. Eng. (Bellingham) 38, 1505-1516 (1999).

Han, S.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Heine, J. J.

J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).

J. J. Heine, S. R. Deans, R. P. Velthuizen, and L. P. Clarke, "On the statistical nature of mammograms," Med. Phys. 26, 2254-2265 (1999).

J. J. Heine, S. R. Deans, and L. P. Clarke, "Multiresolution probability analysis of random fields," J. Opt. Soc. Am. A 16, 6-16 (1999).

J. J. Heine, S. R. Deans, D. Gangadharan, and L. P. Clarke, "Multiresolution analysis of two-dimensional 1/f processes: approximation methods for random variable transformations," Opt. Eng. (Bellingham) 38, 1505-1516 (1999).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution probability analysis of gray scaled images," J. Opt. Soc. Am. A 15, 1048-1058 (1998).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

Hendrick, R. E.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Jacobson, F. L.

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).

Judy, P. F.

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).

Karellas, A.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Karssemeijer, N.

K. J. McLoughlin, P. J. Bones, and N. Karssemeijer, "Noise equalization for detection of microcalcification clusters in direct digital mammogram images," IEEE Trans. Med. Imaging 23, 313-320 (2004).

N. Karssemeijer, "Adaptive noise equalization and recognition of microcalcification clusters in mammograms," Int. J. Pattern Recognit. Artif. Intell. 7, 1357-1376 (1993).

W. Veldkamp and N. Karssemeijer, "Improved correction for signal dependent noise applied to automatic detection of microcalcifications," in Digital Mammography (Kluwer Academic, 1998), pp. 169-176.

Kasturi, R.

Kikinis, R.

K. Krissian, K. Vosburgh, R. Kikinis, and C. F. Westin, "Anisotropic diffusion of ultrasound constrained by speckle noise model," Tech. Rep. 0004 (Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Laboratory of Mathematics in Imaging, 2004).

Krile, T. F.

Krissian, K.

K. Krissian, K. Vosburgh, R. Kikinis, and C. F. Westin, "Anisotropic diffusion of ultrasound constrained by speckle noise model," Tech. Rep. 0004 (Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Laboratory of Mathematics in Imaging, 2004).

Landberg, C. E.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Levis, I.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Loguinov, D.

M. Dai, C. Peng, A. Chan, and D. Loguinov, "Bayesian wavelet shrinkage with edge detection for SAR image despeckling," IEEE Trans. Geosci. Remote Sens. 42, 1642-1648 (2004).

Mangiafico, P. A.

M. B. Williams, P. A. Mangiafico, and P. U. Simoni, "Noise power spectra of images from digital mammography detectors," Med. Phys. 26, 1279-1293 (1999).

McLoughlin, K. J.

K. J. McLoughlin, P. J. Bones, and N. Karssemeijer, "Noise equalization for detection of microcalcification clusters in direct digital mammogram images," IEEE Trans. Med. Imaging 23, 313-320 (2004).

Moon, J.

T. R. Oenning and J. Moon, "Modeling the Lorentzian magnetic recording channel with transition noise," IEEE Trans. Magn. 37, 583-591 (2001).

Oenning, T. R.

T. R. Oenning and J. Moon, "Modeling the Lorentzian magnetic recording channel with transition noise," IEEE Trans. Magn. 37, 583-591 (2001).

Opsahl-Ong, B.

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full field digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).

Peng, C.

M. Dai, C. Peng, A. Chan, and D. Loguinov, "Bayesian wavelet shrinkage with edge detection for SAR image despeckling," IEEE Trans. Geosci. Remote Sens. 42, 1642-1648 (2004).

Pippi, I.

B. Aiazzi, L. Alparone, A. Barducci, S. Baronti, and I. Pippi, "Assessments of noise variance and information content of multi/hyper-spectral imagery," Int. Arch. Photogramm. Remote Sens. 32, 167-174 (1999).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Rajagopalan, A. N.

S. I. Sadhar and A. N. Rajagopalan, "Image estimation in film-grain noise," IEEE Signal Process. Lett. 12, 238-241 (2005).

Ruderman, D. L.

D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).

Sadhar, S. I.

S. I. Sadhar and A. N. Rajagopalan, "Image estimation in film-grain noise," IEEE Signal Process. Lett. 12, 238-241 (2005).

Schulze, M. A.

M. A. Schulze and Q. X. Wu, "Noise reduction in synthetic aperture radar imagery using a morphology-based nonlinear filter," in Proceedings of DICTA95, Digital Image Computing: Techniques and Applications (Publisher, 1995), pp. 661-666.

Simoni, P. U.

M. B. Williams, P. A. Mangiafico, and P. U. Simoni, "Noise power spectra of images from digital mammography detectors," Med. Phys. 26, 1279-1293 (1999).

Sklar, B.

B. Sklar, "Rayleigh fading channels in mobile digital communication systems. Part I: Characterization," IEEE Commun. Mag. 35, 90-100 (1997).

Stauduhar, R.

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution probability analysis of gray scaled images," J. Opt. Soc. Am. A 15, 1048-1058 (1998).

J. J. Heine, S. R. Deans, D. K. Cullers, R. Stauduhar, and L. P. Clarke, "Multiresolution statistical analysis of high resolution digital mammograms," IEEE Trans. Med. Imaging 16, 503-515 (1997).

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