Advanced Stochastic Models for Partially Developed Speckle
Speckled images arise when coherent microwave,
optical, and acoustic imaging techniques are used to image an object, surface or scene. Examples of coherent imaging systems include synthetic aperture radar, laser imaging systems, imaging sonar
systems, and medical ultrasound systems. Speckle noise is a form of object or target induced noise that results when the surface of the object is Rayleigh rough compared to the wavelength of the illuminating radiation. Detection and estimation in images corrupted
by speckle noise is complicated by the nature of the noise and is not
as straightforward as detection and estimation in additive noise. In
this work, we derive stochastic models for speckle noise, with an emphasis on speckle as it arises in medical ultrasound images. The
motivation for this work is the problem of segmentation and tissue classification using ultrasound imaging. Modeling of speckle in this
context involves partially developed speckle model where an underlying Poisson point process modulates a Gram-Charlier series
of Laguerre weighted exponential functions, resulting in a doubly
stochastic filtered Poisson point process. The statistical distribution of partially developed speckle is derived in a closed canonical form.
It is observed that as the mean number of scatterers in a resolution cell is increased, the probability density function approaches an
exponential distribution. This is consistent with fully developed speckle noise as demonstrated by the Central Limit theorem.
[1] J. Goodman, "Statistical Properties of Laser Speckle Patterns," in Speckle and Related Phenomena, 2nd Edition, J. C. Dainty Ed., Springer Verlag, NY 1984.
[2] A. Bovik, D. Munson, "Optimal Detection of Object Boundaries in Uncorrelated Speckle," Optical Engineering, Volume 25, No. 11, Nov.1986.
[3] A. Bovik, "On Detecting Edges in Speckle Imagery," IEEE Transactions
on Acoustics, Speech, and Signal Processing, Vol. 36, No. 10, Oct.1998.
[4] H. Arsenault, "Information Extraction from Images Degraded by Speckle," Proceedings of IGARSS 87 Symposium, 1987, pp. 1317-1322.
[5] P. Kelly, H. Derin, "Adaptive Segmentation of Speckled Images Using a
Hierarchical RFM," IEEE Trans. on Acoustics., Speech, and Signal Processing, Vol. 36, No.10, Oct. 88.
[6] V. Frost and K. Shanmugan, "The Information Content of SAR Images
of Terrain," IEEE Transactions on Aerospace Electronic Systems AES-
19, No.5, 1993, pp. 768-774.
[7] J. S. Daba and M. R. Bell, "Statistics of the Scattering Cross Section of a
Small Number of Random Scatterers," IEEE Transactions on Antennas
and Propagation, Vol. 43, No. 8, Aug. 1995, pp. 773-783.
[8] J. S. Daba and M. R. Bell, "Synthetic-Aperture-Radar Surface Reflectivity Estimation Using a Marked Point-Process Speckle Model," Optical Engineering, Vol. 42, No. 1, Jan. 2003, pp.211-227.
[9] J. S. Daba and M. R. Bell, "Segmentation of Speckled Images Using a Likelihood Random Field Model," Optical Engineering, January 2008.
[10] J. S. Daba and M. R. Bell, "Object Discrimination and Orientation-Determination in Speckled Images," Optical Engineering, Vol. 33, No.
4, April 1994, pp. 1287-1302.
[11] J. Dubois and O. Abdul-Latif, "Detection of Ultrasonic Images in the Presence of a Random Number of Scatterers: A Statistical Learning Approach," Proceedings of World Academy of Science, Engineering and
Technology, Vol. 2, 2005, pp. 326-329.
[12] J. Dubois and O. Abdul-Latif, "SVM-Based Detection of SAR Images in Partially Developed Speckle Noise," Proceedings of World Academy of Science, Engineering and Technology, Vol. 2, 2005, pp. 321-325.
[13] J. Dubois, "Scattering Statistics of Doppler Faded Acoustic Signals
Using Speckle Noise Models," IEEE International Conference on Direct
and Inverse Problems of Electromagnetic and Acoustic Wave Theory,
Lviv, Ukraine, Sept. 2003.
[14] J. Dubois, "Segmentation of Speckled Ultrasound Images Based on a
Statistical Model," Proceedings of the 16th International EURASIP
Conference BIOSIGNAL 2002, Vol. 16, Brno, Czech Republic, June 2002.
[15] J. S. Daba and M. R. Bell, "Estimation of the Surface Reflectivity of
SAR Images Based on a Marked Poisson Point Process Model," IEEE
International Symposium on Signals, Systems, and Electronics, San Francisco, USA, October 25, 1995.
[16] J. S. Daba and M. R. Bell, "Statistical Distributions of Partially
Developed Speckle Based on a Small Number of Constant Scatterers
with Random Phase," IEEE International Geoscience and Remote
Sensing Symposium, California Institute of Technology, Pasadena, CA,
USA, August 8-12, 1994.
[17] J. S. Daba and M. R. Bell, "Object Discrimination and Orientation-
Determination in Synthetic Aperture Radar Images," IEEE International
Geoscience and Remote Sensing Symposium, NASA, Houston, TX,
USA, May 23-29, 1992.
[18] D. Snyder and M. Miller, Random Point Processes in Time and Space,
NY: Springer-Verlag, 2002.
[19] P. Billingsley, Probability and Measure, 2nd ed. New York: Wiley,
1986.
[20] A. Abdi, S. Nader-Esfahani, J. S. Daba and M. R. Bell, "Comments on
Statistics of the Scattering Cross Section of a Small Number of Random
Scatterers," IEEE Transactions on Antennas and Propagation, ISSN
0018-926X, Vol. 48, No. 5, May 2000, pp. 844-845.
[21] R. M. Cramblitt and M. R. Bell, "Marked Regularity Models," IEEE
Transactions on Ultrasonics, Ferromagnetics, and Frequency Control.
Vol. 46, No. 1, January 1999, pp. 24 - 34.
[22] J. W. Goodman, "Some effects of target-induced scintillation on optical
radar performance," Proeedings of the IEEE, Vol. 53, Issue 11, Nov.
1965, pp.1688 - 1700.
[23] J. P. Dubois, "Poisson Modulated Stochastic Model for Partially
Developed Multi-Look Speckle," American Conference on Applied
Mathematics, Harvard University, Cambridge, MA, USA, March 2008.
[1] J. Goodman, "Statistical Properties of Laser Speckle Patterns," in Speckle and Related Phenomena, 2nd Edition, J. C. Dainty Ed., Springer Verlag, NY 1984.
[2] A. Bovik, D. Munson, "Optimal Detection of Object Boundaries in Uncorrelated Speckle," Optical Engineering, Volume 25, No. 11, Nov.1986.
[3] A. Bovik, "On Detecting Edges in Speckle Imagery," IEEE Transactions
on Acoustics, Speech, and Signal Processing, Vol. 36, No. 10, Oct.1998.
[4] H. Arsenault, "Information Extraction from Images Degraded by Speckle," Proceedings of IGARSS 87 Symposium, 1987, pp. 1317-1322.
[5] P. Kelly, H. Derin, "Adaptive Segmentation of Speckled Images Using a
Hierarchical RFM," IEEE Trans. on Acoustics., Speech, and Signal Processing, Vol. 36, No.10, Oct. 88.
[6] V. Frost and K. Shanmugan, "The Information Content of SAR Images
of Terrain," IEEE Transactions on Aerospace Electronic Systems AES-
19, No.5, 1993, pp. 768-774.
[7] J. S. Daba and M. R. Bell, "Statistics of the Scattering Cross Section of a
Small Number of Random Scatterers," IEEE Transactions on Antennas
and Propagation, Vol. 43, No. 8, Aug. 1995, pp. 773-783.
[8] J. S. Daba and M. R. Bell, "Synthetic-Aperture-Radar Surface Reflectivity Estimation Using a Marked Point-Process Speckle Model," Optical Engineering, Vol. 42, No. 1, Jan. 2003, pp.211-227.
[9] J. S. Daba and M. R. Bell, "Segmentation of Speckled Images Using a Likelihood Random Field Model," Optical Engineering, January 2008.
[10] J. S. Daba and M. R. Bell, "Object Discrimination and Orientation-Determination in Speckled Images," Optical Engineering, Vol. 33, No.
4, April 1994, pp. 1287-1302.
[11] J. Dubois and O. Abdul-Latif, "Detection of Ultrasonic Images in the Presence of a Random Number of Scatterers: A Statistical Learning Approach," Proceedings of World Academy of Science, Engineering and
Technology, Vol. 2, 2005, pp. 326-329.
[12] J. Dubois and O. Abdul-Latif, "SVM-Based Detection of SAR Images in Partially Developed Speckle Noise," Proceedings of World Academy of Science, Engineering and Technology, Vol. 2, 2005, pp. 321-325.
[13] J. Dubois, "Scattering Statistics of Doppler Faded Acoustic Signals
Using Speckle Noise Models," IEEE International Conference on Direct
and Inverse Problems of Electromagnetic and Acoustic Wave Theory,
Lviv, Ukraine, Sept. 2003.
[14] J. Dubois, "Segmentation of Speckled Ultrasound Images Based on a
Statistical Model," Proceedings of the 16th International EURASIP
Conference BIOSIGNAL 2002, Vol. 16, Brno, Czech Republic, June 2002.
[15] J. S. Daba and M. R. Bell, "Estimation of the Surface Reflectivity of
SAR Images Based on a Marked Poisson Point Process Model," IEEE
International Symposium on Signals, Systems, and Electronics, San Francisco, USA, October 25, 1995.
[16] J. S. Daba and M. R. Bell, "Statistical Distributions of Partially
Developed Speckle Based on a Small Number of Constant Scatterers
with Random Phase," IEEE International Geoscience and Remote
Sensing Symposium, California Institute of Technology, Pasadena, CA,
USA, August 8-12, 1994.
[17] J. S. Daba and M. R. Bell, "Object Discrimination and Orientation-
Determination in Synthetic Aperture Radar Images," IEEE International
Geoscience and Remote Sensing Symposium, NASA, Houston, TX,
USA, May 23-29, 1992.
[18] D. Snyder and M. Miller, Random Point Processes in Time and Space,
NY: Springer-Verlag, 2002.
[19] P. Billingsley, Probability and Measure, 2nd ed. New York: Wiley,
1986.
[20] A. Abdi, S. Nader-Esfahani, J. S. Daba and M. R. Bell, "Comments on
Statistics of the Scattering Cross Section of a Small Number of Random
Scatterers," IEEE Transactions on Antennas and Propagation, ISSN
0018-926X, Vol. 48, No. 5, May 2000, pp. 844-845.
[21] R. M. Cramblitt and M. R. Bell, "Marked Regularity Models," IEEE
Transactions on Ultrasonics, Ferromagnetics, and Frequency Control.
Vol. 46, No. 1, January 1999, pp. 24 - 34.
[22] J. W. Goodman, "Some effects of target-induced scintillation on optical
radar performance," Proeedings of the IEEE, Vol. 53, Issue 11, Nov.
1965, pp.1688 - 1700.
[23] J. P. Dubois, "Poisson Modulated Stochastic Model for Partially
Developed Multi-Look Speckle," American Conference on Applied
Mathematics, Harvard University, Cambridge, MA, USA, March 2008.
@article{"International Journal of Electrical, Electronic and Communication Sciences:63021", author = "Jihad S. Daba (Jean-Pierre Dubois) and Philip Jreije", title = "Advanced Stochastic Models for Partially Developed Speckle", abstract = "Speckled images arise when coherent microwave,
optical, and acoustic imaging techniques are used to image an object, surface or scene. Examples of coherent imaging systems include synthetic aperture radar, laser imaging systems, imaging sonar
systems, and medical ultrasound systems. Speckle noise is a form of object or target induced noise that results when the surface of the object is Rayleigh rough compared to the wavelength of the illuminating radiation. Detection and estimation in images corrupted
by speckle noise is complicated by the nature of the noise and is not
as straightforward as detection and estimation in additive noise. In
this work, we derive stochastic models for speckle noise, with an emphasis on speckle as it arises in medical ultrasound images. The
motivation for this work is the problem of segmentation and tissue classification using ultrasound imaging. Modeling of speckle in this
context involves partially developed speckle model where an underlying Poisson point process modulates a Gram-Charlier series
of Laguerre weighted exponential functions, resulting in a doubly
stochastic filtered Poisson point process. The statistical distribution of partially developed speckle is derived in a closed canonical form.
It is observed that as the mean number of scatterers in a resolution cell is increased, the probability density function approaches an
exponential distribution. This is consistent with fully developed speckle noise as demonstrated by the Central Limit theorem.", keywords = "Doubly stochastic filtered process, Poisson point process, segmentation, speckle, ultrasound", volume = "2", number = "5", pages = "984-5", }
