Improved estimation of parameters of the homodyned K distribution

David Hruska, Roberto Lavarello, William D. O'Brien, Michael L. Oelze

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The amplitude distribution of the envelope of backscattered ultrasound depends on tissue microstructure. By fitting measured envelope data to a model, parameters can be estimated to describe properties of underlying tissue. The homodyned K distribution is a general model that encompasses the scattering situations modeled by the Rice, Rayleigh, and K distributions. However, parameter estimation for the homodyned K distribution is not straightforward because the model is analytically complex. Furthermore, effects of frequency-dependent attenuation on parameter estimates need to be assessed. An improved parameter estimation algorithm was developed to quickly and accurately estimate parameters of the homodyned K distribution, i.e., the μ (effective number of scatterers per resolution cell) and k (ratio of coherent to diffuse energy) parameters. Parameter estimates were found by fitting estimates of SNR, skewness, and kurtosis of fractional-order moments of the envelope with theoretical values predicted by the homodyned K distribution. The effects of frequency dependent attenuation were approximated by assuming a Gaussian pulse to determine the shift in center frequency of the pulse and hence change in volume of the resolution cell. Computational phantoms were created with varying attenuation coefficients and scanned using a simulated f/4 transducer with a center frequency of 10 MHz. An average of two scatterers per resolution cell (based on the phantoms with no attenuation) was used. The new estimation algorithm was tested and compared with an existing algorithm (based on the even moments of the homodyned K distribution). The new estimation algorithm was found to produce estimates with lower bias and variance. For example, for μ = 2 and k ranging from 0 to 2 in steps of 0.1, the average variance in the μ parameter estimates was 0.067 for the new algorithm and 0.42 for existing algorithm. For the k parameter estimates, the average variance was 0.0069 for the new algorithm and 0.048 for the old algorithm. In the simulations with no attenuation, the μ parameter estimate was 2.53±0.18. In the phantoms with a linear attenuation coefficient of 0.5 dB·MHz -1·cm-1, the estimate was 4.64±0.54. This compared well with the predicted μ value of 4.98.

Original languageEnglish (US)
Title of host publication2009 IEEE International Ultrasonics Symposium and Short Courses, IUS 2009
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Print)9781424443895
StatePublished - 2009
Event2009 IEEE International Ultrasonics Symposium, IUS 2009 - Rome, Italy
Duration: Sep 20 2009Sep 23 2009

Publication series

NameProceedings - IEEE Ultrasonics Symposium
ISSN (Print)1051-0117


Other2009 IEEE International Ultrasonics Symposium, IUS 2009


  • Backscatter
  • Envelope statistic
  • Tissue characterization

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


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