Review of Envelope Statistics Models for Quantitative Ultrasound Imaging and Tissue Characterization

  • François Destrempes
  • Guy Cloutier


The homodyned K-distribution and the K-distribution, viewed as a special case, as well as the Rayleigh and the Rice distributions, viewed as limiting cases, are discussed in the context of quantitative ultrasound (QUS) imaging. The Nakagami distribution is presented as an approximation of the homodyned K-distribution. The main assumptions made are: (1) the absence of log-compression or application of non-linear filtering on the echo envelope of the radiofrequency signal; (2) the randomness and independence of the diffuse scatterers. We explain why other available models are less amenable to a physical interpretation of their parameters. We also present the main methods for the estimation of the statistical parameters of these distributions. We explain why we advocate the methods based on the X-statistics for the Rice and the Nakagami distributions, and the K-distribution. The limitations of the proposed models are presented. Several new results are included in the discussion sections, with proofs in the appendix.


Quantitative ultrasound (QUS) Ultrasound tissue characterization Ultrasound imaging Echo envelope Homodyned K-distribution K-distribution Rice distribution  Rayleigh distribution Nakagami distribution Parameters estimation Moments Log-moments 



The authors acknowledge the continuous financial support of the Canadian Institutes of Health Research and Natural Sciences and Engineering Research Council of Canada.


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratory of Biorheology and Medical UltrasonicsUniversity of Montreal Hospital Research Center (CRCHUM)MontréalCanada
  2. 2.The Department of Radiology, Radio-Oncology and Nuclear MedicineUniversity of MontrealMontréalCanada
  3. 3.The Institute of Biomedical EngineeringUniversity of MontrealMontréalCanada

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