A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions

Author

Shankar, P. Mohana

Author_Institution

Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA, USA

Volume

50

Issue

3

fYear

2003

fDate

3/1/2003 12:00:00 AM

Firstpage

339

Lastpage

343

Abstract

A compound probability density function (pdf) is presented to describe the envelope of the backscattered echo from tissue. This pdf allows local and global variation in scattering cross sections in tissue. The ultrasonic backscattering cross sections are assumed to be gamma distributed. The gamma distribution also is used to model the randomness in the average cross sections. This gamma-gamma model results in the compound scattering pdf for the envelope. The relationship of this compound pdf to the Rayleigh, K, and Nakagami distributions is explored through an analysis of the signal-to-noise ratio of the envelopes and random number simulations. The three parameter compound pdf appears to be flexible enough to represent envelope statistics giving rise to Rayleigh, K, and Nakagami distributions.

Keywords

backscatter; biomedical ultrasonics; gamma distribution; ultrasonic scattering; K distributions; Nakagami distributions; Rayleigh distributions; average cross sections; backscattered echo; compound probability density function; compound scattering pdf; envelope statistics; gamma distribution; gamma-gamma model; random number simulations; randomness; scattering cross sections; signal-to-noise ratio; ultrasonic echo envelope; Acoustic pulses; Acoustic scattering; Analytical models; Backscatter; Nakagami distribution; Probability density function; Rayleigh scattering; Signal analysis; Signal to noise ratio; Statistical distributions; Computer Simulation; Connective Tissue; Image Enhancement; Models, Biological; Models, Statistical; Scattering, Radiation; Sensitivity and Specificity; Statistics as Topic; Stochastic Processes; Ultrasonography;

fLanguage

English

Journal_Title

Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on

Publisher

ieee

ISSN

0885-3010

Type

jour

DOI

10.1109/TUFFC.2003.1193628

Filename

1193628