Advances and Applications in Statistics
Volume 50, Issue 5, Pages 349 - 366
(May 2017) http://dx.doi.org/10.17654/AS050050349 |
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STATISTICAL MODELLING OF LOG-COMPRESSED NAKAGAMI DISTRIBUTED ULTRASOUND ECHO ENVELOPE
Suchismita Maiti, Debashis Nandi and Baisakhi Chakraborty
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Abstract: Rayleigh distribution is most widely considered to describe the statistical behavior of ultrasound echo envelope. However, Rayleigh distribution is not sufficient to describe the statistical behavior of ultrasound echo envelope, especially when the scatterers are very small in number and have periodic alignment. In this context, Nakagami distribution has been found to be more to describe the statistics of ultrasound echo envelope in more general form. On the other side, the range of ultrasound envelope remains very high (120dB) which is beyond the range of the conventional display devices (60dB). Hence, logarithmic compression is a necessary step to reduce the dynamic range for displaying ultrasound image. But it changes the statistics of processed data. Moreover, many speckle noise reduction techniques utilize the statistics of log-compressed ultrasound envelope. In this paper, the probability density function (pdf) of log-compressed Nakagami distributed ultrasound envelope has been derived. First and second moments of the derived pdf have also been calculated. The parameter estimation has been done using method of moments (MOM) and maximum likelihood estimation (MLE). The fitting of derived pdf to the histograms of both simulated and phantom ultrasound data has been demonstrated using the estimated parameters. |
Keywords and phrases: ultrasound echo envelope, statistical modelling, speckle statistics, speckle noise, Nakagami distribution. |
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