The MLE For The Parameters Of The Homodyned K Distribution Based On The Adaptive Particle Swarm Optimization

The homodyned-K(HK)distribution is proved to be a generalized statistical model to analyze ultrasonic echo envelopes by using the physical-meanings of three parameters for tissue characterization.The multi-solution problem of most existing methods based on statistical characteristic equations affects the applications of the estimated parameters.Theoretically,a sole estimation of the model parameters can be obtained with the maximum likelihood estimation(MLE).However,the probability density function(PDF)of the HK distribution used in the MLE is an integral expression whose integrand consists of the Bessel function.Hence,conventional numerical integral algorithms are limited by the poor accuracy and convergence.In the present study,a MLE method based on the Newton-Raphson algorithm is proposed to realize the sole estimation of the HK parameters.In order to improve the accuracy and convergence performance,the cloud adaptive particle swarm optimization(CAPSO)algorithm is proposed for the integral calculation of the PDF of the HK distribution.In the experiments,the parameters of sets of HK distribution samples generated with a model combining the Gaussian and Gamma distributions are estimated by the proposed method.The statistics of estimation errors are calculated,and compared with those reported in literatures to show the accuracy of the proposed method.Experimental results show that the relative root mean squared errors(RMSEs)of the clustering and structure parameters based on the proposed method are 0.41 ± 0.22 and 0.75 ± 0.31,respectively;the RMSE of average computation time is 0.27± 0.11 s under the R2015 Matlab platform.The method performance is also validated by simulated ultrasound signals from the different 3D scatterer distributions based on the Field ? ultrasound software.It demonstrates that the proposed method can obtain a sole estimation for the HK parameters with a small error level,which presents a potential practical value in future applications.