超声零差K分布模型仿真研究
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摘要
目的零差K分布模型是最具有物理意义的超声背向散射信号包络统计分布模型,主要参数包括k(相干散射与弥漫散射的比值)和μ(有效散射子个数),但目前尚缺乏k、μ参数估计算法的系统对比研究,本文系统阐述零差K模型及其参数估算方法,并通过计算机仿真对比研究各类估算算法的性能。方法利用蒙特卡洛仿真产生独立同分布的超声背向散射信号包络样本,利用零差K模型参数估算算法对k和μ参数进行估计,包括偶数阶矩法(Dutt-Greenleaf法和Prager-Berman法)、小数阶矩法、RSK法和XU统计法;最后,进行10组仿真实验,每组进行1 000次仿真,对比分析各类估计算法的性能,包括排除次数、估算误差和运行时间等参数。结果 Dutt-Greenleaf法、Prager-Berman法、小数阶矩法、RSK法和XU统计法的平均排除次数分别为474、915、672、0、0;参数k平均估算误差分别为31. 2%、55. 8%、122. 2%、12. 8%、20. 6%;参数μ平均估算误差分别为23. 2%、41. 9%、16. 3%、6. 8%、3. 0%;平均运行时间分别为0. 72 s、0. 85 s、1. 38 s、298. 34 s、109. 53 s。结论在零差K分布模型参数估计方法中,(1) Dutt-Greenleaf法、Prager-Berman法和小数阶矩法的排除次数较高,RSK法和XU统计法基本无排除;(2) RSK法的k平均估算误差最小,XU统计法的μ平均估算误差最小;(3) Dutt-Greenleaf法、Prager-Berman法、小数阶矩法的平均运行时间远少于RSK法和XU统计法。
Objective The homodyned-K( HK) distribution model is of the most physical meaning for ultrasound backscattered signal envelopes. The HK model parameters include k( ratio of coherent scattering to diffuse scattering) and μ( effective scatterer number). However,a systematic comparison of k and μ estimation methods is not available. The purpose is to introduce the HK model and its parameter estimation methods,and to compare the performance of each estimation algorithm by using computer simulations. Methods Monte Carlo simulation was used to generate independent and identically distributed( i. i. d.) ultrasound backscattered envelope samples that follow the HK distribution. These i. i. d. samples were then used for estimating the HK model parameters k and μ with different estimation algorithms,including the even moment estimator( the Dutt-Greenleaf and the Prager-Berman estimators),the fractional moment estimator,the RSK estimator,and the XU statistics estimator. Ten groups of simulation experiments were conducted. Each group was run for 1 000 times. The performance of each estimation algorithm was evaluated in terms of times of rejection,estimation error,and running time. Results The Dutt-Greenleaf,Prager-Berman,fractional moment,RSK,and XU statistics estimators yielded,respectively,( 1) a mean time of rejection as 474,915,672,0,0;( 2) a mean estimation error for k as 31. 2%,55. 8%,122. 2%,12. 8%,20. 6%;( 3) a mean estimation error for μ as 23. 2%,41. 9%,16. 3%,6. 8%,3. 0%;( 4) a mean running time as 0. 72 s,0. 85 s,1. 38 s,298. 34 s,109. 53 s. Conclusions Among the five estimation methods of HK model parameters,( 1) the Dutt-Greenleaf,the Prager-Berman and the fractional moment estimators had a large number of rejection,yet the RSK and the XU statistics estimators rarely did;( 2) the RSK estimator yielded the minimum average estimation error for estimating k,and the XU statistics estimator produced the minimum average estimation error for estimating μ;( 3) the running times of the Dutt-Greenleaf,the Prager-Berman and the fractional moment estimators were far less those of the RSK and the XU statistics estimators.
Objective The homodyned-K( HK) distribution model is of the most physical meaning for ultrasound backscattered signal envelopes. The HK model parameters include k( ratio of coherent scattering to diffuse scattering) and μ( effective scatterer number). However,a systematic comparison of k and μ estimation methods is not available. The purpose is to introduce the HK model and its parameter estimation methods,and to compare the performance of each estimation algorithm by using computer simulations. Methods Monte Carlo simulation was used to generate independent and identically distributed( i. i. d.) ultrasound backscattered envelope samples that follow the HK distribution. These i. i. d. samples were then used for estimating the HK model parameters k and μ with different estimation algorithms,including the even moment estimator( the Dutt-Greenleaf and the Prager-Berman estimators),the fractional moment estimator,the RSK estimator,and the XU statistics estimator. Ten groups of simulation experiments were conducted. Each group was run for 1 000 times. The performance of each estimation algorithm was evaluated in terms of times of rejection,estimation error,and running time. Results The Dutt-Greenleaf,Prager-Berman,fractional moment,RSK,and XU statistics estimators yielded,respectively,( 1) a mean time of rejection as 474,915,672,0,0;( 2) a mean estimation error for k as 31. 2%,55. 8%,122. 2%,12. 8%,20. 6%;( 3) a mean estimation error for μ as 23. 2%,41. 9%,16. 3%,6. 8%,3. 0%;( 4) a mean running time as 0. 72 s,0. 85 s,1. 38 s,298. 34 s,109. 53 s. Conclusions Among the five estimation methods of HK model parameters,( 1) the Dutt-Greenleaf,the Prager-Berman and the fractional moment estimators had a large number of rejection,yet the RSK and the XU statistics estimators rarely did;( 2) the RSK estimator yielded the minimum average estimation error for estimating k,and the XU statistics estimator produced the minimum average estimation error for estimating μ;( 3) the running times of the Dutt-Greenleaf,the Prager-Berman and the fractional moment estimators were far less those of the RSK and the XU statistics estimators.
引文
[1] Mamou J,Oelze ML. Quantitative ultrasound in soft tissues[M].Heidelberg:Springer,2013.
[2] Oelze ML,Mamou J. Review of quantitative ultrasound:Envelope statistics and backscatter coefficient imaging and contributions to diagnostic ultrasound[J]. IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2016,63(2):336-351.
[3] Han M,Wan J,Zhao Y,et al. Nakagami-m parametric imaging for atherosclerotic plaque characterization using the coarse-to-fine method[J]. Ultrasound in Medicine and Biology,2017,43(6):1275-1289.
[4] Tsui PH,Zhou Z,Lin YH,et al. Effect of ultrasound frequency on the Nakagami statistics of human liver tissues[J]. PLoS One,2017,12(8):e0181789.
[5] Destrempes F,Cloutier G. A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope[J]. Ultrasound in Medicine and Biology,2010,36(7):1037-1051.
[6] Tsui PH,Wan YL,Tai DI,et al. Effects of estimators on ultrasound Nakagami imaging in visualizing the change in the backscattered statistics from a Rayleigh distribution to a preRayleigh distribution[J]. Ultrasound in Medicine and Biology,2015,41(8):2240-2251.
[7]魏颖,林江莉,彭玉兰,等.利用零差K分布模型参数识别乳腺肿瘤[J].中国医学影像技术,2006,22(8):1266-1268.Wei Y,Lin JL,Peng YL,et al. Use of homodyned K-distribution parameter for characterizing breast neoplasms[J]. Chinese Journal of Medical Imaging Technology,2006,22(8):1266-1268.
[8] Byra M,Nowicki A,Wróblewska-Piotrzkowska H,et al.Classification of breast lesions using segmented quantitative ultrasound maps of homodyned K distribution parameters[J].Medical Physics,2016,43(10):5561-5569.
[9] Hao X,Bruce CJ,Pislaru C,et al. Characterization of reperfused infarcted myocardium from high-frequency intracardiac ultrasound imaging using homodyned K distribution[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2002,49(11):1530-1542.
[10] Mamou J,Coron A,Oelze ML,et al. Three-dimensional highfrequency backscatter and envelope quantification of cancerous human lymph nodes[J]. Ultrasound in Medicine and Biology,2011,37(3):345-357.
[11] Ghoshal G,Lavarello RJ,Kemmerer JP,et al. Ex vivo study of quantitative ultrasound parameters in fatty rabbit livers[J].Ultrasound in Medicine and Biology,2012,38(12):2238-2248.
[12] Jakeman E,Tough RJA. Generalized K distribution:a statistical model for weak scattering[J]. Journal of the Optical Society of America A,1987,4(9):1764-1772.
[13] Dutt V,Greenleaf JF. Ultrasound echo envelope analysis using a homodyned K distribution signal model[J]. Ultrasonic Imaging,1994,16(4):265-287.
[14] Prager RW,Gee AH,Treece GM,et al. Decompression and speckle detection for ultrasound images using the homodyned kdistribution[J]. Pattern Recognition Letters,2003,24(4-5):705-713.
[15] Prager RW,Gee AH,Treece GM,et al. Analysis of speckle in ultrasound images using fractional order statistics and the homodyned k-distribution[J]. Ultrasonics,2002,40(1-8):133-137.
[16] Hruska DP,Oelze ML. Improved parameter estimates based on the homodyned K distribution[J]. IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2009,56(11):2471-2481.
[17] Destrempes F,Porée J,Cloutier G. Estimation method of the homodyned K-distribution based on the mean intensity and two log-moments[J]. SIAM Journal on Imaging Sciences,2013,6(3):1499-1530.
[18] Cristea A. Ultrasound tissue characterization using speckle statistics[D]. Lyon:UniversitéClaude Bernard Lyon 1,2015.
[2] Oelze ML,Mamou J. Review of quantitative ultrasound:Envelope statistics and backscatter coefficient imaging and contributions to diagnostic ultrasound[J]. IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2016,63(2):336-351.
[3] Han M,Wan J,Zhao Y,et al. Nakagami-m parametric imaging for atherosclerotic plaque characterization using the coarse-to-fine method[J]. Ultrasound in Medicine and Biology,2017,43(6):1275-1289.
[4] Tsui PH,Zhou Z,Lin YH,et al. Effect of ultrasound frequency on the Nakagami statistics of human liver tissues[J]. PLoS One,2017,12(8):e0181789.
[5] Destrempes F,Cloutier G. A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope[J]. Ultrasound in Medicine and Biology,2010,36(7):1037-1051.
[6] Tsui PH,Wan YL,Tai DI,et al. Effects of estimators on ultrasound Nakagami imaging in visualizing the change in the backscattered statistics from a Rayleigh distribution to a preRayleigh distribution[J]. Ultrasound in Medicine and Biology,2015,41(8):2240-2251.
[7]魏颖,林江莉,彭玉兰,等.利用零差K分布模型参数识别乳腺肿瘤[J].中国医学影像技术,2006,22(8):1266-1268.Wei Y,Lin JL,Peng YL,et al. Use of homodyned K-distribution parameter for characterizing breast neoplasms[J]. Chinese Journal of Medical Imaging Technology,2006,22(8):1266-1268.
[8] Byra M,Nowicki A,Wróblewska-Piotrzkowska H,et al.Classification of breast lesions using segmented quantitative ultrasound maps of homodyned K distribution parameters[J].Medical Physics,2016,43(10):5561-5569.
[9] Hao X,Bruce CJ,Pislaru C,et al. Characterization of reperfused infarcted myocardium from high-frequency intracardiac ultrasound imaging using homodyned K distribution[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2002,49(11):1530-1542.
[10] Mamou J,Coron A,Oelze ML,et al. Three-dimensional highfrequency backscatter and envelope quantification of cancerous human lymph nodes[J]. Ultrasound in Medicine and Biology,2011,37(3):345-357.
[11] Ghoshal G,Lavarello RJ,Kemmerer JP,et al. Ex vivo study of quantitative ultrasound parameters in fatty rabbit livers[J].Ultrasound in Medicine and Biology,2012,38(12):2238-2248.
[12] Jakeman E,Tough RJA. Generalized K distribution:a statistical model for weak scattering[J]. Journal of the Optical Society of America A,1987,4(9):1764-1772.
[13] Dutt V,Greenleaf JF. Ultrasound echo envelope analysis using a homodyned K distribution signal model[J]. Ultrasonic Imaging,1994,16(4):265-287.
[14] Prager RW,Gee AH,Treece GM,et al. Decompression and speckle detection for ultrasound images using the homodyned kdistribution[J]. Pattern Recognition Letters,2003,24(4-5):705-713.
[15] Prager RW,Gee AH,Treece GM,et al. Analysis of speckle in ultrasound images using fractional order statistics and the homodyned k-distribution[J]. Ultrasonics,2002,40(1-8):133-137.
[16] Hruska DP,Oelze ML. Improved parameter estimates based on the homodyned K distribution[J]. IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2009,56(11):2471-2481.
[17] Destrempes F,Porée J,Cloutier G. Estimation method of the homodyned K-distribution based on the mean intensity and two log-moments[J]. SIAM Journal on Imaging Sciences,2013,6(3):1499-1530.
[18] Cristea A. Ultrasound tissue characterization using speckle statistics[D]. Lyon:UniversitéClaude Bernard Lyon 1,2015.