In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
文摘目的:探讨实时剪切波弹性成像(shear wave elastography,SWE)在不同大小甲状腺TI-RADS 3~4类结节鉴别诊断中的应用。方法:常规超声观察164例患者(共197个结节)甲状腺结节的边界、内部回声、是否合并钙化、纵横比、内部及周边血流情况等,依据甲状腺TI-RADS分类方法对相应的甲状腺状腺结节进行分类,同时进行剪切波弹性成像,记录结节杨氏模量最大值(Emax),绘制ROC曲线,获得鉴别诊断甲状腺良恶性结节的Emax最佳界值。其中TI-RADS 3~4类结节186个,分直径≤10 mm组(Ⅰ组)和直径>10 mm组(Ⅱ组)。以病理结果为金标准,分别绘制ROC曲线,评价Emax值在Ⅰ、Ⅱ组病变中的应用价值。结果:杨氏模量Emax界值为52.5 k Pa。Ⅰ组和Ⅱ组的敏感性、准确性及特异性分别为57.4%、66.2%及90.0%和87.5%、79.5%及68.8%,ROC曲线下面积(area under the curve,AUC)分别为0.810和0.842。结论:SWE界值鉴别诊断甲状腺良恶性结节差异有统计学意义;SWE对>10 mm甲状腺结节良恶性鉴别诊断更有应用价值;SWE对≤10 mm甲状腺结节应用价值有限。
基金Supported by the National Natural Science Foundation of China(11601076)the Science and Technology Project of Jiangxi Provincial Education Department(GJJ170473)
基金Supported by the National Natural Science Foundation of China(11601076)the Youth Science Foundation of Jiangxi Province(20151BAB21100420151BAB211012)
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.