中文摘要：

针对医学超声图像清晰度低，易受乘性噪声污染等问题，提出了一种基于Gauss曲率的超声图像去噪算法，并构造一种Gauss曲率扩散函数，自适应控制扩散速度，克服了传统去噪算法不能保护弱边缘的缺点。根据变分法得到Euler-Lagrange方程，给出一种计算平衡系数的方法，并引入图像差异范数作为终止迭代准则。数值实验仿真结果显示，该算法能够有效去除医学超声图像中的噪声，较好地保留超声图像中大量存在的弱边缘信息，本算法的PSNR比传统算法提高了大约4dB。

英文摘要：

A medical ultrasound image denoising algorithm based on the gauss curvature is proposed ac- cording to the medical ultrasound image characteristics which have low definition and is vulnerable to be pollu- ted by the multiplicative noise. A new Gauss curvature diffusion function is constructed and the diffusion veloc- ity can be controlled adaptively. It overcomes the shortcoming that the traditional denoising algorithm can not protect the weak edges. A method of calculating equilibrium coefficient is presented based on the Euler-La- grange equation which is obtained by the variation method. The image difference norm is introduced as the iter- ation stopping criterion. Numerical simulation results show that the new algorithm can remove the noise in medical ultrasound image effectively and retain the weak edge information exist in the ultrasound image. The experimental data shows that the PSNR of the new algorithm is about 4dB higher than the traditional algo-rithms.