中文摘要：

针对基于梯度变换的图像增强算法抗噪声干扰能力差的问题，引入曲率滤波理论，提出了基于高斯曲率滤波和梯度变换的图像增强算法.该算法通过对图像梯度场进行非线性变换来增强图像对比度，通过构造能量泛函，采用梯度下降法从变换后的梯度场重构出增强后的图像，并利用高斯曲率滤波对梯度下降法迭代过程中的重构图像及其各阶偏微分进行平滑，有效解决了图像重构过程中的噪声非线性放大和扩散问题，同时保留了丰富的细节信息.采用多组边缘模糊图像进行仿真实验，实验结果表明该算法在增强图像边缘对比度的同时，能够有效抑制噪声.

英文摘要：

For the noise amplification problem during gradient transform based image enhancement, an improved algorithm combined with Gaussian curvature filter was proposed. First, the nonlinear gradient transformation is utilized for image gradient field to enhance the contrast. Then the enhanced image is reconstructed by minimizing an energy functional through gradient descent method. During iteration of gradient descent, the reconstructed image and its first and second derivatives are smoothed by Gaussian curvature filter, which can solve the promblems of nonlinear amplification and diffusion of noise in image reconstruction and preserve details. The experimental results with various images show the proposed algorithm can effectively suppress noises and enhance the image edges contrast at the same time.