中文摘要：

有限Ridgelet变换是一种为了克服Wavelet在高维信号处理中的不足而提出的图像处理新方法。通过Radon变换将图像边缘奇异性转变为点奇异性，再利用Wavelet变换针对点奇异性进行处理。根据图像经Radon变换后能量分布紧缩集中，该文提出一种新的Ridgelet改进算法，该算法在图像Ridgelet变换过程中，按能量高低分为两种能量系数矩阵再分别进行降噪处理，并在融合重构以后，再次利用Wavelet变换提取低能量图像中的细节信息并将之融合，二次加强图像细节。使得输出信噪比及图像细节保持上得到大幅度提高。仿真试验表明在受噪声干扰严重情况下，该方法的输出信噪比及视觉效果均优于其他算法。

英文摘要：

The Finite Ridgelet Transform （FRIT） is a new image processing method which could conquer the defect of Wavelet in high dimension. The method changes the line singularity in the image into the point singularity via the Radon transform, deals the point singularity with Wavelet transform. It is shown that the energy is compact by using the Radon transform on the image, and the characteristic on the Ridgelet transform is applied in the image processing which obtains the good result in the denoising and the edge keeping of the image. Especially under the strong noisy, it is better than other methods.