Abstract: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.