The finite ridgelet transform proposed by Donoho has successful application in edge detection and segmentation of images with high-noise, but it has a drawback which is due to annoying "wrap-around" effect to the finite Radon transform. As a result, it may also produce "alias" edges and "holes" in the reconstructed image. In this paper, we present a new finite ridgelet transform based on the "natural straight line", which can overcome the above drawback and implement the inverse discrete Radon transform. At the last, we employ the proposed algorithm for segmenting the synthetic aperture radar (SAR) image and obtain satisfied segmentation result