Restoring blurred images is challenging because both the blur kernel and the sharp image are unknown, which makes this problem severely under constrained. Recently many single image blind deconvolution methods have been proposed, but these state-of-the-art single image deblurring techniques are still sensitive to image noise, and can degrade their performance rapidly especially when the noise level of the input blurred images increases. In this work, we estimate the blur kernel accurately by applying a series of directional low-pass filters in different orientations to the input blurred image, and effectively constructing the Radon transform of the blur kernel from each filtered image. Finally, we use a robust non-blind deconvolution method with outlier handling, which can effectively reduce ringing artifacts, to generate the final results. Our experimental results on both synthetic and real-world examples show that our method achieves comparable quality to existing approaches on blurry noisy-free images, and higher quality outputs than previous approaches on blurry and noisy images.