The ridgelet transform was developed over several years to break the limitations of the wavelet transform. In this paper, a novel image denoising algorithm is proposed that incorporates the dual-tree complex wavelets into the ordinary ridgelet transform. The approximate shift invariant property of the dual-tree complex wavelet and the high directional sensitivity of the ridgelet transform make the new method a very good choice for image denoising. We apply the digital complex ridgelet transform to the denoising of some standard images embedded in white noise. A simple hard thresholding of the complex ridgelet coefficients is used. Experimental results show that by using dual-tree complex ridgelets, our algorithms obtain higher Peak Signal to Noise Ratio (PSNR) for all the denoised images with different noise levels. The new modified ridgelet denoising algorithm--MRDA is better than Wiener2 and the classical CRDA ridgelet image denoising. Complex ridgelet could be applied to curvelet image denoising as well.