In order to preserve singularities in denoising, we propose a new scheme by adding dilated singularity prior to noisy images. The singularities are detected by canny operator firstly and then dilated using mathematical morphology for finding pixels “near” singularities instead of “on” singularities. The denoising results for pixels near singularities are obtained by nonlocal means in spatial domain to preserve singularities while the denoising results for pixels in smooth regions are obtained by EM algorithm constrained by a mask formed by downsampled spatial image with dilated singularity prior to suiting the sizes of the subbands of wavelets. The final denoised results are got by combining the above two results. Experimental results show that the scheme can preserve singularity well with relatively high PSNR and good visual quality.