Abstract: The Gaussian white noises in images degrade the LS model, because it can not satisfy low rank property of low rank matrix and the sparse property of sparse matrix. To overcome the disadvantages of LS model, this paper proposed a new model which added the Gaussian restraint to the LS model, named LSE model, to remove random impulse noise and Gaussian white noise in images simultaneously. The experimental results show that compared with LS model，the LSE model can guarantee visual effect and keep the details. The PSNR of the denoised image improved about 0.1-2dB compared with LS model. In the case of Gaussian noise is small, the PSNR of the denoised image improved about 0.5-2.5dB compared with BM3D.