Considerable noise is present in some multispectral images acquired by remote-sensing satellites. The current traditional de-noising methods not only fail to completely remove the noise

but also cause image blurring and spatial-resolution degradation. This study aims to mitigate the tradeoff between the removal of noise and the reservation of information. To solve this problem

we propose an improved and high-performing sparse representation approach that processes the high-frequency portions in the difference images based on the initial image and the Gaussian-filtered image to remove the noise. In this study

sparse representation is applied to the information in a remote-sensing image to accurately represent important information

which includes edge and texture. By contrast

the noise that is mainly concentrated in the high-frequency portion cannot be represented. We used data sparsity to reconstruct the high-frequency portion without noise. The algorithm completely preserves the low-frequency information and reconstructs the high-frequency information by sparse representation based on whether or not such information can be represented by fewer atoms from the over-complete dictionary. Theoretical analysis and experimental results show that the proposed method outperforms the traditional de-noising methods and the sparse representation method. In terms of visual quality

the proposed method reconstructs the image with clear color and apparent structure.The results of the objective assessment show that the proposed method can achieve a higher peak signal-to-noise ratio than the other methods and provide a feasible solution to remove noise effectively and considerably highlight the details of the original images.