In order to reduce the loss of spectral and color information of multispectral images with noise after dimensionality reduction, a robust PCA compression method based on weights (WRPCA) was proposed. Firstly, based on the special performance of the human eye, the spectrum of the multispectral image was weighted by the human visual sensitivity function (color matching function of the CIE1931 standard observer), and then the weighted spectrum was used to reduce the image using the Robust PCA method. Finally, the image was reconstructed. In the experiment, WRPCA was tested under the same conditions as the WSPCA method. From the experimental data analysis, it was found that the WSPCA method was not good for the compression and reconstruction of the image due to the influence of noise, while the WRPCA method was not affected by the noise, and could make the reconstructed image in spectral precision and chromaticity. The accuracy and other aspects were superior to the WSPCA method. Therefore, the WRPCA method could achieve effective compression of noise-containing multispectral images and minimize color information loss.