In addition to typical random noise, remote sensing hyperspectral images are generally affected by non-periodic partially deterministic disturbance patterns due to the image formation process and characterized by a high degree of spatial and spectral coherence. This paper presents a new technique that faces the problem of removing the spatial coherent noise known as vertical stripping (VS) usually found in images acquired by push-broom sensors, in particular for the Compact High Resolution Imaging Spectrometer (CHRIS). The correction is based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. The proposed method introduces a way to exclude the contribution of the spatial high frequencies of the surface from the destripping process that is based on the information contained in the spectral domain. Performance of the proposed algorithm is tested on sites of different nature, several acquisition modes (different spatial and spectral resolutions) and covering the full range of possible sensor temperatures. In addition, synthetic realistic scenes have been created, adding modeled noise for validation purposes. Results show an excellent rejection of the noise pattern with respect to the original CHRIS images. The analysis shows that high frequency VS is successfully removed, although some low frequency components remain. In addition, the dependency of the noise patterns with the sensor temperature has been found to agree with the theoretical one, which confirms the robustness of the presented approach. The approach has proven to be robust, stable in VS removal, and a tool for noise modeling. The general nature of the procedure allows it to be applied for destripping images from other spectral sensors.