Spectral imaging offers useful additional information to improve or expand imaging applications such as biomedical images, identification of cultures, and surveillance. These applications take advantage of features involved in a spectral scene captured using, for instance, the Coded Aperture Snapshot Spectral Imagers (CASSI), that naturally embodies the compressing sensing principles, whose potential is diminished because in practice, sensing matrix loses the ideal characteristics. This paper uses a deep learning based method in order to correct the real-compressed measurements and estimate the ideal-corrected measurements. The correction is estimated from a matrix form of compressed measurements, with the representation of compressed spatial dimensions and the number of projections captured as shots. The performance of the model is measured using peak signal-to-noise ratio, and the structural similarity index, upon the recovered data cube with the gradient projection for sparse reconstruction algorithm. The outcomes show how the deep learning-based method improves the quality in reconstruction against image ground truth when the noise is not concerning.