Aiming at the application of spectral images in the fields of color high fidelity reproduction in specific reproduction environments, this paper proposes universal low-complexity, color-high-fidelity spectral image compression methods based on visual characteristics in specific illumination, which could enhance algorithms' versatility, improve compression efficiency, and further facilitate images' storage and transmission. This paper first studies the color reproduction principle of spectral images in specific reproduction environments, designs a measurement method for the color error of reconstructed spectral images, and then proposes distortion guidelines for spectral image color fidelity compression in specific illumination. Based on the color distortion guidelines, the compression principle is derived. Then spectral preprocessing, spatial-spectral de-redundancy methods, encoding methods, and optimization strategies are designed, and finally, spectral image compression methods for high-fidelity reproduction are proposed. In terms of distortion guidance criteria, first the color decomposition environment of spectral images is constructed, and a matrix operator is proposed to extract color perception information from spectral images under specific lighting (single or mixed lighting); then, through the color perception information extraction operator, color perception error is used to measure the deviation of spectral images in the color measurement; finally, the color perception distortion criterion of the spectral image is proposed to guide the compression process. Based on this criterion, a targeted compression principle is proposed, and the compression flow of this paper is designed. First, the color perception weighted preprocessing of the spectral data is performed, and the color perception information extraction operator is used to obtain spectral color perception data under specific reproduction conditions that still maintains spectral characteristics; then, based on the color perception compression principle, APWS-RA encoding is performed on the color perception spectral data. The method is named W_SF-APWS-RA. Spectral image decoding is divided into two stages. First, the compressed bit stream is encoded inversely to form a reconstructed spectral color perception data matrix; then, the reconstructed spectral image is obtained by multiplying the inverse matrix of the perception information extraction operator and the reconstructed spectral color perception data matrix. Experiments show that at the same bit rate, compared with the existing low-complexity APWS, APWS-RA, and universal color-high-fidelity WF-APWS-RA compression, WsF-APWS-RA codings can not only more effectively retain spectral color information under specific reproduction conditions, but also have the best variable illumination color reproduction stability. Meanwhile, it can also effectively improve the accuracy of spectral reconstruction. Therefore, the new methods can also be generalized to remote sensing and other fields, and have important practical value.