This paper is mainly concerned with the study of compression of optically Discrete Cosine Transform (DCT)-based double random phase encoding (DRPE) encrypted images. The objective of image encryption is to secure the image to be transmitted over the communication media, while the objective of compression is to reduce the bandwidth or the communication process. The adopted encryption scheme in this paper depends on the optical encryption using DCT-based DRPE. The optical DCT-based DRPE encryption is implemented to secure the image content to be transmitted. Optical encryption in DCT domain has proved its efficiency and feasibility. The DCT-based DRPE is selected as the tool of encryption as it is considered as a substitution tool that changes the pixel values to realize the diffusion property. The compression with JPEG and SPIHT techniques is studied in order to reduce the bandwidth of the communication process, but it adds some source of errors on the encrypted data that may affect the decryption output. The main objective here is to obtain decryption outputs that are as close as possible to the original images even with compression applied on the encrypted images. The impact of compressing DCT-based DRPE encrypted images is studied and analyzed at several bit rates using JPEG and SPIHT compression strategies. The extensive simulation experiments reveal that the optical DCT-based DRPE encryption is a very good candidate as an encryption tool. Also, the outcome results demonstrate that the optically DCT-based DRPE encrypted image may be effectively compressed using SPIHT than JPEG especially at low bit rates.
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