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The robust coding of natural images and the effective compression ofencrypted images have been studied individually in recent years. However,little work has been done in the robust coding of encrypted images. Theexisting results in these two individual research areas cannot be combineddirectly for the robust coding of encrypted images. This is because the robustcoding of natural images relies on the elimination of spatial correlationsusing sparse transforms such as discrete wavelet transform (DWT), which isineffective to encrypted images due to the weak correlation between encryptedpixels. Moreover, the compression of encrypted images always generates codestreams with different significance. If one or more such streams are lost, thequality of the reconstructed images may drop substantially or decoding errormay exist, which violates the goal of robust coding of encrypted images. Inthis work, we intend to design a robust coder, based on compressive sensingwith structurally random matrix, for encrypted images over packet transmissionnetworks. The proposed coder can be applied in the scenario that Alice needs asemi-trusted channel provider Charlie to encode and transmit the encryptedimage to Bob. In particular, Alice first encrypts an image using globallyrandom permutation and then sends the encrypted image to Charlie who samplesthe encrypted image using a structural matrix. Through an imperfect channelwith packet loss, Bob receives the compressive measurements and reconstructsthe original image by joint decryption and decoding. Experimental results showthat the proposed coder can be considered as an efficient multiple descriptioncoder with a number of descriptions against packet loss.

Robust Coding of Encrypted Images via Structural Matrix