  The robust coding of natural images and the effective compression of
encrypted images have been studied individually in recent years. However,
little work has been done in the robust coding of encrypted images. The
existing results in these two individual research areas cannot be combined
directly for the robust coding of encrypted images. This is because the robust
coding of natural images relies on the elimination of spatial correlations
using sparse transforms such as discrete wavelet transform (DWT), which is
ineffective to encrypted images due to the weak correlation between encrypted
pixels. Moreover, the compression of encrypted images always generates code
streams with different significance. If one or more such streams are lost, the
quality of the reconstructed images may drop substantially or decoding error
may exist, which violates the goal of robust coding of encrypted images. In
this work, we intend to design a robust coder, based on compressive sensing
with structurally random matrix, for encrypted images over packet transmission
networks. The proposed coder can be applied in the scenario that Alice needs a
semi-trusted channel provider Charlie to encode and transmit the encrypted
image to Bob. In particular, Alice first encrypts an image using globally
random permutation and then sends the encrypted image to Charlie who samples
the encrypted image using a structural matrix. Through an imperfect channel
with packet loss, Bob receives the compressive measurements and reconstructs
the original image by joint decryption and decoding. Experimental results show
that the proposed coder can be considered as an efficient multiple description
coder with a number of descriptions against packet loss.
