When directly applying optical transforms, such as fractional Fourier transform (FrFT), to a single image or real image (input image), the resulting image will become complex-valued, which leads to the doubling of data volume. This data expansion problem can be found in many existing single-image optical encryption schemes. We propose a folding technique to offset the data expansion by constructing a complex input image of half size. And we devise an optical single-image encryption scheme based on double FrFTs, in which this technique together with compressed sensing can bring about the possible maximum compression of encrypted images. Moreover, the chaos-based random circular shift for scrambling is introduced to enhance security. The chaotic random signum matrix is also tried as the measurement matrix, and it displays a good performance. Simulation results demonstrate the validity and security of the proposed scheme.
"Halving the dimension of a single image to be encrypted optically to avoid data expansion," Optical Engineering 55(6), 064111 (28 June 2016). https://doi.org/10.1117/1.OE.55.6.064111