We investigate the robustness of an image encryption technique that uses random phase encoding in both the input plane and the Fourier plane when the encrypted image has been distorted. The distortions include different types of noise, loss of encrypted data, and the binarization of the encrypted image. It is shown that decryption transforms the noise added to the encrypted image to a wide-sense stationary additive white noise. Consequently, regardless of the type of the noise added to the encrypted image, the quality of the recovered image can be improved by processing techniques designed for filtering out additive white noise. The double-phase encryption technique distributes the input image over the entire output plane, which provides robustness to the distortions due to loss of encrypted data. Regarding the binarization, it enables easy implementation and data compression while recovering images of good quality may be possible. © 1997 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(97)

We investigate the performance of an image encryption technique that uses random-phase encoding in both the input plane and the Fourier plane, using partial information of the encrypted image. We first investigate the phase-only information of the encrypted data for decryption. A binary version of the phase-only information is also considered for decryption. Binary images are well suited for optical display and practical implementation. Using partial information of the encrypted image, a reconstructed complex image is generated, which is used for decryption. Tests are performed for both gray-scale and binary images. We show that the phase information of the encrypted image is very important in the reconstruction of the decrypted image. Computer simulations show that for the images tested here, binarization of the encrypted image can recover the original image with low mean squared error.

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