A method for hiding information utilizing double-random phase-encoding technique
Introduction
The double-random phase-encoding technique, which was proposed by Refregier and Javidi in 1995, has been receiving much interest because of its high-level data security. The encoded image is a phase-amplitude (i.e., complex) function whose real and imaginary parts can be regarded as realization of independent white and stationary random processes. This property makes it impossible to recover the information with the usual phase-recovery algorithms [1]. So the double-random phase-encoding technique could be utilized in many areas, such as user identification, copyright preservation and military message transmission [2], [3], [4], [5], [6]. When embedding the encoded image into a host image, the gray level superposition method with proper superposition weights is used to prevent unauthorized reading of the message while allowing the message to be read as needed, and the host image is not subjected to severe degradation [4].
Two methods are presently used to recover the message from the composed image. The first involves the subtraction of the host image from the composed image, and then decryption using the double-random phase-decoding technique. In some cases, the disadvantage of this method is that the host image has to be transmitted along with the composed image. The second method involves the decryption of the composed image by the double-random phase-decoding technique directly, but the host image will be modified to a form of noise added to the reconstructed image. This results in degradation of the quality of the reconstructed image [7].
In this paper, we propose an improved method for embedding a double-random phase-encoded message into a host image. The real and imaginary parts of the double-random phase-encoded data are embedded into a sufficiently large host image, allowing decryption to be performed directly on the composed image as needed. This process of decryption does not require the original host image and the quality of the reconstructed image will not be affected by the host image. Finally, the influence of the superposition weight on the quality of the composed and reconstructed image will be discussed.
Section snippets
Standard method for hiding information
Considering a discrete system, assume M and N are the pixel numbers of row and column, respectively, i=0,1,2,…,N−1 and j=0,1,2,…,N−1. Let f(xi,yi) denote the image to be encoded, ϕ(xi,yj) the encoded image. Let n(xi,yj) and b(ξi,ηj) denote two independent random functions uniformly distributed from 0 to 1 in space domain and frequency domain, respectively. The double-random phase-encoding and decoding process will be expressed as [1], [2], [3], [4], [5], [6], [7]:
Expanding host image method for hiding information
Here, the expanding host image method is proposed. Once the host image has been chosen, it is enlarged (e.g., from size M×N to size 2M×2N). The steps are specified as following: where h0, h denote, respectively, the host image before and after being enlarged. This is actually extending from one pixel to four pixels in neighboring rows and columns. Then, the real and imaginary parts of the
Numerical simulation
A numerical simulation has been implemented on an original host image, which consisted of 256×256 pixels with 256 gray levels. We initially enlarge the size to 512×512 using the method in Eq. (5), and then superimpose the double-random phase-encoded data on the enlarged host image according to Eq. (6).
The enlarged host image and the composed images carrying encoded data are shown in Fig. 1, where the weighting parameter α is 0.01, 0.08 and 0.2. Fig. 2(a) shows the image to be encoded, and the
Conclusion
An image encrypted by the double-random phase-encoding technique can be hidden in an enlarged host image through gray-level superposition method. During the process of recovering the hidden image, decryption could be performed on the composed image directly without using original host image, and the quality of reconstructed image is quite satisfactory. Optimum performance for a specific hiding image could be achieved by adjusting the superposition weight. The optimum superposition weight seems
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