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A two-layer watermarking scheme based on computational ghost imaging and singular value decomposition is proposed. In the first layer, the original watermark is encoded into a significantly small number of measured intensities in the process of computational ghost imaging to constitute a new watermark. In the second layer, the significant blocks chosen from the host image based on spatial frequency are combined to the reference image, which is used to embed the new watermark by using the singular value decomposition. Differing from other watermarking schemes, the information of original watermark can be verified without clear visualization via calculating the nonlinear correlation map between the original one and the reconstructed one. Besides optical parameters such as wavelength and propagation distance, a series of phase-only masks are used as security keys, which can enlarge the key space and enhance the level of security. The results illustrate the feasibility and effectiveness about the proposed watermarking mechanism, which provides an effective alternative for the related work. [ABSTRACT FROM AUTHOR]

• Differing from other interference-based image encryption schemes, two retrieved phase-only masks are considered as two main keys to enhance the security level. • The annoying silhouette problem existed in the interference-based image encryption approaches can be effectively avoided. • Two main keys are directly related to original pain images, and the cryptosystem has high resistance against the potential attacks. • Additional parameters such as the conditions of the logistic map, wavelength, and axial distance can further enhance the security of the cryptosystem. A novel double-image encryption approach has been proposed based on optical interference and logistic map. Initially, original images are rearranged into two scrambled components with the use of the random sequence engendered based on the logistic map with the given conditions such as initial value and bifurcate parameter. One component is used as the input image of the framework of double random phase encoding and encrypted into the ciphertext. Another is decomposed into two phase masks, which are placed into the input plane and transform plane of double random phase encoding, respectively. To strength the nonlinearity of the cryptosystem, these phase masks considered as the main secret keys are further encoded by the aid of two random sequences. Because these keys are produced in the encryption process and directly related to original images, the proposed scheme has high resistance against the potential attacks such as chosen plaintext attack. Meanwhile, the parameters such as wavelength, axial distance, and conditions of the logistic map are considered as additional keys, which can enhance the security level further. Most importantly, the annoying silhouette problem existed in the interference-based encryption methods can be avoided effectively. A set of numerical simulations are presented to demonstrate the validity and feasibility of the proposed technique. [ABSTRACT FROM AUTHOR]

Highlights • The inherent silhouette problem can be removed since two layers based on different optical techniques are combined into a single whole to enhance the security. • The cross-talk disturbance can be avoided since plain images are encrypted in sequence using cascaded fractional Fourier transforms. • A hierarchical authority management can be implemented among multiple users in the proposed multiple-image encryption scheme. Abstract An optical approach of silhouette-free multiple-image encryption based on interference is proposed, with two layers to enhance the level of security. In the first layer, a group of plain images are encoded into an amplitude distribution, called interim, using the cascaded fractional Fourier transforms. In the second layer, the interim is encrypted into two noisy ciphertext images. The two layers are compactly combined into a single whole to assure that the inherent silhouette problem is removed through the involvement of a random phase-only mask as the built-in function of cryptosystem. In addition to the phase mask keys generated in the process of encryption, the security is enhanced further by considering the fractional order as an additional key. Numerical simulations are given to demonstrate the feasibility and validity of this approach. [ABSTRACT FROM AUTHOR]

Highlights • A novel single-pixel correlated imaging scheme based on a serial of pairs of noisy phase profiles is proposed. • The pairs of phase profiles are retrieved from the Hadamard matrix using fast iterative phase retrieval algorithm. • The quality of reconstructed images can be improved greatly with much less measured intensities compared with conventional ghost imaging system. Abstract A single-pixel correlated imaging scheme based on iterative phase retrieval algorithm, which can encode an original object into a series of measured intensities, is proposed in this paper. Initially, a plenty of intensity patterns are derived from the Hadamard matrix with the certain order, and a pair of noisy phase profiles can be obtained by decomposing an intensity pattern via an iterative phase retrieval algorithm. When a pair of phase profiles is cascaded and sequentially embedded into two spatial light modulators in the proposed optical configuration, a measured intensity can be recorded by the bucket detector without spatial resolution. By only making the use of second-order correlation algorithm, the object with high quality can be reconstructed with measured intensities. Meanwhile, the number of recording the measured intensities can be reduced greatly in the process of imaging, which results in high efficiency. The reported approach provides an effective alternative for enriching the related research on single-pixel correlated imaging systems. [ABSTRACT FROM AUTHOR]

A novel optical color image watermarking scheme considering human visual characteristics is presented in gyrator transform domain. Initially, an appropriate reference image is constructed of significant blocks chosen from the grayscale host image by evaluating visual characteristics such as visual entropy and edge entropy. Three components of the color watermark image are compressed based on compressive sensing, and the corresponding results are combined to form the grayscale watermark. Then, the frequency coefficients of the watermark image are fused into the frequency data of the gyrator-transformed reference image. The fused result is inversely transformed and partitioned, and eventually the watermarked image is obtained by mapping the resultant blocks into their original positions. The scheme can reconstruct the watermark with high perceptual quality and has the enhanced security due to high sensitivity of the secret keys. Importantly, the scheme can be implemented easily under the framework of double random phase encoding with the 4f optical system. To the best of our knowledge, it is the first report on embedding the color watermark into the grayscale host image which will be out of attacker's expectation. Simulation results are given to verify the feasibility and its superior performance in terms of noise and occlusion robustness. [ABSTRACT FROM AUTHOR]

• A novel iterative phase retrieval algorithm with high convergent speed is designed to encode an image into a pair of uncorrelated phase-only masks. • A modified nonlinear correlation algorithm with high discrimination capability is proposed to implement the authentication process. • A new computational ghost imaging configuration is proposed, where the reconstruction result with high quality can be obtained with a low number of measurements. Single-pixel correlated imaging has been developed as one of the most promising techniques in the past decades. In this paper, a new mechanism of single-pixel correlated imaging is designed for multiple-image authentication. The object wave is sequentially modulated by a series of phase-only mask pairs embedded into two cascaded spatial light modulators. The modulated wave passes through the input image located in the object plane, and its intensity is recorded as one of the ciphertext values by using a single-pixel bucket detector without spatial resolution. The sparse data of plaintext images are obtained with the multiple-level wavelet transform and used to construct an interim image with the help of binary amplitude masks. The interim image with a smaller size than that of plaintext images is considered as the input of single-pixel correlated imaging, which can guarantee the number of measurements reduced. Simultaneously, the phase-only mask pairs are retrieved from the 2D patterns formed with the row vectors of the spatially orthogonal Hadamard matrix by using an efficient iterative phase retrieval algorithm. Because the redundancy between speckle patterns generated with these phase-only mask pairs is greatly restrained, the number of measurements can be further reduced. Moreover, the related binary amplitude masks are employed as the secret keys so that the security level is also extensively enhanced. Given the above, the proposed method can significantly achieve the goal of multiple-image verification and provide a different research approach for optical authentication based on single-pixel correlated imaging. [ABSTRACT FROM AUTHOR]