Flexible multiple-image encryption algorithm based on log-polar transform and double random phase encoding technique

We present a novel multiple-image encryption algorithm by combining log-polar transform with double random phase encoding in the fractional Fourier domain. In this algorithm, the original images are transformed to annular domains by inverse log-polar transform and then the annular domains are merged into one image. The composite image is encrypted by the classical double random phase encoding method. The proposed multiple-image encryption algorithm takes advantage of the data compression characteristic of log-polar transform to obtain high encryption efficiency and avoids cross-talk in the meantime. Optical implementation of the proposed algorithm is demonstrated and numerical simulation results verify the feasibility and the validity of the proposed algorithm.     

Color image security system using double random-structured phase encoding in gyrator transform domain

A novel method for encoding color information based on a double random phase mask and a double structured phase mask in a gyrator transform domain is proposed. The amplitude transmittance of the Fresnel zone plate is used as structured phase-mask encoding. A color image is first segregated into red, green, and blue component images. Each of these component images are then independently encrypted using first a random phase mask placed at the image plane and transmitted through the first structured phase mask. They are then encoded by the first gyrator transform. The resulting information is again encrypted by a second random phase mask placed at the gyrator transform plane and transmitted through the second structured phase mask, and then encoded by the second gyrator transform. The system parameters of the structured phase mask and gyrator transform in each channel serve as additional encryption keys and enlarge the key space. The encryption process can be realized with an electro-optical hybrid system. The proposed system avoids problems arising from misalignment and benefits of a higher space-bandwidth product. Numerical simulations are presented to confirm the security, validity, and possibility of the proposed idea.     

Single-channel color image encryption using a modified Gerchberg-Saxton algorithm and mutual encoding in the Fresnel domain

A single-channel color image encryption is proposed based on the modified Gerchberg-Saxton algorithm (MGSA) and mutual encoding in the Fresnel domain. Similar to the double random phase encoding (DRPE), this encryption scheme also employs a pair of phase-only functions (POFs) as encryption keys. But the two POFs are generated by the use of the MGSA rather than a random function generator. In the encryption process, only one color component is needed to be encrypted when these POFs are mutually served as the second encryption keys. As a result, a more compact and simple color encryption system based on one-time-pad, enabling only one gray cipheretext to be recorded and transmitted when holographic recording is used, is obtained. Moreover, the optical setup is lensless, thus easy to be implemented and the system parameters and wavelength can be served as additional keys to further enhance the security of the system. The feasibility and effectiveness of the proposed method are demonstrated by numerical results.     

Multiple images encryption method via spiral phase mask rotations under a JTC system

A method of multiple-image encryption via spiral phase mask rotations based on the joint transform correlator encryption system was proposed. Multiple images can be encrypted into one ciphertext through this approach. When decrypted the ciphertext, we have no need to produce too many key masks, only need rotate the key mask to the angle corresponding to the plaintext. The system also has good resistance to occlusion attack and differential attack. Computer simulations initially verified the correctness of this method, and the experimental results also confirmed its validity further.     

Multiple-image encryption scheme with a single-pixel detector

Abstract

A multiple-image encryption (MIE) scheme with a single-pixel detector has been proposed according to the principle of ghost imaging. In this scheme, each of the spatially coherent laser beams is modified by a set of phase-mask keys and illuminates on a secret image. All of the transmitted lights are recorded together by a single-pixel (bucket) detector to obtain a ciphertext, but anyone of the secret images can be decrypted from the ciphertext independently without any mutually overlapped despite some noise in them. The MIE scheme will bring convenience for data storage and transmission, especially in the case that different secret images need to be distributed to different authorized users, because the ciphertext is a real-valued function and this scheme can effectively avoid the secret images being extracted mutually. The basic principle of the MIE scheme is described theoretically and verified by computer simulations. Finally, the feasibility, robustness and encryption capacity are also tested numerically.     

Multiple-image encryption by compressive holography

We present multiple-image encryption (MIE) based on compressive holography. In the encryption, a holographic technique is employed to record multiple images simultaneously to form a hologram. The two-dimensional Fourier data of the hologram are then compressed by nonuniform sampling, which gives rise to compressive encryption. Decryption of individual images is cast into a minimization problem. The minimization retains the sparsity of recovered images in the wavelet basis. Meanwhile, total variation regularization is used to preserve edges in the reconstruction. Experiments have been conducted using holograms acquired by optical scanning holography as an example. Computer simulations of multiple images are subsequently demonstrated to illustrate the feasibility of the MIE scheme.     

Role of phase key in the double random phase encoding technique: an error analysis

We perform a numerical analysis of the double random phase encryption-decryption technique to determine how, in the case of both amplitude and phase encoding, the two decryption keys (the image- and Fourier-plane keys) affect the output gray-scale image when they are in error. We perform perfect encryption and imperfect decryption. We introduce errors into the decrypting keys that correspond to the use of random distributions of incorrect pixel values. We quantify the effects that increasing amounts of error in the image-plane key, the Fourier-plane key, and both keys simultaneously have on the decrypted image. Quantization effects are also examined.     

Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain

We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.     

A New Multi Chaos-Based Compression Sensing Image Encryption

The advancements in technology have substantially grown the size of image data. Traditional image encryption algorithms have limited capabilities to deal with the emerging challenges in big data, including compression and noise toleration. An image encryption method that is based on chaotic maps and orthogonal matrix is proposed in this study. The proposed scheme is built on the intriguing characteristics of an orthogonal matrix. Gram Schmidt disperses the values of pixels in a plaintext image by generating a random orthogonal matrix using logistic chaotic map. Following the diffusion process, a block-wise random permutation of the data is performed using multi-chaos. The proposed scheme provides sufficient security and resilience to JPEG compression and channel noise through a series of experiments and security evaluations. It enables Partial Encryption (PE) for faster processing as well as complete encryption for increased security. The higher values of the number of pixels change rates and unified average change intensity confirm the security of the encryption scheme. In contrast to other schemes, the proposed approach can perform full and partial encryption depending on security requirements.     

Optical encryption system that uses phase conjugation in a photorefractive crystal

We implement an optical encryption system based on double-random phase encoding of the data at the input and the Fourier planes. In our method we decrypt the image by generating a conjugate of the encrypted image through phase conjugation in a photorefractive crystal. The use of phase conjugation results in near-diffraction-limited imaging. Also, the key that is used during encryption can also be used for decrypting the data, thereby alleviating the need for using a conjugate of the key. The effect of a finite space-bandwidth product of the random phase mask on the encryption system's performance is discussed. A theoretical analysis is given of the sensitivity of the system to misalignment errors of a Fourier plane random phase mask.     

Coaxial holographic encoding based on pure phase modulation

We describe a simple technique for coaxial holographic image recording and reconstruction, employing a spatial light modulator (SLM) modified in pure phase mode. In the image encoding system, both the reference beam in the outside part and the signal beam in the inside part are displayed by an SLM based on the twisted nematic LCD. For a binary image, the part with amplitude of "1" is modulated with random phase, while the part with amplitude of "0" is modulated with constant phase. After blocking the dc component of the spatial frequencies, a Fourier transform (FT) hologram is recorded with a uniform intensity distribution. The amplitude image is reconstructed by illuminating the reference beam onto the hologram, which is much simpler than existing phase modulated FT holography techniques. The technique of coaxial holographic image encoding and recovering with pure phase modulation is demonstrated theoretically and experimentally in this paper. As the holograms are recorded without the high-intensity dc component, the storage density with volume medium may be increased with the increase of dynamic range. Such a simple modulation method will have potential applications in areas such as holographic encryption and high-density disk storage systems.     

Study on the influence of key errors on the deciphered image in the double random phase encryption system by applying affine cryptography

In this paper, an explanation of the double random phase encryption technique using affine cryptography is proposed. The principle of this technique to decipher an optical image may be regarded as an optical realization of the affine cryptography. During the deciphering process of double random phase encryption based on the 4-f optical system, if there are errors in the random phase, which plays as a decryption key, these errors will be added to the encrypted image in the form of noise. The signal-to-noise ratio of the decrypted image has been analysed under the situation that the errors had occurred, both in the position of lateral direction and the value of the pixel function from the random phase mask. Furthermore, the fault tolerance of orientation in the decipher system has been discussed when only a part of the random phase mask is used.     

Lensless multiple-image optical encryption based on improved phase retrieval algorithm

A novel architecture of the optical multiple-image encryption based on the modified Gerchberg-Saxton algorithm (MGSA) by using cascading phase only functions (POFs) in the Fresnel transform (FrT) domain is presented. This proposed method can greatly increase the capacity of the system by avoiding the crosstalk, completely, between the encrypted target images. Each present stage encrypted target image is encoded as to a complex function by using the MGSA with constraining the encrypted target image of the previous stage. Not only the wavelength and position parameters in the FrT domain can be keys to increase system security, the created POFs are also served mutually as the encryption keys to decrypt target image from present stage into next stage in the cascaded scheme. Compared with a prior method [Appl. Opt.48, 2686-2692 (2009)], the main advantages of this proposed encryption system is that it does not need any transformative lenses and this makes it very efficient and easy to implement optically. Simulation results show that this proposed encryption system can successfully achieve the multiple-image encryption via fewer POFs, which is more advantageous in simpler implementation and efficiency than a prior method where each decryption stage requires two POFs to accomplish this task.     

压缩感知在医学超声成像中的仿真应用研究

为了解决医学超声成像系统中面临的采样率高,数据量大的问题,提出将压缩感知理论方法用于医学超声成像。首先建立了超声信号在时域的稀疏表达模型,然后利用模拟信息转换器对信号进行稀疏采样,最后使用最优化方法完成回波信号重建,利用合成发射孔径方式完成最终超声成像。为了验证算法的有效性,利用Field II对点目标以及复杂组织目标进行了仿真实验,在均方误差、分辨率、对比度以及成像质量上与常规成像结果对比分析。结果表明,采用1/2奈奎斯特采样频率,以30%原始数据所完成的成像仍然可保证良好的图像质量。采用压缩感知理论可以大幅度降低医学超声系统的采样率及总数据量。     

基于圆柱衍射与离散余弦变换的图像光学加密算法

目的为了实现多幅图像的同步加密,并增强加密系统的抗破译能力,提出一种基于圆柱衍射域的相位截断与离散余弦变换的多图像光学加密算法。方法首先引入压缩感知(CS,Compress Transform)方法,对输入明文实施压缩;基于离散余弦变换DCT(Discrete Cosine Transform)对压缩明文完成分解,获取相应的DCT系数,形成系数矩阵;构建迭代复数,将每个压缩明文对应的系数矩阵融合为一个复矩阵,通过DCT逆变换,形成一幅组合图像。联合Hilbert变换与波带片相位模型,构建调制掩码;引入圆柱衍射域的相位截断机制,联合调制掩码,对组合图像实施光学加密,获取密文与私钥。结果实验数据表明,相对于已有的多图像同步加密方法而言,所提算法具备更高的加密安全性,密文熵值以及相邻像素间的相关系数分别达到了7.998,0.0012,且具有强烈的密钥敏感性。结论所提加密算法可以抵御网络中外来攻击,在图像信息防伪领域具有一定的参考价值。     

A kind of multilevel authentication system for multiple-image by modulated real part synthesis and iterative phase multiplexing

A kind of multilevel authentication system for multiple-image based on modulated real part synthesis and iterative phase multiplexing in the Fresnel domain is proposed. In the design process of the low-level authentication system, a series of normalized real part information are iteratively generated by phase retrieval algorithm in the Fresnel domain, and the final private keys for different individual low-level certification images can be fabricated by binary amplitude modulation, superposition, synthesis, and sampling; while in the design process of the high-level authentication system, the final private keys for different individual high-level certification images can be generated by iterative phase information encoding and multiplexing. During the high-level authentication, the meaningful certification image can be reconstructed by the inverse Fresnel transform with the corresponding correct private keys, meanwhile, the correlation coefficient is utilized as judgment criterion; while in the low-level authentication, with the help of correct keys, the noise-like image with meaningless information can be recovered, but a remarkable peak output in the nonlinear correlation coefficient can be generated, which is adopted as the criterion to judge whether the low-level authentication is successful or not. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.     

Image encoding based on a damped triangular function and a discrete sequence

An encoding system based on a damped triangular function is presented. The image encoding is implemented by a computational algorithm, which transforms the image intensity to a triangular function. This procedure generates a random pattern from the original image. Thus, a secret image is obtained to perform the electronic transmission. The decoding algorithm is implemented by an inverse discrete damped triangular function. This procedure generates a discrete sequence by sampling the damped triangular function. The sequence contains the key data to compute the image decoding. Then, the original image is retrieved by matching the intensity of the secret image in the discrete sequence. The viability of the proposed method is established based on the quality of the image encoding and decoding. These parameters are evaluated based on traditional encoding methods to provide evidence of the power of the proposed method. Thus, the contribution of the proposed technique in the field of image encoding is stated. The technique is tested by encoding real objects and its results are presented in computational form.     

Information hiding technique with double phase encoding

We propose a technique for information hiding using double phase encoding. The proposed method uses a weighted double phase-encoded hidden image added to a host image referred to as the transmitted image. We develop an analytical presentation for the system performance using the statistical properties of double phase encoding. The peak signal-to-noise-ratio metric is used as a measure for the degradation in the quality of the host image and the recovered hidden image. We test, analytically, the distortion of the hidden image that is due to the host image and the effect of occlusion of the pixels of the transmitted image (that is, the host image containing the hidden image). Moreover, we discuss the effect of using only the real part of the transmitted image to recover the hidden image. Computer simulations are presented to test the system performance against these types of distortion. The simulations illustrate the system ability to recover the hidden image under distortions and the robustness of the hidden image against removal trials.     

基于改进SL0算法的MSFA模式多光谱图像去马赛克方法

针对MSFA模式多光谱图像去马赛克算法精度较低和计算复杂等缺点,利用压缩感知理论在信号恢复方面的优势,提出一种新的光谱图像去马赛克算法。采用随机模式的多光谱滤波阵列MSFA获得马赛克图像,通过将MSFA采样值等效为压缩感知理论中的感知矩阵采样所得数据,将去马赛克问题转化为压缩感知稀疏信号恢复问题,并利用多光谱图像的谱间相关性,给出基于压缩感知框架的多光谱图像去马赛克模型,最后采用改进的光滑0范数算法求解去马赛克问题,得到重构的多光谱图像。客观评价指标显示,该算法的峰值信噪比值相较于克罗内克压缩感知和组稀疏两种算法有明显提高;主观评价结果表明,该算法能有效减少重构图像中的锯齿现象,具有更好的视觉效果。     

Multiple-phase retrieval for optical security systems by use of random-phase encoding

The technique of the multiple phase encoding for optical security and verification systems is presented in this paper. This technique is based on a 4-f optical correlator that is a common architecture for optical image encryption and verification systems. However, two or more phase masks are iteratively retrieved by use of the proposed multiple phases retrieval algorithm (MPRA) to obtain the target image. The convergent speed of the iteration process in the MPRA is significantly increased and the recovered image is much more similar to the target image than those in previous approaches. In addition, the quantization effects due to the finite resolution of the phase levels in practical implementation are discussed. The relationships between the number of phase masks and the quantized phase levels are also investigated. According to the simulation results, two and three phase masks are enough to design an efficient security verification system with 64 and 32 phase levels, respectively.