Random Binary Matrix Research Articles

Multi-functional liquid crystal devices based on random binary matrix algorithm

ABSTRACT Multi-functional diffraction gratings have found broad applications in laser processing, medicine, beam manipulation, etc. However, based on the existing schemes there are still some challenges in fabricating the diffraction gratings with the controllable and arbitrary diffraction intensity of each order, multiple phase distribution, and polarisation of the output. Here, we propose a new phase mixing algorithm based on the random binary matrix and describe the theoretical foundation and experimental realisation of the proposed scheme. Using the new algorithm, several phase-mixing devices were fabricated, and the experiment verified the relationship of the light intensity, polarisation, phase and the algorithm. Our approach is practical to mix the phases of several diffraction gratings to realise the controllable diffraction orders, offering an innovative idea for the research of the liquid crystal phase mixing devices.

Multiple Image Watermarking with Discrete Cosine Transform

Multiple image watermarking is an advanced concept of singular watermarking techniques. The existing singular digital image watermarking techniques cannot obtain all the design goals, such as imperceptibility, robustness, security, and capacity simultaneously with perfection. Hence, the multiple image watermarking technique is designed that embeds several watermarks into the same host image for conveying multiple information. This paper proposed a multiple image watermarking technique with Discrete Cosine Transform (DCT) for ensuring the low computational time for embedding, encryption, decryption as well as extraction of the watermark images. Here, DCT is used to ensure the visual quality of the host image, and a random binary matrix is used to improve the security of the digital image. We have given a basic framework for multiple image watermarking. Our experimental results show satisfactory performance.

Underwater image compression using energy based adaptive block compressive sensing for IoUT applications

Internet of Underwater Things (IoUT) consists of a large number of interconnected resource-constrained underwater devices that are capable of monitoring vast unexplored water bodies. Specifically, these devices are equipped with cameras to capture the underwater scenes and communicate them with each other and also with the cloud. However the data generated is very high which limits the performance of the IoUT devices in terms of computational capabilities and battery lifetime. Block Compressed Sensing technique which performs block by block fixed sampling can be utilized to achieve data compression however it ends up in image distortions after reconstruction. To unravel this issue, Adaptive Block Compressive Sensing technique is used. In this paper, Energy based Adaptive Block Compressive Sensing (EABCS) with Orthogonal Matching Pursuit reconstruction algorithm is proposed to improve the sampling performance and visual quality of the reconstructed image. Sparse binary random matrix is used as measurement matrix as it is highly sparse. With this energy based adaptive strategy, higher measurements are assigned to blocks with higher energy and vice versa. The proposed EABCS technique has achieved better compression with approximately 25–30% of measurements/samples with an increase in Peak signal to noise ratio of about 3–5 dB and structural similarity Index of around 0.1–0.3 with respect to other adaptive strategies. Percentage of space saving is also about 60–70%.

Full Stokes single photon compressive polarization imaging.

We demonstrate a full Stokes polarization imaging system based on compressed sampling and single photon counting. The control and synchronization counting module based on field-programmable gate array is specially developed to control the rotation stage for polarization imaging at different directions. Additionally, it can load the binary random matrix into a digital micro-mirror device controller for each measurement and count the single photon pulse output from the photon counting photomultiplier tube simultaneously. The system can realize high-sensitivity single photon compressive imaging of the target under different polarization directions. On this basis, the high-quality Stokes parameter images and the angle of the linear polarization image can be obtained. The experimental results show that the polarization information can be reconstructed at a very low sampling ratio.

On the Rank of a Random Binary Matrix

We study the rank of a random $n \times m$ matrix $\mathbf{A}_{n,m;k}$ with entries from $GF(2)$, and exactly $k$ unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all ${n \choose k}$ such columns.
 We obtain an asymptotically correct estimate for the rank as a function of the number of columns $m$ in terms of $c,n,k$, and where $m=cn/k$. The matrix $\mathbf{A}_{n,m;k}$ forms the vertex-edge incidence matrix of a $k$-uniform random hypergraph $H$. The rank of $\mathbf{A}_{n,m;k}$ can be expressed as follows. Let $|C_2|$ be the number of vertices of the 2-core of $H$, and $|E(C_2)|$ the number of edges. Let $m^*$ be the value of $m$ for which $|C_2|= |E(C_2)|$. Then w.h.p. for $m<m^*$ the rank of $\mathbf{A}_{n,m;k}$ is asymptotic to $m$, and for $m \ge m^*$ the rank is asymptotic to $m-|E(C_2)|+|C_2|$.
 In addition, assign i.i.d. $U[0,1]$ weights $X_i, i \in {1,2,...m}$ to the columns, and define the weight of a set of columns $S$ as $X(S)=\sum_{j \in S} X_j$. Define a basis as a set of $n-𝟙 (k\text{ even})$ linearly independent columns. We obtain an asymptotically correct estimate for the minimum weight basis. This generalises the well-known result of Frieze [On the value of a random minimum spanning tree problem, Discrete Applied Mathematics, (1985)] that, for $k=2$, the expected length of a minimum weight spanning tree tends to $\zeta(3)\sim 1.202$.

Measurement Matrix Construction for Large-area Single Photon Compressive Imaging.

We have developed a single photon compressive imaging system based on single photon counting technology and compressed sensing theory, using a photomultiplier tube (PMT) photon counting head as the bucket detector. This system can realize ultra-weak light imaging with the imaging area up to the entire digital micromirror device (DMD) working region. The measurement matrix in this system is required to be binary due to the two working states of the micromirror corresponding to two controlled elements. And it has a great impact on the performance of the imaging system, because it involves modulation of the optical signal and image reconstruction. Three kinds of binary matrix including sparse binary random matrix, m sequence matrix and true random number matrix are constructed. The properties of these matrices are analyzed theoretically with the uncertainty principle. The parameters of measurement matrix including sparsity ratio, compressive sampling ratio and reconstruction time are verified in the experimental system. The experimental results show that, the increase of sparsity ratio and compressive sampling ratio can improve the reconstruction quality. However, when the increase is up to a certain value, the reconstruction quality tends to be saturated. Compared to the other two types of measurement matrices, the m sequence matrix has better performance in image reconstruction.

Large-area single photon compressive imaging based on multiple micro-mirrors combination imaging method

We demonstrate a single photon compressive imaging system with the image plane up to the entire digital micro-mirror device (DMD) work area. A parallel light source is designed to reduce the influence of light scattering on imaging resolution and a photon counting photomultiplier tube (PMT) with a large photosensitive area is used to effectively collect light reflected from the full screen of DMD. A control and counting circuit, based on Field-Programmable Gate Array (FPGA), is developed to load binary random matrix into the DMD controller for each measurement, and to count single-photon pulse output from PMT simultaneously. To reduce imaging time and huge memory occupation for image reconstruction, a multiple micro-mirrors combination imaging method is proposed. The signal-to-noise ratio and detection limit of the imaging system is theoretically deduced. Theoretical analysis and experimental results show that micro-mirrors combination imaging method is more suitable for faster imaging in a weaker-light-level environment. In order to achieve high imaging quality, the size of the combined pixels and the average time of each measurement should be moderate, so that the impact of Poisson shot noise is minimized.

Energy efficient surveillance system using WVSN with reweighted sampling in modified fast Haar wavelet transform domain

Wireless visual sensor network (WVSN) consists of a large number of nodes that are capable of acquiring, compressing and transmitting images. Surveillance becomes a vital application area of WVSN as they can be deployed in various environments to monitor and collect information. The lifetime of the nodes in the network depends on the energy consumption. Hence in this paper, block compressed sensing (BCS) based image transmission technique that utilizes Energy based Reweighted sampling (ERWS) in Modified Fast Haar Wavelet Transform (MFHWT) domain is proposed to reduce energy consumption considerably. Sparse binary random matrix is used to acquire CS measurements in MFHWT domain. In addition, the proposed technique also maintains the image quality. The developed algorithm is applied and tested for a car parking lot monitoring system. It is evident from the simulation results that the proposed method achieves better PSNR values even for fewer measurements. Experimental analysis is performed using Atmega 128 processor of Mica mote in WinAVR by Atmel. The proposed method has approximately 85.5% lesser energy consumption than other Compressed Sensing (CS) methods. Lossless Entropy Coding is applied to the ERWS measurements and considerable reduction in number of transmitted bits is also achieved. The algorithm has also been tested in WINGZ mote in real time.

An Efficient Semi-fragile Watermarking Scheme for Tamper Localization and Recovery

To solve the problem that remote sensing images are vulnerable to be tampered, a semi-fragile watermarking scheme was proposed. Binary random matrix was used as the authentication watermark, which was embedded by quantizing the maximum absolute value of directional sub-bands coefficients. The average gray level of every non-overlapping 4×4 block was adopted as the recovery watermark, which was embedded in the least significant bit. Watermarking detection could be done directly without resorting to the original images. Experimental results showed our method was robust against rational distortions to a certain extent. At the same time, it was fragile to malicious manipulation, and realized accurate localization and approximate recovery of the tampered regions. Therefore, this scheme can protect the security of remote sensing image effectively.

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

Fragile image watermarking scheme based on VQ index sharing and self-embedding

In this paper, we propose a self-embedding fragile watermarking scheme using vector quantization (VQ) and index sharing. First, the principle contents of original image are compactly represented by a series of VQ indices. Then, after permutation, the binary bits of VQ indices are extended to generate reference-bits by a random binary matrix, which can make all reference-bits share the information of VQ index bits from different regions of the whole image. The image is embedded with watermark-bits including hash-bits for tampering localization and reference-bits for content recovery, and is transmitted to receiver side. Tampered regions in the received, suspicious image can be accurately located and then be recovered by VQ index reconstruction. Experimental results demonstrate that the proposed scheme can achieve successful content recovery for larger tampering rate and obtain better visual quality of recovered results than the reported schemes.

Degree sequences of random digraphs and bipartite graphs

We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one of the two colour classes. This problem can alternatively be described in terms of the row and sum columns of random binary matrix or the in-degrees and out-degrees of a random digraph, in which case we can optionally forbid loops. It can also be cast as a problem in random hypergraphs, or as a classical occupancy, allocation, or coupon collection problem. In each case, provided the two colour classes are not too different in size nor the number of edges too low, we define a probability space based on independent binomial variables and show that its probability masses asymptotically equal those of the degrees in the graph model almost everywhere. The accuracy is sufficient to asymptotically determine the expectation of any joint function of the degrees whose maximum is at most polynomially greater than its expectation.

Accelerated Air-coupled Ultrasound Imaging of Wood Using Compressed Sensing

Air-coupled ultrasound has shown excellent sensitivity and specificity for the nondestructive imaging of wood-based material. However, it is time-consuming, due to the high scanning density limited by the Nyquist law. This study investigated the feasibility of applying compressed sensing techniques to air-coupled ultrasound imaging, aiming to reduce the number of scanning lines and then accelerate the imaging. Firstly, an undersampled scanning strategy specified by a random binary matrix was proposed to address the limitation of the compressed sensing framework. The undersampled scanning can be easily implemented, while only minor modification was required for the existing imaging system. Then, discrete cosine transform was selected experimentally as the representation basis. Finally, orthogonal matching pursuit algorithm was utilized to reconstruct the wood images. Experiments on three real air-coupled ultrasound images indicated the potential of the present method to accelerate air-coupled ultrasound imaging of wood. The same quality of ACU images can be obtained with scanning time cut in half.

Estimation of Vectors Similarity by Their Randomized Binary Projections

We analyze the estimation of the angle, scalar product, and the Euclidean distance of real-valued vectors using binary vectors with controlled sparsity. Transformation is carried out by projection using a binary random matrix with elements {0,1} and the output threshold transformation. We also provide a comparative analysis of the error obtained while estimating the similarity measures of input vectors by some similarity measures of output binary vectors based on their scalar product.

Formation of Similarity-Reflecting Binary Vectors with Random Binary Projections

We propose a transformation of real input vectors to output binary vectors by projection using a binary random matrix with elements {0,1} and thresholding. We investigate the rate of convergence of the distribution of vector components before binarization to the Gaussian distribution as well as its relationship to the estimation error of the angle between the input vectors by the binarized output vectors. It is shown that for the choice of projection parameters that provide nearly-Gaussian distribution, the experimental and analytical errors are close.

Vector Data Transformation Using Random Binary Matrices

This article proposes to use a binary random matrix with the elements {0,1} to project input floating-point vectors onto output floating-point vectors of smaller dimension. The accuracies of estimates of the scalar product, Euclidean distance, and norm of input vectors are analyzed with respect to output vectors. It is analytically and experimentally shown that an error for the proposed random projection is smaller than that for a ternary random matrix.

Reliable recognition of masked binary matrices. Connection to information security in map systems

General questions compressed representation of a given set of binary matrices of the same size by associative masking. Existence and uniqueness are proved: 1) identification in a random binary matrix of one of the matrices of the set of masked patterns of the same size; 2) mistaken recognition on this set of matrices by mask immersed in a random sequence of the inversion of any number of unmasked bits. Connection of these questions with reliability of protection of cartographical data is established at action of interference misinformation in a corporate network.

Double image encryption based on phase-amplitude hybrid encoding and iterative phase encoding in fractional Fourier transform domains

A new method for double image encryption is proposed that is based on amplitude-phase hybrid encoding and iterative random phase encoding in fractional Fourier transform (FrFT) domains. In the iterative random phase encoding operation, a binary random matrix is defined to encode two original images to a single complex-valued image, which is then converted into a stationary white noise image by the iterative phase encoding with FrFTs. Compared with the previous schemes that uses fully phase encoding, the proposed method reduces the difference between two original images in key space and sensitivity to the FrFT orders. The primitive images can be retrieved exactly by applying correct keys with initial conditions of chaotic system, the pixel scrambling operation and the FrFT orders. Computer simulations demonstrate that the encryption method has impressively high security level and certain robustness against data loss and noise interference.

On the Generation of Random Numbers for Symmetric Cryptography Utilizing Astronomical Data

In this paper, a novel method for obtaining the random numbers utilizing astronomical data is proposed. The method uses two different algorithms for generation of random numbers sequence. Astronomical data collected from the scientific study of the universe, especially of the relative motions, relative positions of astronomical objects are utilized in our algorithms. The first algorithm uses a particular astronomical object in a fixed position for the random number generation. The random sequence is obtained from the relative positions of other astronomical objects with reference to the selected object. The second algorithm selects any diverse astronomical object as a reference in a varying mode for computation of the relative positions of different objects with that reference to generate the random number stream. Both algorithms use mathematical equations for computing the next jump or hop to the other astronomical object. The generated random numbers obtained from the two algorithms are tested with a standard statistical test suite including, frequency test, run test, random binary matrix rank test, complexity test, universal test and entropy test. The results obtained from the statistical tests of the two algorithms are compared with the other publicly available random number generation techniques, like, linear congruential and modular exponentiation. The preliminary results show that the algorithms perform well. The random numbers generated by our method has sufficient period and unpredictability that makes them suitable for consideration as encryption keys in symmetric cryptography.

Double image encryption by using iterative random binary encoding in gyrator domains

We propose a double image encryption by using random binary encoding and gyrator transform. Two secret images are first regarded as the real part and imaginary part of complex function. Chaotic map is used for obtaining random binary matrix. The real part and imaginary part of complex function are exchanged under the control of random binary data. An iterative structure composed of the random binary encoding method is designed and employed for enhancing the security of encryption algorithm. The parameters in chaotic map and gyrator transform serve as the keys of this encryption scheme. Some numerical simulations have been made, to demonstrate the performance this algorithm.