Measurement Matrix Research Articles

Sequential color ghost imaging based on compressed sensing algorithm of post-processing measurement matrix

Compressed sensing algorithm can be used in color ghost imaging to restore the image of object at the less demand of measurements times. However, the quality of the reconstructed color image is usually not satisfactory. In this paper, we propose a sequential color ghost imaging method that can complete color ghost imaging in a simple architecture and improve the quality of color image, which is optimize compressed sensing that can get better result of compressed sensing algorithm by post-processing the measurement matrix and establishing a new compressed sensing process. Under the condition of the same measurement times and reconstruction algorithm, compared with the unpost-processing one, the quality and detail of reconstructed image by the post-processing measurement matrix is quite improved especially with the increase of measurement times. Discussions on factors affecting the quality of the new compressed sensing process, such as the number of measurement and the detection noise intensity, are also conducted. Numerical simulation and physical experiment verified our proposed method.

An integrated adaptive Kalman filter for improving the reliability of navigation systems

Abstract Integrated GPS/INS using Kalman filter is the best technique for improving navigation accuracy. Assuming that the covariance matrices are known and constant, a conventional Kalman filter (CKF) is usually used, however, when they are unknown and time-varying, several adaptive estimation approaches have to be developed to estimate the statistical information of the measurement (R), process (Q), and state (P) covariance matrices. In many situations, blunders/faults in the measurement model and/or sudden changes in the dynamic model may occur during the navigation period. Therefore, the CKF, as well as the adaptive Kalman filter (AKF) will exhibit abnormal behavior and may lead the filter to be suboptimal or even diverge. In this study, the Sage-Husa adaptive Kalman filter (SHAKF) and innovation-based adaptive Kalman filter (IAKF) approaches are employed for adapting the measurement covariance matrix(R). In the case of abrupt changes in the dynamic model, the state covariance matrix (P) is adapted using the strong tracking filter (STF). The performance of these adaptive approaches is evaluated before and after simulating a fault of different sizes in the measurement and dynamic models. The results show that with a large window width, the SHAKF outperforms the CKF and IAKF. However, when the system encounters any fault either in the measurement or dynamic model, the SHAKF loses its optimality and diverges. The sensitivity of the SHAKF to the fault is because the R matrix accumulates with the propagation of the recursive noise estimator. On the other hand, the IAKF and STF provide better performance than both the CKF and SHAKF because the gain matrix is adaptively adjusted to mitigate the influence of the fault, and therefore, they behave normally when a fault of any size occurs in the measurement and/or dynamic model.

A visually secure image encryption scheme based on adaptive block compressed sensing and non-negative matrix factorization

The traditional block compressive sensing theory cannot make full use of the difference of image block information characteristics for sampling, and the measurement matrix cannot fully measure the image according to the image block information characteristics. To solve these problems, we design an adaptive block compressed sensing (ABCS) algorithm, and we propose a visually secure image encryption scheme based on ABCS and non-negative matrix factorization (NMF). First, the plain image is decomposed by Tetrolet transform. Then, we perform matrix shuffling to optimize the sparsity of the sparse matrix. Next, adaptive sampling and measurement are performed according to the information distribution characteristics between the image blocks to compress the image to a quarter of its original size. Last, we design a scrambling–diffusion framework based on tetrominoes to obtain the secret image, which is then embedded into the carrier image by means of NMF to obtain a visually secure cipher image. The experimental results show that the proposed scheme can consider the security of image information transmission and the integrity of reception, and has good resistance to various attacks.

Doubly iteratively reweighted algorithm for constrained compressed sensing models

We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and nonconvex loss functions such as the Cauchy loss function and the Tukey biweight loss function in the constraint. Our framework employs iteratively reweighted $$\ell _1$$ and $$\ell _2$$ schemes to construct subproblems that can be efficiently solved by well-developed solvers for basis pursuit denoising such as SPGL1 by van den Berg and Friedlander (SIAM J Sci Comput 31:890-912, 2008). We propose a new termination criterion for the subproblem solvers that allows them to return an infeasible solution, with a suitably constructed feasible point satisfying a descent condition. The feasible point construction step is the key for establishing the well-definedness of our proposed algorithm, and we also prove that any accumulation point of this sequence of feasible points is a stationary point of the constrained compressed sensing model, under suitable assumptions. Finally, we compare numerically our algorithm (with subproblems solved by SPGL1 or the alternating direction method of multipliers) against the SCP $$_\textrm{ls}$$ in Yu et al. (SIAM J Optim 31: 2024-2054, 2021) on solving constrained compressed sensing models with the log-penalty function as the objective and the Cauchy loss function in the constraint, for badly scaled measurement matrices. Our computational results show that our approaches return solutions with better recovery errors, and are always faster.

High-Sensitivity Transverse-Load and Axial-Strain Sensor Based on Air-Bubble Fabry–Pérot Cavity and Fiber Sagnac Loop Cascaded

We have designed a highly sensitive optical fiber transverse load and axial strain sensor based on the cascaded Fabry–Perot (F–P) cavity and fiber Sagnac loop. F–P cavity is composed of an air-bubble formed by a Section of quartz capillary discharge. Fiber Sagnac loop is made by winding a Section of panda fiber (PF) through a 3 dB coupler. When the free spectral ranges (FSRs) of two interferometers are similar, they are cascaded to form the optical Vernier effect, which amplifies the sensitivity of the sensor. The experimental results show that the sensitivities of transverse load and axial strain of the sensor are up to 19.1 nm/N and 28.9 pm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula> , respectively. The sensitivities of a single F–P cavity for measuring the transverse load and the axial strain are 1.5 nm/N and 2.4 pm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula> , respectively. It can be seen that by using the optical Vernier effect, the sensitivity of the transverse load and axial strain of the sensor is improved by 12.7 and 12 times, respectively. The measurement matrix is constructed by using the sensitivities of a single F–P cavity and the cascaded structure to realize the simultaneous measurement of the transverse load and axial strain and eliminate the cross-sensitivity between them. The designed sensor has a certain attraction in small load and small strain monitoring.

Experimental Study on Measuring Petzval Image Plane of Streak Tube with Single Image

In the process of image reconstruction of compressed sensing algorithms, building a measurement matrix related to the parameters of the imaging system is necessary to improve its imaging quality. Additionally, building a compressed ultrafast imaging system based on a streak camera, which includes aberrations in the imaging system, is necessary. However, the aberration coefficient of the streak tube can be obtained only by numerical calculation based on the known internal structure of the streak tube, and it does not apply to a tube with an unknown structure. Based on the Lagrange–Helmholtz relation, which is widely established in electronic optical imaging systems, this study proposes a method to obtain the Petzval image plane of a streak tube by measuring only a single image without considering the internal structure of the streak tube. This method provides a reference for the construction of the measurement matrix in the application of the compressed sensing algorithm; additionally, it provides a test scheme for the performance index of the streak tube after assembly in commercial production to further optimize the assembly process and improve the yield of production.

Dual-parameter optical fiber sensor for temperature and humidity based on PMMA-microsphere and FBG composite structure

In this work, we proposed and experimentally demonstrated an optical fiber temperature and humidity sensor composed of a polymethyl methacrylate (PMMA)-microsphere and a fiber Bragg grating (FBG), and realize monitoring the environment temperature and humidity simultaneously. The experimental results show that when the relative humidity (RH) change from 35% to 85%, the response sensitivity of the Fabry-Pérot (F-P), which is formed between PMMA-microsphere and the fiber end-face, is about 127 pm/%RH. However, the FBG in the structure is not sensitive to humidity. When temperature changes from 33 °C to 58 °C, the response sensitivity of the F-P and FBG are about 45.68 pm/°C and 10 pm/°C, respectively. When temperature and humidity change simultaneously, these two-parameters can be monitored simultaneously by using the dual-parameter measurement matrix method. The optical fiber dual-parameter sensor offers numerous advantages, such as low cost, high sensitivity, and easy fabrication.

Framework for Segmented threshold [formula omitted] gradient approximation based network for sparse signal recovery

Signal reconstruction from compressed sensed data need iterative methods since the sparse measurement matrix is analytically non invertible. The iterative thresholding and ℓ0 function minimization are of special interest as these two operations provide sparse solution. However these methods need an inverse operation corresponding to the measurement matrix for estimating the reconstruction error. The pseudo-inverse of the measurement matrix is used in general for this purpose. Here a sparse signal recovery framework using an approximate inverse matrix Q and iterative segment thresholding of ℓ0 and ℓ1 norm with residue addition is presented. Two recovery algorithms are developed using this framework. The ℓ0 based method is later developed to a basis function dictionary based network for sparse signal recovery. The proposed framework enables the users experiment with different inverse matrix to achieve better efficiency in sparse signal recovery and implement the algorithm in computationally efficient way.

Compressed phase coding-based optical image encryption

With the development of artificial intelligence technology, the traditional inflexible optical image encryption system has been difficult to resist security attacks such as chosen-plaintext attack and known-plaintext attack, and its security has been greatly challenged. Therefore, an optical image encryption method based on compressed phase coding is proposed, in which a spatial light modulator (SLM) is used to encode the phase of the optical system randomly, and then combined with the measurement matrix in the single pixel sampling process to build a flexible key system. In the encryption process, a phase-only SLM is firstly implemented to realize phase encoding of the original plaintext image and loading the phase key. Then the modulated reference light is implemented to further hide the complex amplitude distribution of the encrypted image. Finally, the encoded object light and reference light are coherently superimposed in the digital micromirror device (DMD), and the inner product operation is carried out with the measurement matrix to realize further encryption and collected by the single pixel detector. Both simulation and experiment proved that the proposed compressed phase coding-based image encryption system is similar to "one time one pad" cryptographic system, which greatly improves the security of the optical encryption system.

Recovery analysis of log-sum minimization under mutual incoherence property

The log-sum minimization has been widely employed in signal and image processing. In this paper, in order to analyze its applicable conditions and achievable boundary for compressed sensing (CS) scenarios, some theoretical derivations of the log-sum minimization are studied based on the mutual incoherence property (MIP) of a measurement matrix. Firstly, the existing condition of the global minimum is demonstrated for the log-sum minimization without noise perturbation. Secondly, for the iterative threshold log-sum (ITL) algorithm, the theoretical performance guarantee of recovering sparse signals disturbed by noise is proposed. Additionally, comprehensive experimental results verify the theoretical analysis for the log-sum item and display the advantages and disadvantages of five sparse estimation algorithms, i.e., the ITL algorithm, ℓ1/2 regularization, ℓ1 regularization, ℓ0 regularization and orthogonal matching pursuit (OMP).

Exploiting 3D fractal cube and chaos for effective multi-image compression and encryption

At present, some image compression and encryption algorithms have been presented to protect digital images by combining chaos and compressed sensing (CS). However, some of them still suffer from security and efficiency shortcomings. To solve these issues, a multi-image compression and encryption based on 3D fractal cube, CS and chaos is introduced in this paper. Firstly, the multiple plain images are sparsified by the Haar Wavelet Transform (HWT), and measured by CS to obtain the measurement value matrices. Herein, a four-wing hyperchaotic system is adopted to generate the measurement matrix for CS. Subsequently, a 3D fractal cube (3D-FC) is defined and generated iteratively by constructing the initial 3D-FC. Based on it, the obtained measurement value matrices are shuffled to reduce the high correlation between the adjacent pixels. Next, the cipher images are obtained after the cipher-associated adaptive diffusion based on GF (28) is performed on the confused image. Moreover, we have conducted extensive experiments to verify the encryption efficiency, compression performance, and security. Both simulation results and performance analysis confirm that the present algorithm has satisfactory performance in these aspects.

A Novel Approach to Tele-Ultrasound Imaging: Compressive Beamforming in Fourier Domain for Ultrafast Ultrasound Imaging

Tele-ultrasound imaging is useful in various situations. Plane wave imaging provides a method for ultrafast ultrasound with very high frame rates, which sacrifices image quality and leads to the problem of a large amount of data and low signal transmission speed in telemedicine imaging. In this paper, a novel compressive frequency-wavenumber domain beamforming method is introduced, which integrates Stolt’s f-k method and compressed sensing theory on the lateral wavenumber. The data load is reduced by the sparsity of the echo signal parallel to the transducer, which requires a smaller measurement matrix during compressed sensing to reduce memory usage and accelerate the transmission rate. The signal is compressed in the Fourier domain to obtain greater stability and better image quality after reconstruction than if it was compressed in the temporal domain. Simulated data and experimental acquisitions were used to compare compressive Fourier domain beamforming with conventional delay-and-sum (DAS) beamforming. The results showed that compressive beamforming within the wavenumber domain provides the image with higher quality from less data.

Spatial–Temporal Complex Graph Convolution Network for Traffic Flow Prediction

Traffic flow prediction remains an ongoing hot topic in the field of Intelligent Transportation System. The state-of-the-art traffic flow prediction models can effectively extract both spatial and temporal features of traffic flow data, but ignore the correlation and external interference between traffic nodes. To this end, this paper proposes a novel method based on Spatial–Temporal Complex Graph Convolution Network (ST-CGCN) for traffic flow prediction. Specifically, we first constructs the distance matrix, the data correlation matrix, and the comfort measurement matrix according to the geographical locations, the historical data record, and the external interference between traffic nodes. Then, these three matrices are fused into a complex correlation matrix by introducing self-learning dynamic weights to improve the joint modeling ability of spatial–temporal features and external factors. Next, a spatial feature extraction module and a temporal feature extraction module are designed to characterize dynamic spatial–temporal features. The spatial feature extraction module consists of a graph convolution operator with a proposed complex correlation matrix and a residual unit. The temporal feature extraction module consists of a 3D convolution operator and a Long Short-Term Memory (LSTM). Experiments constructed on five real-world datasets demonstrate that the new proposed ST-CGCN is more effective than several existing deep learning based traffic flow prediction models. The key source code and data are available at https://github.com/Bounger2/ST-CGCN.

A novel spectrogram visual security encryption algorithm based on block compressed sensing and five-dimensional chaotic system

Based on block compressed sensing theory, combined with a five-dimensional chaotic system, we propose and analyze a novel spectrogram visual security encryption algorithm. This research is devoted to solving the compression, encryption and steganography problems of spectrograms involving large data volumes and high complexity. First, the discrete wavelet transform is applied to the spectrogram to generate the coefficient matrix. Then, block compressed sensing is applied to compress and preencrypt the spectrogram. Second, we design a new five-dimensional chaotic system. Then, several typical evaluation methods, such as the phase diagram, Lyapunov exponent, bifurcation diagram and sample entropy, are applied to deeply analyze the chaotic behavior and dynamic performance of the system. Moreover, the corresponding Simulink model has been built, which proves the realizability of the chaotic system. Importantly, the measurement matrix required for compressed sensing is constructed by the chaotic sequence. Third, dynamic Josephus scrambling and annular diffusion are performed on the secret image to obtain the cipher image. Finally, an improved least significant bit embedding method and alpha channel synchronous embedding are designed to obtain a steganographic image with visual security properties. To make the initial keys of each image completely different from other images, the required keys are produced using the SHA-256 algorithm. The experimental results confirm that the visual security cryptosystem designed in this study has better compression performance, visual security and reconstruction quality. Furthermore, it is able to effectively defend against a variety of conventional attack methods, such as statistical attacks and entropy attacks.

A divide-and-conquer method for compression and reconstruction of smart meter data

As smart grid sensors, smart meters generate abundant valuable data, laying the foundation for data-driven applications. However, the data collection brings huge communication pressure to electric utilities. In this context, considering that different types of devices have different power consumption patterns, and different types of data compression methods have their own applicable scenarios, we propose a divide-and-conquer method for compression and reconstruction of smart meter data. First, based on algorithm of voice activity detection (VAD), a load power fluctuation segment location method is proposed, which is combined with load event detection method to divide the load data into the event segments, fluctuation segments, and steady-state segments. Then, for the fluctuation segments, a cloud-device collaboration adaptive strategy based on the compressive sensing (CS) theory is designed, in which the sparse basis and measurement matrix are updated accordingly to ensure the high reconstruction accuracy in different scenarios. For the steady-state segments, a data compression method based on the improved symbolic aggregation approximation (SAX) is established, in which the dividing rectangle (DIRECT) algorithm and the irregular time partitioning method are combined to reduce the data volume for transmission without losing important information. For the event segments, the original data values are retained since the event power curves are relatively more complex and short duration. Finally, the received compressed data are reconstructed into the original power time series data in the master station on cloud to support advanced data analytics. Comparative experiments are conducted on the private and public datasets of 12 households in North America and China. The results show that our method has higher data reconstruction accuracy and compression efficiency compared to the existing methods.

A lightweight and secure sensing model for body area networks in the Internet of Things in biological warfare applications

In the era of communicational technologies, body area networks (BAN) provide useful and applicable devices for monitoring soldiers' health, of paramount importance for the governments and countries' security. However, BANs face two main challenges of security and energy, due to limitations in energy, memory, and process of the utilized sensors. Despite the developments of many solutions to tackle the stated challenges, the simultaneous consideration of energy and security has been overlooked in the majority of them. Besides, in some of the recommended solutions, the energy consumption is not optimum, resulting from discarding information content in data sampling. In addition, another group of the current methods is not practical, not guaranteeing security, given the high computational costs and the entropic inefficiency of encryption keys. Therefore, in the present study, a lightweight and secure sensing model is recommended for BANs, applicable in biological warfare. In the proposed model, the data are sampled according to their entropies, then compressed and encrypted simultaneously considering their sparsity levels, aiming at reducing energy consumption and boosting security. To synchronize two functions of compression and encryption, a measurement matrix, a type of sub-Gaussian matrix, is used. Furthermore, the biological data associated with the under-care soldier is encrypted using a key, guaranteeing the secure transfer of data to the smart healthcare center. In this process, the key is generated from the time interval calculated from the heart rate of the under-care soldier. The simulation data reveal that the proposed sensing model causes a reduction in energy consumption while providing security, compared to the previous methods.

Improved sparsity adaptive matching pursuit algorithm based on compressed sensing

Traditional greedy algorithms need to know the sparsity of the signal in advance, while the sparsity adaptive matching pursuit algorithm avoids this problem at the expense of computational time. To overcome these problems, this paper proposes a variable step size sparsity adaptive matching pursuit (SAMPVSS). In terms of how to select atoms, this algorithm constructs a set of candidate atoms by calculating the correlation between the measurement matrix and the residual and selects the atom most related to the residual. In determining the number of atoms to be selected each time, the algorithm introduces an exponential function. At the beginning of the iteration, a larger step is used to estimate the sparsity of the signal. In the latter part of the iteration, the step size is set to one to improve the accuracy of reconstruction. The simulation results show that the proposed algorithm has good reconstruction effects on both one-dimensional and two-dimensional signals.

Fault Diagnosis of Rotating Machinery Based on Two-Stage Compressed Sensing

Intelligent on-site fault diagnosis and professional vibration analysis are essential for the safety and stability of rotating machinery operation. This paper represents a fault diagnosis scheme based on two-stage compressed sensing for triaxial vibration data, which realizes fault diagnosis for rotating machinery based on compressed data and data reconstruction for professional vibration analysis. In the 1st stage, the triaxial vibration signals are compressed using a pre-designed hybrid measurement matrix; these compressed data can be used both for time-frequency transform and for vibration data reconstruction. In the 2nd stage, the frequency spectra of the triaxial vibration signals are fused and further compressed using another pre-designed joint measurement matrix, which inhibits the high-frequency noises simultaneously. Finally, the fused spectra are employed as feature vectors in sparse-representation-based classification, where the proposed batch matching pursuit (BMP) algorithm is utilized to calculate the sparse vectors. The two-stage compression scheme and the BMP algorithm minimize the computational cost of on-site fault diagnosis, which is suitable for edge computing platforms. Meanwhile, the compressed vibration data can be reconstructed, which provides evidence for professional vibration analysis. The method proposed in this study is validated by two practical case studies, in which the accuracies are 99.73% and 96.70%, respectively.

Research on reconstruction algorithm of power quality data based on self-encoding network

Taking on the problems of unstable reconstruction performance and high reconstruction method computational cost induced by the unpredictability of the measurement matrix during power quality signal reconstruction, this research provides a power quality reconstruction model based on a self-encoding network and compressed sensing for the first time. The model includes a noise-adding module, an encoder module and a decoder module. The noise-adding module adds a specific amount of white noise in relation to the original signal to simulate the disturbance signal collected in the real scene. The encoder module uses a nonlinear measurement method to observe the power quality signal, and the decoder module completes the signal through a compressed sampling matching tracking algorithm. Refactoring. The outcomes of the experiment reveal that the compressed reconstruction model proposed in this paper significantly improves the efficiency and stability of power quality signal reconstruction.

The Study of the Relationship Between the Russian and Buryat Languages Using the Matrix of Proximity Measures Between Consonant Word Classes

The article proposes a new approach to study the connection between the Russian and Buryat languages, borrowings in the Buryat language, based on the methods of historical and mathematical linguistics. For the work, a frequency Russian-Buryat dictionary was used, in which each word was transformed using consonant classes, after which the Ratcliffe-Obershelp pairwise similarity metrics were calculated for the words of the dictionary and their transformed forms. But on the basis of the data obtained, a matrix of measures of proximity of consonant classes (MMCC) of words of two languages was built. Additionally, for a number of measures of each word, statistical characteristics were calculated - average, minimum, maximum, variance estimate. For Buryat words, the correlation coefficients of a series of measures that characterize the similarity of words were determined. As a result of the calculations, a measure of the similarity of the consonant classes of words in the Russian and Buryat languages was obtained, which characterizes the mutual influence of languages and the amount of borrowing of Russian forms in the Buryat language. The paper shows the effectiveness of the method of the matrix of similarity measures of consonantal classes of words for comparing languages.