Random Measurement Matrix Research Articles

A compressed sensing random measurement matrix construction method: block sparse random measurement matrix

A compressed sensing random measurement matrix construction method: block sparse random measurement matrix

A signal-adaptive measurement matrix construction algorithm for compressed sensing of sEMG data

Abstract Surface electromyography (sEMG), serving as a pivotal wearable technology, is a promising tool to assess and monitor muscle function. Yet, the efficacy of a sEMG system faces inevitable constraints, primarily stemming from the challenges of transmission and energy consumption induced by big data. Compressed sensing (CS) is a promising data acquisition solution that takes advantage of the signal sparseness in a particular basis to significantly reduce the number of samples. Current CS methods usually employ random or deterministic measurement matrix to compress sEMG signal. However, these measurement matrices do not integrate the signal feature, which limits the performance of these CS methods. To address this problem, this paper proposes an improved CS method for sEMG data compression. This proposed method introduces a measurement matrix construction algorithm to produce a deterministic matrix tailored for processing sEMG signals. The deterministic measurement matrix integrates the characteristics of the magnitudes of sEMG signals. The sEMG signals acquired from the upper limb muscles of the stroke survivors were applied to evaluate the proposed CS method, with results showing that it achieves better reconstruction accuracy and robustness than the CS methods with other measurement matrices. The proposed method employing basis pursuit (BP) in the signal reconstruction presents better performance than that employing orthogonal matching pursuit (OMP). Hence, we can conclude that the proposed CS algorithm is of key importance for the popularization of sEMG in the wearable health monitoring devices.

An image compression-then-encryption algorithm using piecewise asymptotic deterministic random measurement matrix

An image compression-then-encryption algorithm using piecewise asymptotic deterministic random measurement matrix

Visual image encryption algorithm based on compressed sensing and 2D cosine -type logistic map

A new two-dimensional cosine-type Logistic map (2D-CTLM) is proposed in this paper. Performance analysis shows that 2D-CTLM has good ergodicity, complex behavior, and a wide range of chaotic regions. To study its application, an adaptive embedded high visual security image encryption scheme is proposed by combining the system with two-dimensional compression sensing to address the shortcomings of fixed embedding positions and low transmission efficiency in existing schemes. The embedding position is fixed when the ciphertext image is embedded into the carrier image. When embedded in an inappropriate location, it will affect the decryption quality and the imperceptibility of the steganographic image. Firstly, the initial value of 2D-CTLM system is generated by using the information entropy of plaintext image and counter to generate random measurement matrix, which is used to compress and encrypt plaintext image from two directions at the same time. Secondly, the compressed cipher image is scrambled by the initial matrix generated by the GOL (game of life) rules in two-dimensional cellular automata to obtain the ciphertext image. Finally, the most suitable embedding position in the carrier image is found by combining information entropy and edge entropy. Then the unquantized ciphertext image is embedded into it by ST (slant transform) embedding method to obtain a high visual security image. To improve the transmission efficiency, the color carrier image can be selected to transmit three gray plaintext images at the same time, maintain high-quality reconstruction effect. SHA-512 and the information entropy of plaintext image are used to generate the initial value of encryption and measurement matrix, enhance the correlation between the algorithm and plaintext image, and effectively resist known plaintext and selective plaintext attacks. Simulation results and performance analysis show that compared with the existing encryption schemes, the encryption scheme has excellent visual effect, good decryption quality and good robustness.

Design of artificial intelligence image encryption algorithm based on hyperchaos

The artificial intelligence is an inevitable breakthrough direction, and the privacy protection of images in the artificial intelligence environment has become a hotspot. An image encryption algorithm that can be applied in the AI-based work combining compression sensing with Rabinovich hyperchaos is proposed. Firstly, the plaintext image will be transformed into a sparse form by DWT transform. With the improved hyperchaotic sequence, the double reset mechanism of the bit plane and the encryption engine function are designed to perform circular diffusion operation. Finally, the combined random Gaussian measurement matrix will perform compressed sensing sampling on the encrypted image. Simulation experiments show that the encryption algorithm can pass the plaintext sensitivity test (with the NPCR of 0.9978 and the UACI of 0.3337), the correlation test (with the best result of −0.0021), and the information entropy test (with the result of 7.9987), which shows high security to resist several types of attacks.

Joint optimization methods for Gaussian random measurement matrix based on column coherence in compressed sensing

In compressed sensing, a measurement matrix Φ having low coherence with sparse dictionary Ψ can achieve better signal reconstruction performance. To improve the signal reconstruction performance, this paper proposes two joint optimization algorithms for the Gaussian random measurement matrix to minimize the coherence between the measurement matrix Φ and the sparse dictionary Ψ. First, a joint optimization algorithm is proposed that can simultaneously reduce the average mutual coherence μg and the mutual coherence μ based on an alternating projection strategy. Then, to further decrease the coherence between Φ and Ψ, an improved shrinkage method based on K-order cumulative coherence μK is proposed. Furthermore, another joint optimization algorithm is proposed by fusing this improved shrinkage method, which can simultaneously decrease the average mutual coherence μg and the K-order cumulative coherence μK. Simulation results show that the two proposed joint optimization algorithms outperform existing algorithms in reducing coherence and improving reconstruction performance.

The power quality detection and synchrophasor measurement based on compressive sensing

In order to improve the effect of power quality detection and synchrophasor measurement, this paper studies power quality detection and synchrophasor measurement with the support of compressive sensing technology. Based on the DFT synchrophasor measurement, this paper uses the RDFT recursive formula to simplify the DFT calculation amount, and uses the least squares estimation method to fit the phase angle sequence to calculate the system frequency. According to the obtained frequency estimation value, re-sampling is carried out to correct the original sampling point, and the frequency secondary calculation is iteratively performed, the detection accuracy of high frequency and phase angle, and the linear measurement of the signal is realized by using the Gaussian random measurement matrix, and the compressed sensing signal is obtained. The experimental data statistics show that the model proposed in this paper for power quality detection and synchrophasor measurement based on compressive sensing has a good effect.

Block compressive sensing chaotic embedded encryption for MCF-OFDM transmission system.

In this paper, we propose a block compressive sensing (BCS) based chaotic embedded encryption scheme for multi-core fiber orthogonal frequency division multiplexing (MCF-OFDM) system. BCS technology is used to recover the entire desired information from the small amounts of data. Meanwhile, a four-dimensional discrete chaotic encryption model generates four masking factors, which are respectively used for coefficient random permutation (CRP), measurement matrix, diffusion and singular value decomposition (SVD) embedding to achieve ultra-high security encryption of four different dimensions. In terms of compressive sensing, CRP can make the discrete cosine transform (DCT) coefficient distribute randomly to improve the sampling efficiency of BCS. Compared with the data without compressive sensing, the data volume is reduced by 75%. In chaotic encryption, SVD technology embeds secret images of noise-like after initial encryption into carrier images to generate encrypted images with visual security. The key space reaches 10120 and it realizes the dual protection of source image data and external representation. The proposed scheme using a 2km 7-core optical fiber achieves a 78.75 Gb/s transmission of encrypted OFDM signals. The received optical power is greater than -14 dBm, and the bit error rate (BER) of core1-core7 is lower than 10-3. When the compression ratio sets to 0.25 and the attack range of encrypted data is up to 30%, the image can still recover the outline and general information. The experimental results show that this scheme can improve the security performance and reduce the complexity of information transmission system. Furthermore, the scheme combines The BCS chaotic embedded encryption technology with MCF-OFDM system, which has a good application prospect in the future optical networks.

Radio Resource Allocation Algorithm of the M2M Communication System in 5G Era

M2M is a concept and a general term for all technologies that enhance the communication and network capabilities of machines and equipment. It is a combination of different types of communication technologies. M2M enables all devices and users to share information, saving operation time and improving work efficiency. M2M is not a simple data transmission, but it is an intelligent and interactive communication between machines. Even if no real-time signal is sent, the machine will actively communicate according to the established program and select intelligently according to the obtained data. The communication system refers to the general term of the technology that completes the information transmission function. The modern communication system is mainly realized by the propagation of electromagnetic waves in free space or the transmission mechanism in the guiding medium. When the wavelength of the electromagnetic wave reaches the light wave range, such a telecommunication system is called an optical communication system, and the communication system in the other electromagnetic wave range is called an electromagnetic communication system, abbreviated as a telecommunication system. The purpose of this paper is to explore the study of wireless data sharing method for M2M mobile telecommunication systems in the 5G era. It is expected that the new algorithm will make the wireless resource allocation more reasonable and improve the resource utilization rate. The performance of the deterministic measurement matrix proposed in this paper is close to or even better than that of the random measurement matrix. The M-SP algorithm greatly improves the performance of the SP algorithm. The experimental results of this paper show that when the number of microbase stations is 10, the energy consumption of the direct algorithm is 175000 W, the energy consumption of the indirect algorithm is 350000 W, and the energy consumption of the direct algorithm is much smaller than that of the indirect algorithm.

A Compressed Sensing Measurement Matrix Construction Method Based on TDMA for Wireless Sensor Networks.

Compressed sensing theory has been widely used for data aggregation in WSNs due to its capability of containing much information but with light load of transmission. However, there still exist some issues yet to be solved. For instance, the measurement matrix is complex to construct, and it is difficult to implement in hardware and not suitable for WSNs with limited node energy. To solve this problem, a random measurement matrix construction method based on Time Division Multiple Access (TDMA) is proposed based on the sparse random measurement matrix combined with the data transmission method of the TDMA of nodes in the cluster. The reconstruction performance of the number of non-zero elements per column in this matrix construction method for different signals was compared and analyzed through extensive experiments. It is demonstrated that the proposed matrix can not only accurately reconstruct the original signal, but also reduce the construction complexity from to (), on the premise of achieving the same reconstruction effect as that of the sparse random measurement matrix. Moreover, the matrix construction method is further optimized by utilizing the correlation theory of nested matrices. A TDMA-based semi-random and semi-deterministic measurement matrix construction method is also proposed, which significantly reduces the construction complexity of the measurement matrix from to , and improves the construction efficiency of the measurement matrix. The findings in this work allow more flexible and efficient compressed sensing for data aggregation in WSNs.

Orthogonal-triangular decomposition ghost imaging

Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix Q and an upper triangular matrix R . Then let the off-diagonal values of R equal to 0.0, the diagonal elements of R equal to a constant k, where k is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.

Communication-Efficient Federated Learning Based on Compressed Sensing

In this article, we investigate the problem of federated learning (FL) in a communication-constrained environment of the Internet of Things (IoT), where multiple IoT clients train a global model collectively by communicating model updates with a central server instead of sending raw data sets. To ease the communication burden in IoT systems, several approaches have been proposed for the FL tasks, including sparsification methods and data quantization strategies. To overcome the shortcomings of the existing methods, we propose two new FL algorithms based on compressed sensing (CS) referred to as the CS-FL algorithm and the 1-bit CS-FL algorithm, both of which compress the upstream and downstream data while communicating between the clients and the central server. The proposed algorithms improve upon the existing algorithms by letting the clients send analog and 1-bit data, respectively, to the server after compression with a random measurement matrix. Based on that, in CS-FL and 1-bit CS-FL, the clients update the model locally utilizing the result of sparse reconstruction obtained by iterative hard thresholding (IHT) and binary IHT (BIHT), respectively. Experiments conducted on the MNIST and the Fashion-MNIST data sets reveal the superiority of the proposed algorithm over the baseline algorithms, SignSGD with a majority vote, FL based on sparse ternary compression, and FedAvg.

Adaptive Compressed Spectrum Sensing Using Neural Networks in Cognitive Radio Networks

In today's era of Internet of Things (IoT) applications, Cognitive Radio (CR) is recognized as the most promising technology to access the unused spectrum. Such CR networks can be easily built using Wide-band spectrum sensing. However, the processing of wide-band signals involves a high sampling rate. In such scenario, Compressed Spectrum Sensing (CSS) overcomes the challenges of real-time signal recovery and sampling. CSS uses Sparse signals which are widely used in many applications as they aid in processing large data. Beyond sparsity, all the real-world signals will have special structures (like Restricted Isometric property, Null space property). Moreover, it is very hard to determine the domain in which the signal is sparse. To find this we need a random measurement matrix which plays an important role in extracting the sparse coefficients of the signal. In this paper, a customized neural network is employed to identify the peculiar structures of sparse signals for efficient recovery in real time. The neural network learns and trains an adaptive measurement matrix from the sparse signals to reduce the sensing overhead. The transmitter and receiver systems are configured using Universal Software Radio Peripheral (USRP) boards with LabVIEW® and MATLAB® extensions for peer to peer communications. The implementation results depict the superior performance of neural network based recovery in assimilating the additional structures of real-time signals.

Sampling Sparse Representations with Randomized Measurement Langevin Dynamics

Stochastic Gradient Langevin Dynamics (SGLD) have been widely used for Bayesian sampling from certain probability distributions, incorporating derivatives of the log-posterior. With the derivative evaluation of the log-posterior distribution, SGLD methods generate samples from the distribution through performing as a thermostats dynamics that traverses over gradient flows of the log-posterior with certainly controllable perturbation. Even when the density is not known, existing solutions still can first learn the kernel density models from the given datasets, then produce new samples using the SGLD over the kernel density derivatives. In this work, instead of exploring new samples from kernel spaces, a novel SGLD sampler, namely, Randomized Measurement Langevin Dynamics (RMLD) is proposed to sample the high-dimensional sparse representations from the spectral domain of a given dataset. Specifically, given a random measurement matrix for sparse coding, RMLD first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the measurement matrix. The algorithm analysis shows that RMLD indeed projects a given dataset into a high-dimensional Gaussian distribution with Laplacian prior, then draw new sparse representation from the dataset through performing SGLD over the distribution. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of RMLD beyond baseline methods.

Construction of compressive measurement matrix based on sinusoidal function called Sinusoidal Sensing Matrix (SSM)

Compression sensing theory enables a safe reconstruction of signals under certain conditions. Random measurement (sensing) matrix Φ is one of the necessary conditions which give a strong impact on the behavior of the method used to reconstruct the signal. A deterministic method is therefore proposed to construct a new matrix called Sinusoidal Sensing Matrix (SSM) for compressing sensing theorem. The SSM matrix depends on its built upon generating equation used both Sin and Cos function depend upon the number of compressed samples. This new matrix is very simple and easy to create but very effective and can be generated in transmission and distention end without a need to send it, only need in Rx side knowledge of signal length. The new matrix interval meets the Restricted Isometry Property (RIP) characteristic with high probability.The simulation experiments of one- and two- dimensional signals, using a new matrix show a superior in evaluating recovered signals with parameters and the visual effect of the restored images.

An Optimization Method for the Layout of Soil Humidity Sensors Based on Compressed Sensing

In the farmland Internet of Things, to achieve precise control of production, it is necessary to obtain more data support, which requires the deployment of many sensors, and this will inevitably bring about high investment and high‐cost problems. This paper mainly studies the optimization of sensor placement in the agricultural field. Through compressed sensing and algorithm optimization, the number of sensors used is reduced and the cost is reduced on the premise of ensuring the effect. At present, there are many mature sensor layout optimization methods, but these methods will have incomplete parameters due to experimental conditions and environmental factors. They are more suitable for structural health monitoring and lack research in agricultural applications. Considering that the sensor layout optimization can be converted into the characteristics of image compression selection and the compression effect of the compressed sensing theory is better, therefore, this paper proposes a sensor layout optimization method based on compressed sensing. Due to the structural characteristics of the existing measurement matrix in the compressed sensing theory, the specific position distribution of the optimized sensor layout cannot be obtained directly. This paper improves the existing sparse random measurement matrix to determine the number of sensors required for a given region and the function of the specific location of each sensor. The experimental results show that soil moisture can be measured with a small error of 0.91 by using 1/3 of the original sensor number. The result of data reconstruction using 1/6 of the original sensor is average, and the average error is up to 1.68, which is suitable for the environment with small data fluctuation.

Color image encryption based on chaotic compressed sensing and two-dimensional fractional Fourier transform

Combining the advantages of structured random measurement matrix and chaotic structure, this paper introduces a color image encryption algorithm based on a structural chaotic measurement matrix and random phase mask. The Chebyshev chaotic sequence is used in the algorithm to generate the flip permutation matrix, the sampling subset and the chaotic cyclic matrix for constructing the structure perceptual matrix and the random phase mask. The original image is compressed and encrypted simultaneously by compressed sensing, and re-encrypted by two-dimensional fractional Fourier transform. Simulation experiments show the effectiveness and reliability of the algorithm.

Visual privacy-preserving level evaluation for multilayer compressed sensing model using contrast and salient structural features

Recognition and classification tasks in images or videos are ubiquitous, but they can lead to privacy issues. People increasingly hope that camera systems can record and recognize important events and objects, such as real-time recording of traffic conditions and accident scenes, elderly fall detection, and in-home monitoring. However, people also want to ensure these activities do not violate the privacy of users or others. The sparse representation classification and recognition algorithms based on compressed sensing (CS) are robust at recognizing human faces from frontal views with varying expressions and illuminations, as well as occlusions and disguises. This is a potential way to perform recognition tasks while preserving visual privacy. In this paper, an improved Gaussian random measurement matrix is adopted in the proposed multilayer CS (MCS) model to realize multiple image CS and achieve a balance between visual privacy-preserving and recognition tasks. The visual privacy-preserving level evaluation for MCS images has important guiding significance for image processing and recognition. Therefore, we propose an image visual privacy-preserving level evaluation method for the MCS model (MCS-VPLE) based on contrast and salient structural features. The basic concept is to use the contrast measurement model based on the statistical mean of the asymmetric alpha-trimmed filter and the salient generalized center-symmetric local binary pattern operator to extract contrast and salient structural features, respectively. The features are fed into a support vector regression to obtain the image quality score, and the fuzzy c-means algorithm is used for clustering to obtain the final evaluated image visual privacy-preserving score. Experiments on three constructed databases show that the proposed method has better prediction effectiveness and performance than conventional methods.

Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function

In this work, a novel learning-based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state-of-the-art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter-column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real-world data confirm the superiority of the proposed approach to the less recent methods.

Color image compression and encryption scheme based on compressive sensing and double random encryption strategy

Based on compressive sensing and double random encryption strategy, a novel color image compression and encryption scheme is proposed in this paper. The architecture of compression, confusion and diffusion is adopted. Firstly, the red, green and blue components of color plain image are converted to three sparse coefficient matrices by discrete wavelet transform (DWT), and then a double random position permutation (DRPP) is introduced to confuse the coefficient matrices. Subsequently, Logistic-Tent system is utilized to generate the asymptotic deterministic random measurement matrix based on chaotic system and plain image (ADMMCP), which is used to measure the coefficient matrices to obtain measurement value matrices. Moreover, simultaneous double random pixel diffusion between inter-intra components (SDRDIC) is presented to modify the elements of measurement value matrices to obtain the final cipher image. A 4-D hyperchaotic system is applied to produce chaotic sequences for confusion and diffusion, the initial conditions of the used chaotic systems are controlled by the SHA 512 hash value of plain image and external keys, such that the proposed image cryptosystem may withstand known-plaintext and chosen-plaintext attacks. Experimental results and security analyses verify the effectiveness of the proposed cipher.