Measurement Matrix Research Articles

Comparison of Common Algorithms for Single-Pixel Imaging via Compressed Sensing.

Single-pixel imaging (SPI) uses a single-pixel detector instead of a detector array with a lot of pixels in traditional imaging techniques to realize two-dimensional or even multi-dimensional imaging. For SPI using compressed sensing, the target to be imaged is illuminated by a series of patterns with spatial resolution, and then the reflected or transmitted intensity is compressively sampled by the single-pixel detector to reconstruct the target image while breaking the limitation of the Nyquist sampling theorem. Recently, in the area of signal processing using compressed sensing, many measurement matrices as well as reconstruction algorithms have been proposed. It is necessary to explore the application of these methods in SPI. Therefore, this paper reviews the concept of compressive sensing SPI and summarizes the main measurement matrices and reconstruction algorithms in compressive sensing. Further, the performance of their applications in SPI through simulations and experiments is explored in detail, and then their advantages and disadvantages are summarized. Finally, the prospect of compressive sensing with SPI is discussed.

An Efficient Compressive Sensing Event-Detection Scheme for Internet of Things System Based on Sparse-Graph Codes

This work studied the event-detection problem in an Internet of Things (IoT) system, where a group of sensor nodes are placed in the region of interest to capture sparse active event sources. Using compressive sensing (CS), the event-detection problem is modeled as recovering the high-dimensional integer-valued sparse signal from incomplete linear measurements. We show that the sensing process in IoT system produces an equivalent integer CS using sparse graph codes at the sink node, for which one can devise a simple deterministic construction of a sparse measurement matrix and an efficient integer-valued signal recovery algorithm. We validated the determined measurement matrix, uniquely determined the signal coefficients, and performed an asymptotic analysis to examine the performance of the proposed approach, namely event detection with integer sum peeling (ISP), with the density evolution method. Simulation results show that the proposed ISP approach achieves a significantly higher performance compared to existing literature at various simulation scenario and match that of the theoretical results.

An association rule mining model for the application of construction technologies during COVID-19

COVID −19 impedes construction productivity, increases costs and delays the project schedule, disrupts health and safety regulations, and reduces profit margins. To flatten the COVID −19 curve and continue operations amid the pandemic, construction companies are digitising construction activities, processes and procedures using technology. This article reports on a study examining the use of construction technologies by Nigerian surveyors through a questionnaire. The questionnaires were sent to more than 300 surveying firms based on snowballing technique. Association rule mining (ARM) was used to model the correlations between the different construction technologies. A total of 91 association rules were identified using 6 measurement matrices. The first 30 rules are presented in this study. This study contributes to the body of knowledge on the sustainability and post-pandemic redesign of surveying practise in terms of repositioning service delivery. The findings are of interest to solution and technology providers to meet market demand. From an ontological perspective, the key findings of this study can be applied to surveying practise in and outside Nigeria and to other professionals in the construction sector. The implication is that construction technologies in the Nigerian construction sector are still in their infancy.

Linear sequential filtering based on the debiased measurement matrix of the converted pseudo measurement for radar target tracking

For radar target tracking with nonlinear position and range rate measurements, a linear sequential filtering method based on the debiased measurement matrix of the converted pseudo measurement (DMM-LSF) is proposed. A novel and simple linear measurement matrix is constructed based on the relationship between the pseudo measurement and target's state vector. To estimate the involved unknown parameters in the measurement matrix, the filtering results from the linear position filter are utilized in the sequential linear filter, where a totally linear sequential filtering framework is formed. The measurement matrix estimation error is fully considered, which is incorporated into original converted pseudo measurement error and a new synthetical measurement error is formed. The statistic characteristics of the synthetical measurement error are deduced, resulting a debiased measurement matrix. Simulation results demonstrate the effectiveness of the proposed DMM-LSF algorithm. Compared with existing algorithms, the proposed one can achieve the best tracking performance for non-maneuvering and maneuvering target tracking in different scenes.

Measurement Matrix Optimization Based on Target Prior Information for Radar Imaging

Radar target imaging can provide important information for target monitoring and recognition. In order to reduce the data amount and save radar resources, the target imaging methods based on compressed sensing have received extensive attention. In these methods, the measurement matrix will directly affect the target imaging quality and data down-sampling rate. However, most of the existing researches on measurement matrix optimization did not take into account the full use of target characteristic information and the internal consistency between the measurement matrix structure and the data sampling process, which makes it difficult to obtain the optimal imaging quality and down-sampling rate. To solve the above problems, this paper makes full use of the target imaging prior information, and takes the minimum dimension of the measurement matrix and the maximum similarity between the obtained image and expected image as the goal of measurement matrix optimization. On this basis, aims at the kind of signal which is composed of a group of sub-pulses with stepped frequency, a joint optimization model of measurement matrix and imaging performance based on the target imaging prior is established with the consideration of the 0-1 constraint of the measurement matrix structure caused by the physical observation process of the sparse stepped frequency signals. And then the corresponding sparse reconstruction algorithm is proposed. Thus, the optimal measurement matrix and high-resolution imaging results can be obtained, and the radar data down-sampling rate can be improved significantly. Simulation results indicate the effectiveness of the proposed method.

Three Phase Current Transformer Calibration Without External Reference IT Using Synchrophasors: An SVD Approach

Recently a pragmatic data centric method to calibrate substation capacitive voltage transformers (CVT) by exploiting local redundancy in substation CVT PMU data has been proposed. It does not require any external reference CVT. This paper extends the above philosophy to current transformer (CT) calibration problem. Once a line terminals CVTs are calibrated, then estimate of the three phase line currents can be deduced. Currents in a bus, for each of the three phases sum to zero. Hence, the corresponding measurement matrix will be rank deficient. Singular value decomposition's low rank approximation property is used to filter the noise and then a linear least squares problem is solved to calibrate remaining substation CTs. The method then can be intrinsically extended to calibrate other CTs of the network without using other series line impedances. Results are presented with both simulated and field PMU data of 400 kV lines.

Vector approximate message passing with sparse Bayesian learning for Gaussian mixture prior

Compressed sensing (CS) aims for seeking appropriate algorithms to recover a sparse vector from noisy linear observations. Currently, various Bayesian-based algorithms such as sparse Bayesian learning (SBL) and approximate message passing (AMP) based algorithms have been proposed. For SBL, it has accurate performance with robustness while its computational complexity is high due to matrix inversion. For AMP, its performance is guaranteed by the severe restriction of the measurement matrix, which limits its application in solving CS problem. To overcome the drawbacks of the above algorithms, in this paper, we present a low complexity algorithm for the single linear model that incorporates the vector AMP (VAMP) into the SBL structure with expectation maximization (EM). Specifically, we apply the variance auto-tuning into the VAMP to implement the E step in SBL, which decrease the iterations that require to converge compared with VAMP-EM algorithm when using a Gaussian mixture (GM) prior. Simulation results show that the proposed algorithm has better performance with high robustness under various cases of difficult measurement matrices.

Boundedness of atmospheric Ekman flows with two-layer eddy viscosity

In this paper, we study the boundedness of atmospheric Ekman flows with classical boundary conditions. We consider the system with a two-layer eddy viscosity, consisting of a constant eddy viscosity in the upper layer and a continuous eddy viscosity in the lower layer. We analyze the boundedness of the solution by using the logarithmic matrix norm.

Transformer Vibration Signal Feature Extraction Based on Compressed Sensing and Wavelet Packet

Transformers are important equipment in the power system. Aiming at the collection, transmission, storage, and processing of massive high-dimensional vibration data in the process of transformer vibration online monitoring, this paper proposes a transformer vibration signal feature extraction method based on compressed sensing and wavelet packets. Firstly, the PartHadamard measurement matrix is used to compress the transformer vibration signal, and then the characteristics of the transformer vibration signal are extracted based on the wavelet packet decomposition and normalized wavelet information entropy. The proposed method completes feature extraction on the measured vibration data of the transformer, and three classification algorithms are applied to carry out simulation experiments. The results show that the proposed feature extraction method can effectively extract the vibration characteristics reflecting the operating state of the transformer while greatly reducing the dimension of vibration data, which provides a reference for the online monitoring of transformer vibration.

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including good reconstruction performance, low memory cost and low computing resources. Low-density-parity check (LDPC) codes and CS codes can be closely related. This paper presents a method of constructing compressed sensing measurement matrices based on quasi-cyclic (QC) LDPC codes and arithmetic sequence sets. The cyclic shift factor in each submatrix of QC-LDPC is determined by arithmetic sequence sets. Compared with random matrices, the proposed method has great advantages because it is generated based on a cyclic shift matrix, which requires less storage memory and lower computing resources. Because the restricted isometric property (RIP) is difficult to verify, mutual coherence and girth are used as computationally tractable indicators to evaluate the measurement matrix reconstruction performance. Compared with several typical matrices, the proposed measurement matrix has the minimum mutual coherence and superior reconstruction capability of CS signal according to one-dimensional (1D) signals and two-dimensional (2D) image simulation results. When the sampling rate is 0.2, the maximum (minimum) gain of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) is up to 2.89 dB (0.33 dB) and 0.031 (0.016) while using 10 test images. Meanwhile, the reconstruction time is reduced by nearly half.

Sparse Bayesian learning approach for discrete signal reconstruction

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.

Heavy-ball-based hard thresholding algorithms for sparse signal recovery

The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a k-sparse signal if the restricted isometry constant of the measurement matrix satisfies δ3k<0.618 and δ3k<0.577, respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions δ2k<0.356 and δ2k<0.377, respectively. Moreover, the finite convergence of HBHTP and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.

Non-adaptive algorithms for threshold group testing with consecutive positives

Abstract Given up to $d$ positive items in a large population of $n$ items ($d \ll n$), the goal of threshold group testing is to efficiently identify the positives via tests, where a test on a subset of items is positive if the subset contains at least $u$ positive items, negative if it contains up to $\ell $ positive items and arbitrary (either positive or negative) otherwise. The parameter $g = u - \ell - 1$ is called the gap. In non-adaptive strategies, all tests are fixed in advance and can be represented as a measurement matrix, in which each row and column represent a test and an item, respectively. In this paper, we consider non-adaptive threshold group testing with consecutive positives in which the items are linearly ordered and the positives are consecutive in that order. We show that by designing deterministic and strongly explicit measurement matrices, $\lceil \log _{2}{\lceil \frac {n}{d} \rceil } \rceil + 2d + 3$ (respectively, $\lceil \log _{2}{\lceil \frac {n}{d} \rceil } \rceil + 3d$) tests suffice to identify the positives in $O \left ( \log _{2}{\frac {n}{d}} + d \right )$ time when $g = 0$ (respectively, $g&amp;gt; 0$). The results significantly improve the state-of-the-art scheme that needs $15 \lceil \log _{2}{\lceil \frac {n}{d} \rceil } \rceil + 4d + 71$ tests to identify the positives in $O \left ( \frac {n}{d} \log _{2}{\frac {n}{d}} + ud^{2} \right )$ time, and whose associated measurement matrices are random and (non-strongly) explicit.

Sparse Channel Estimation With Distorted Signals for UWB OFDM Systems

The power amplifier (PA) is an indispensable part of ultra-wideband (UWB) orthogonal frequency division multiplexing (OFDM) systems. Nevertheless, it will produce nonlinear distortions, degrading the accuracy of channel estimation and thus the performance of the system. To improve the system performance, it is essential to investigate channel estimation using distorted signals. Taking advantage of the sparsity of the UWB channel, a sparse channel estimation method using distorted signals is proposed in this letter, referred to as sparse channel estimation combined with power amplifier nonlinear cancellation (SCE-PANC). Within SCE-PANC, the measurement matrix is constructed only with pilot subcarriers and nonlinear distortions will be eliminated iteratively. The numerical results show that the proposed method has a better performance than the state-of-the-art methods.

Improved Sparse Vector Code Based on Optimized Spreading Matrix for Short-Packet in URLLC

Recently, the sparse vector code (SVC) is emerging as a promising solution for short-packet transmission in ultra-reliable and low-latency communication (URLLC). In the SVC process, the encoding and decoding stages are jointly modeled as a standard compressed sensing (CS) problem. Hence, this letter aims at improving the decoding performance of SVC by optimizing the spreading matrix (i.e., measurement matrix in CS). To this end, two greedy algorithms to minimize the mutual coherence value of the spreading matrix in SVC are proposed. Specially, for practical applications, the spreading matrices are further required to be bipolar whose entries are constrained as +1 or −1. As a result, the optimized spreading matrices are highly efficient for storage, computation, and hardware realization. Simulation results reveal that, compared with the existing work, the block error rate (BLER) performance of SVC can be improved significantly with the optimized spreading matrices.

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.

Optimal Configuration of Distribution Network Wideband Measurement Unit Considering Wideband Measurement

With the large-scale integration of distributed generation (DG) and the increase in interaction with users, a large amount of wide-band information other than power frequency has been introduced into the distribution networks. The synchronous wide-band measurement is an important means to improve the situational awareness ability of the distribution network operation, hence, its optimization configuration has received more and more attention. To achieve the full observability of the network with the least measurement devices and achieve the goal of more accurate wide-band state estimation, this paper proposes a deployment method considering the wide-band information and the topology observability. Under the premise of ensuring that the network is completely observable, by comprehensively considering the redundancy of measurement and the conditioning number of the measurement matrix as well as the attenuation characteristics of the wide-band signal, the observability of the nodes considering wide-band information is re-determined and the topology matrix is modified. Simulation and analysis are carried out in the IEEE34 node distribution network system to verify the reliability and effectiveness of the proposed method.

Smart meter data transmission based on compressed sensing

To achieve high-precision load recognition for residential electricity consumption and to solve the transmission problem of collecting large amounts of current data from household appliances by smart meters, a data transmission method based on compressed sensing is proposed to reduce data transmission costs. Firstly, a dictionary learning algorithm is used to sparsely represent the current data of household appliances, and the over-complete dictionary matrix is used as the sparse matrix; then a random Gaussian matrix is used as the measurement matrix for data transmission, and finally, regular orthogonal matching pursuit algorithm is used to complete the data reconstruction. The experimental results show that the reconstruction effect of this method is better than the traditional reconstruction method under the same compression ratio.

Double Color Image Visual Encryption Based on Digital Chaos and Compressed Sensing

Image encryption is an effective way to protect images in secure transmission or storage. In this paper, we propose a novel double color image visual encryption algorithm based on the improved Chebyshev map (ICM) and compressed sensing. Firstly, a new nonlinear term is introduced into the classical one-dimensional Chebyshev map, and then the ICM is used to generate the secret code stream for the encryption algorithm. Next, the key-controlled sensing measurement matrices are constructed through the ICM, and they are used to compress the integer wavelet coefficients of two plain images. Subsequently, the compressed images are dislocated by dislocation matrices and diffused by an ICM-generated diffusion matrix, respectively. Finally, the encrypted images are embedded into the carrier image using the least significant bit embedding algorithm. Experimental results demonstrate that the proposed method has good visual safety, large key space, and high key sensitivity.

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.