Measurement Matrix Research Articles

Fast Algorithm of Passive Bistatic Radar Detection Based on Batches Processing of Sparse Representation and Recovery

In the passive bistatic radar (PBR) system,methods exist to address the issue of detecting weak targets without being influenced by non-ideal factors from adjacent strong targets. These methods utilize the sparsity in the delay-Doppler domain of the cross ambiguity function (CAF) to detect weak targets. However, the modeling and solving of this method involve substantial memory consumption and computational complexity. To address these challenges, this paper establishes a target detection model for PBR based on batch processing of sparse representation and recovery. This model partitions the CAF into blocks, identifies blocks requiring processing based on the presence of targets, and improves the construction and utilization of the measurement matrix. This results in a reduction in the computational complexity and memory resource requirements for sparse representation and recovery, and provides favorable conditions for parallel execution of the algorithm. Experimental results indicate that the proposed approach increases the number of blocks by a factor of four, and reduces the number of real multiplications by approximately an order of magnitude. Hence, compared with the traditional approach, the proposed approach enables fast and stable detection of weak targets.

FPGA implementation of IIR elliptic filters for de-noising ECG signal

De-noising of ECG signal is very much necessary to monitor the heart health and to diagnose disease. This paper presents a real time de-noising system that efficiently wiped out the noises from corrupted ECG signal and improves its SNR which enhances the interpretation of features present in ECG signal. This proposed system is designed with three Infinite Impulse Response (IIR) elliptic filters in cascaded direct form II structure and is implemented on the FPGA platform. Total 376 ECG samples are taken from the open access public database physiobank. All the architectural level FPGA designs have been developed in Xilinx System Generator (XSG) and implemented on Xilinx Zynq 7000 board. Our design utilized only 3.87 % of the total available resource and consumed 0.321 watt on-chip power. Worst Negative Slack (WNS) for the critical path is 2.101 ns. The positive value of WNS signifies our hardware design implementation run successfully by meeting the required time constraint. To judge the performance of the proposed design, the measurement matrices SNR Improvement, RMSE, PRD, SSNR and SINAD are calculated and achieved 81.11% , 88.89% and 85.41% accuracy for ECG recordings of ECG-ID, MIT-BIH Normal Sinus Rhythm and MIT-BIH Arrhythmia database respectively. The novelty of this proposed denoising system is its robustness, which work satisfactorily for Baseline Wander (BW), Electrode Motion (EM), Power Line Interference (PLI), Muscle or Electromyography (EMG) and as well as Additive White Gaussian Noise (AWGN).

Exploiting 2D-SDMCHM and matching embedding driven by flag-shaped hexagon prediction for visually meaningful medical image cryptosystem

With the proliferation of advanced medical technologies and smart wearable devices, a considerable volume of patient data and medical images is being generated and stored, leading to an escalating concern over patient privacy violations and manipulation. Therefore, safeguarding the secrecy and integrity of medical images is paramount for preserving patient privacy and ensuring accurate medical diagnostics. To tackle this challenge, this paper introduces a novel approach, the Visually Meaningful Medical Image Cryptosystem (VMMIC), leveraging a 2-Dimensional Sinusoidal Discrete Memristor Coupled Hyperchaotic Map (2D-SDMCHM) to protect the privacy of medical images. The innovation of this study is primarily reflected in three aspects: Firstly, a novel Discrete Memristor (DM) model is proposed, upon which a new 2D-SDMCHM is constructed. Comparative analysis showcases its superior chaos robustness, as evidenced by evaluations through bifurcation diagrams, phase trajectories, Lyapunov exponents, and Shannon entropy. Secondly, we introduce a measurement matrix optimization algorithm based on Optimal Matrix Arrangement (OMA) for Compressive Sensing (CS), aimed at minimizing the coherence of the measurement matrix, thereby enhancing reconstruction accuracy. Lastly, a Matching Embedding Method Driven by Flag-Shaped Hexagon Prediction (MEMFHP) is introduced to ensure lossless concealment of confidential information. Experimental findings and comparative evaluations affirm the VMMIC's capability to meet high standards of reconstruction quality, steganography, and efficiency in handling medical images, while also demonstrating robustness against various attacks. Consequently, the proposed VMMIC holds significant promise for practical implementation in engineering applications.

Randomized approximation of summable sequences — adaptive and non-adaptive

We prove lower bounds for the randomized approximation of the embedding ℓ1m↪ℓ∞m based on algorithms that use arbitrary linear (hence non-adaptive) information provided by a (randomized) measurement matrix N∈Rn×m. These lower bounds reflect the increasing difficulty of the problem for m→∞, namely, a term logm in the complexity n. This result implies that non-compact operators between arbitrary Banach spaces are not approximable using non-adaptive Monte Carlo methods. We also compare these lower bounds for non-adaptive methods with upper bounds based on adaptive, randomized methods for recovery for which the complexity n only exhibits a (loglogm)-dependence. In doing so we give an example of linear problems where the error for adaptive vs. non-adaptive Monte Carlo methods shows a gap of order n1/2(logn)−1/2.

Denoising Ambulatory Electrocardiogram Signal Using Interval Dedependent Thresholds based Stationary Wavelet Transform

Noise contamination in electrocardiogram (ECG) monitoring systems can lead to errors in analysis and diagnosis, resulting in a high false alarm rate (FAR). Various studies have been conducted to reduce or eliminate noise in ECG signals. However, some noise characteristics overlap with the frequency range of ECG signals, which occur randomly and are transient. This results in shape alteration and amplitude reduction in P and R waves. The author proposed a framework for eliminating noise in ECG signals using the stationary wavelet transform method and interval-dependent thresholds (IDT) based on the change point detection method to address these challenges. The proposed framework decomposes the input electrocardiogram (ECG) signal at a specific level using the Stationary Wavelet Transform method, resulting in detail and approximation coefficients. Interval detection focuses on the initial detailed coefficient, d1, chosen due to its significant content of noise coefficients, especially high-frequency noise. Subsequently, threshold values are computed for each interval. Hard and soft thresholding processes are then applied individually to each interval. Finally, reconstruction occurs using the inverse stationary wavelet transform method on the threshold coefficient outcomes. Two measurement matrices, root mean square error (RMSE) and percentage root mean squared difference (PRD), were used to measure the performance of the proposed framework. In addition, the proposed framework was compared to stationary wavelet transform (SWT) and discrete wavelet transform (DWT). The test results showed that the proposed method outperforms DWT and SWT. The proposed framework obtained an average increase in RMSE scores of 18% and 45% compared to the SWT and DWT methods, respectively, and PRD values of 17% and 37% compared to the SWT and DWT methods, respectively. So, using IDT in the stationary wavelet transform method can improve the denoising performance. With the development of this new framework for denoising ECG signals, we hope it can become an alternative method for other researchers to utilize in denoising ECG signals.

Structured Measurement Matrices Based on Deterministic Fourier Matrices and Gram Matrices

Structured Measurement Matrices Based on Deterministic Fourier Matrices and Gram Matrices

Robust sparse representation based on fitting error decomposition

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.

Super-Resolution Microscopy with Dense Grid After Interpolation

The conventional camera image’s pixel size of super-resolution (SR) microscopy is almost the point spread function’s standard deviation, and the grid of a SR image is 1/8 of the pixel size in conventional compressed sensing-based SR microscopy. Here, based on smaller grid size and smaller pixel size, we proposed and generated different measurement matrices, and then compared and analyzed the SR reconstruction results based on the interpolated conventional camera image and different measurement matrices. The quality of the measurement matrix is related to the interpolation’s size. The larger the interpolation’s size, the better its performance. The quality of SR reconstruction depends not only on the measurement matrix’s performance, but also on the grid size. It is found that dense grid based on the size of interpolation equal to 2 can help to obtain the best SR reconstruction in simulation experiments when added Gaussian noise is lower.

Vibration signals reconstruction with diffusion model for bearing fault diagnosis

Rotating bearing plays an important role in many mechanical equipment operation, such as satellite in orbit. There are in urgent need of constructing effective prognosis and diagnosis system oriented rotating bearing. Traditional bearing fault diagnosis methods enhance fault feature with sparsity-assisted prior, which are not suitable for complex vibration signals. Meanwhile, it is difficult to extract fault feature from under-sampled vibration signals. In this paper, we firstly utilize generation diffusion model to learn probability distribution of bearing fault data. As a deep generation prior, we combine the diffusion model and reconstruction problem with regularization term. The unsupervised learning method is not restricted to specific measurement matrix. The experiment in Machinery Failure Prevention Technology (MFPT) Dataset verifies the effectiveness of our algorithm. Compared with the sparse model (L1-norm) and hierarchical hyper-Laplacian prior induced model (HHLP), our method achieves better reconstruction signal to noise ratio (SNR) performance and maintains the fault frequency information from different under-sampled data.

A multiple-image encryption method based on bimodal biometric keys

In this paper, a multiple-image encryption method based on bimodal biometric keys is proposed, which has the advantages of high level of security, high encryption efficiency, high security and good convenience as well as strong robustness of bimodal biometric keys. In the encryption process, each plaintext image is firstly encoded into corresponding QR code and subsequently encrypted by using a compressive encryption method with fingerprint chaotic measurement matrix of each encryption user and a filtering encryption method in discrete cosine transform domain with iris chaotic mask of each encryption user successively, then the encryption complex amplitude is generated with the help of grating modulation technology and matrix splicing technology, thereafter the encryption complex amplitude is finally encrypted into two hologram ciphertexts by using a two-step phase-shift digital holography with fingerprint chaotic phase mask of encryption administrator. In the decrytion process, the decryption administrator first passes the fingerprint authentication and then the decryption complex amplitude is generated, thereafter multiple-image decryption can be achieved through the fingerprint authentication and iris authentication of each decryption user. In order to demonstrate the feasibility of the proposed multiple-image encryption method, a series of numerical simulations are performed, and the simulation results show that the proposed method exhibits high feasibility as well as level of security and the bimodal biometric keys possess high security and strong robustness.

Illumination pattern optimization in tomography based on the Kalman estimation filter and optimal experiment design

Tomography is widely used in medical imaging or industrial non-destructive testing applications. One costly and time consuming operation in any form of tomography is the process of data acquisition where a large number of measurements are made and collected data is used for image reconstruction. Data acquisition can slow down tomography to the point that the scanner cannot catch up with the speed of changes in the medium under test. By optimizing the information content of each measurement, we can reduce the number of measurements needed to achieve the target precision. Development of algorithms to optimize the information content of tomography measurements is the main goal of this article. Here, the dynamics of the medium and tomography measurements are formulated in the form of a Kalman estimation filter. A mathematical algorithm is developed to compute the optimal measurement matrix which minimizes the uncertainty left in the estimation of the distribution the tomography scanner is reconstructing. Results, as presented in the paper, show noticeable improvement is the quality of generated images when the medium is scanned by optimal measurements instead of traditional raster or random scanning protocols.

Design, implementation, and analysis of a compressed sensing photoacoustic projection imaging system.

Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner. We extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery. We implement a CS PAPI system for a compression factor of 4:3, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results. CS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

Privacy-security oriented chaotic compressed sensing data collection in edge-assisted mobile crowd sensing

As a data-centric network, the Mobile Crowd Sensing (MCS) collects and uploads sensing data through intelligent terminal devices carried by workers. However, due to resource limitations, the confidentiality, integrity and communication cost issues of sensing data have not been well coordinated and resolved in the actual MCS data collection process. In this regard, this paper proposes an edge computing-assisted MCS Chaotic Compressed Sensing Secure Data Collection scheme (CCS-SDC), which supports the secure collection of sensing data and saves communication cost. In CCS-SDC, workers first use the encryption algorithm based on chaos theory to encrypt the collected sensing data, and then adopt the hash location algorithm based on chaos theory to calculate the corresponding hash verification code of the sensing data. After receiving the encrypted sensing data transmitted by the worker, the edge server recomputes the hash verification code of the encrypted sensing data and verifies the integrity of the data, which can locate the changed sensing task data to a certain extent. Then the sensing data is compressed and sampled based on the generated chaos measurement matrix to reduce the amount of data transmission and further enhance the confidentiality of the sensing data. In addition, the same hash positioning algorithm is used between the edge server and the sensing platform to protect data integrity. For the changed data located by integrity verification, in addition to choosing to let workers re-sense and submit, the sensing platform can also choose to discard the changed sensing data under appropriate circumstances, and still reconstruct and decrypt the remaining data through the proposed algorithm to obtain effective original sensing data. The experimental evaluation results on real data sets show that CCS-SDC achieves the best effects, not only achieving lower sensing data communication cost than other related schemes, but also better protecting the confidentiality and integrity of sensing data, which is very useful for resource-constrained MCS data collection scenarios.

Exploiting high-quality reconstruction image encryption strategy by optimized orthogonal compressive sensing

Compressive sensing is favored because it breaks through the constraints of Nyquist sampling law in signal reconstruction. However, the security defects of joint compression encryption and the problem of low quality of reconstructed image restoration need to be solved urgently. In view of this, this paper proposes a compressive sensing image encryption scheme based on optimized orthogonal measurement matrix. Utilizing a combination of DWT and OMP, along with chaos, the proposed scheme achieves high-security image encryption and superior quality in decryption reconstruction. Firstly, the orthogonal optimization method is used to improve the chaotic measurement matrix. Combined with Part Hadamard matrix, the measurement matrix with strong orthogonal characteristics is constructed by Kronecker product. Secondly, the original image is sparsely represented by DWT. Meanwhile, Arnold scrambling is used to disturb the correlation between its adjacent pixels. Following this, the image is compressed and measured in accordance with the principles of compressive sensing and obtain the intermediate image to be encrypted. Finally, the chaotic sequence generated based on 2D-LSCM is used to perform on odd-even interleaved diffusion and row-column permutation at bit-level to obtain the final ciphertext. The experimental results show that this scheme meets the cryptographic requirements of obfuscation, diffusion and avalanche effects, and also has a large key space, which is sufficient to resist brute-force cracking attacks. Based on the sparse and reconstruction algorithm of compressive sensing proposed in this paper, it has better image restoration quality than similar algorithms. Consequently, the compressive sensing image encryption scheme enhances both security and reconstruction quality, presenting promising applications in the evolving landscape of privacy protection for network big data.

Stability of solutions of systems of Volterra integral equations

In this paper, we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of Volterra linear integral equations are studied with perturbed right hand sides of the equations. These new sufficient conditions are expressed in terms of logarithmic norms of matrices consisting of coefficients of equations and derivatives of their kernels. For Volterra integro-differential equations we also provide sufficient conditions for stability of solutions when the initial conditions are perturbed.

A Finite Element Analysis-Unascertained Measure Theory-Based Hybrid Approach to Safety Assessment for Pipelines Subject to Landslide Disasters

Abstract Pipeline safety faces a prevalent threat in mountainous areas due to landslides. The advent of landslides introduces the risk of pipeline leaks or ruptures, posing a significant threat to the environment, with the potential for casualties. Throughout the occurrence of landslides, uncertainties abound, yet few studies have addressed the incorporation of uncertainties in assessing pipeline safety. This work proposes a novel hybrid approach to the safety assessment for pipelines under landslides. The use of finite element analysis (FEA) models the pipeline under the action of landslides. The numerical outcomes, combined with unascertained measure theory (UMT), develop a multi-indicator unascertained measure (UM) matrix. Random forest (RF) algorithm is employed to determine the weight of indicators in the matrix. The hybrid application of set pair theory and the UM evaluation vector finally determine the pipeline safety degree and level. The proposed methodology has been well-validated through a case study on an in-service pipeline. The results indicate that the case pipeline safety degree is 2.777, 2.132, 3.132, 3.904, and 2.240, respectively. The corresponding safety level is III, II, III, IV, and II, respectively, which is consistent with the pipeline's actual condition. Different from the conventional safety assessment approach, the proposed methodology demonstrates the enhanced effectiveness, facilitating a more precise evaluation of the pipeline's safety condition.

Hide Digital Images in Encrypted Image Files After Two Stages

This paper introduces a novel encryption technique for concealing digital images within encrypted files through a two-stage process. The methodology incorporates sparse coding and compressive sensing, leveraging a learned dictionary to recover the sparse coding of plain images. Comprising compressive sampling and random projection with a Gaussian measurement matrix, the approach achieves joint compression and encryption. Pseudorandom encryption and chaos-based block scrambling are subsequently applied to produce the final encrypted image. Experimental results using 256 × 256 test photographs from the USC-SIPI dataset demonstrate the superiority of the proposed method in terms of both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). The study also conducts key sensitivity analysis, revealing the method's susceptibility to changes in the secret key, and statistical attack analysis, demonstrating its robustness against attacks exploiting statistical information. In conclusion, the proposed encryption technique not only ensures cryptographic strength but also excels in image reconstruction quality, making it a promising solution for secure image transmission and storage

Image encryption scheme using a new 4-D chaotic system with a cosinoidal nonlinear term in WMSNs

To protect the sensitive data captured in the wireless media sensor networks (WMSNs), this paper propounds a novel data encryption scheme by employing a new chaotic system and the semi-tensor product compressive sensing model driven by a linear congruence generator. In this scheme, the coefficients yielded by sparsely decomposing the plaintext image onto a wavelet packet basis are firstly compressed using a key-controlled measurement matrix. To minimize the threat of various attacks, the compressed image is then subjected to bidirectional diffusion manipulation to conceal its statistical properties under the control of chaotic sequences. Additionally, it is worth explaining that a lightweight 4D-chaotic system with only one nonlinear term is designed to accommodate the resource-constrained situation in WMSNs. Finally, theoretical analysis and investigations affirm its significant enhancement in visual security, compressibility, and encryption efficiency. Moreover, the proposed scheme is significantly superior to existing relevant encryption ones.

A robust decision-making framework to improve reservoir water quality using optimized selective withdrawal strategies

In arid locations such as Oman, improving the quality of water released from a reservoir can be daunting. This is particularly true for Wadi Dayqah Dam, which struggles to provide sufficient, high-quality water for downstream needs. The study's objective was to establish more reliable operational guidelines, as well as identify vulnerable outlets and release ratios. To do so, a multi-objective optimization algorithm (NSGA-II) was combined with a selective withdrawal approach, using CE-QUAL-W2 and an Artificial Neural Network to simulate water quality in a reservoir. Then, a Robust Decision Making (RDM) approach was utilized to diagnose solutions that maintain acceptable water quality according to users’ requirements. Finally, scenario discovery models (Patient Rule Induction Method (PRIM) and Classification and Regression Tree (CART)) were used to calculate vulnerable outlets and release ratios based on the established threshold. The study adopted an XLRM framework to manage a proposed model under climate change scenarios and specify the effects of involved factors. XLRM stands for eXogenous factors, Levers used by the policy-makers, Relationships between L and X, and Measurement matrix to evaluate scenarios. This study found that a higher-quality reservoir release correlated with more activated outlets and decreased pollutant concentration. Evaluating robust solutions showed that vulnerability increased under scenarios with lower annual rainfall, and water released from low and mid-level outlets was more vulnerable than that from the surface. To enhance operational stability and reduce vulnerability, the suggestions advocate for a strategic approach in releasing varying water ratios from outlets situated at different levels. Specifically, the proposal emphasizes the controlled release of both smaller and larger volumes of water from outlets positioned at lower and higher levels within the dam structure, respectively. This deliberate variation in water release aims to bolster the overall resilience of the operational framework, contributing to a more robust and reliable system.

Adaptive under-sampling strategy for fast imaging in compressive sensing-based atomic force microscopy

Compressive sensing (CS) can reconstruct the rest information almost without distortion by advanced computational algorithm, which significantly simplifies the process of atomic force microscope (AFM) scanning with high imaging quality. In common CS-AFM, the partial measurements randomly come from the whole region to be measured, which easily leads to detail loss and poor image quality in regions of interest (ROIs). Consequently, important microscopic phenomena are missed probably. In this paper, we developed an adaptive under-sampling strategy for CS-AFM to optimize the process of sampling. Under a certain under-sampling ratio, the weight coefficient of ROIs and regions of base (ROBs) were set to control the distribution of under-sampling points and corresponding measurement matrix. A series of simulations were completed to demonstrate the relationship between the weight coefficient of ROIs and image quality. After that, we verified the effectiveness of the method on our homemade AFM. Through a lot of simulations and experiments, we demonstrated how the proposed method optimized the sampling process of CS-AFM, which speeded up the process of AFM imaging with high quality.