Measurement Matrix Research Articles

Review of the research on the qualitative theory of differential equations at St. Petersburg University. II. Locally qualitative analysis of essentially nonlinear systems

This article is the second one in a series of articles devoted to a review of the results of scientific research that have been carried out at the Department of Differential Equations of St.Petersburg University over the past three decades and continue to be carried out at the present time. The first article talked about studies of stable periodic points of diffeomorphisms with homoclinic points and systems of differential equations with weakly hyperbolic invariant sets. This paper presents the results of locally qualitative analysis of essentially nonlinear systems in the neighbourhood of the zero solution, obtained by employees and graduates of the department. A system is said to be essentially nonlinear if the Taylor series expansion of its right-hand sides does not contain linear terms. The study of such systems, firstly, is complicated by a more complex picture of the behavior of solutions compared to quasilinear systems. Secondly, there are not even theoretical formulas for the general solution of a nonlinear first-approximation system, the presence of which is so helpful in the quasi-linear case. All this complicates analysis and significantly limits technical capabilities. Therefore, almost any new results and any new methods of working with such systems are of great interest. One of the most effective tools for working with essentially nonlinear systems turned out to be the logarithmic Lozinsky norms. In a sense, they are an analogue of the characteristic exponents (eigenvalues) used in the theory of quasilinear systems. Research conducted at the department has demonstrated the wide possibilities of using logarithmic norms in a wide variety of problems.

Yb@TiO2 nanoparticles as a SELDI-TOF MS matrix for the simultaneous measurement of Tetrabromobisphenol A and Perfluorooctane sulfonate

Ytterbium modified TiO2 nanoparticles (Yb@TiO2), synthesized by a sol–gel process, were employed as an efficient adsorbent and matrix for the analysis of Perfluorooctane sulfonate (PFOS) and Tetrabromobisphenol A (TBBPA) via surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS). The detection limits for PFOS and TBBPA are achievement with 0.01 pg ·mL−1. The results of the analysis of camellia oil samples show good recovery (80.3%–86.8%) with a low detection limit for TBBPA.

NesTD-Net: Deep NESTA-Inspired Unfolding Network With Dual-Path Deblocking Structure for Image Compressive Sensing.

Deep compressive sensing (CS) has become a prevalent technique for image acquisition and reconstruction. However, existing deep learning (DL)-based CS methods often encounter challenges such as block artifacts and information loss during iterative reconstruction, particularly at low sampling rates, resulting in a reduction of reconstructed details. To address these issues, we propose NesTD-Net, an unfolding-based architecture inspired by the NESTA algorithm, designed for image CS. NesTD-Net integrates DL modules into NESTA iterations, forming a deep network that continuously iterates to minimize the l1 -norm CS problem, ensuring high-quality image CS. Utilizing a learned sampling matrix for measurements and an initialization module for initial estimate, NesTD-Net then introduces Iteration Sub-Modules derived from the NESTA algorithm (i.e., Yk , Zk , and Xk ) during reconstruction stages to iteratively solve the l1 -norm CS reconstruction. Additionally, NesTD-Net incorporates a Dual-Path Deblocking Structure (DPDS) to facilitate feature information flow and mitigate block artifacts, enhancing image detail reconstruction. Furthermore, DPDS exhibits remarkable versatility and demonstrates seamless integration with other unfolding-based methods, offering the potential to enhance their performance in image reconstruction. Experimental results demonstrate that our proposed NesTD-Net achieves better performance compared to other state-of-the-art methods in terms of image quality metrics such as SSIM and PSNR, as well as visual perception on several public benchmark datasets.

Fast Construction of Measurement Matrix and Sensing Matrix with Dual Adaptive Cross Approximation

Fast Construction of Measurement Matrix and Sensing Matrix with Dual Adaptive Cross Approximation

Phase transition and higher order analysis of Lq regularization under dependence.

We study the problem of estimating a [Formula: see text]-sparse signal [Formula: see text] from a set of noisy observations [Formula: see text] under the model [Formula: see text], where [Formula: see text] is the measurement matrix the row of which is drawn from distribution [Formula: see text]. We consider the class of [Formula: see text]-regularized least squares (LQLS) given by the formulation [Formula: see text], where [Formula: see text] [Formula: see text] denotes the [Formula: see text]-norm. In the setting [Formula: see text] with fixed [Formula: see text] and [Formula: see text], we derive the asymptotic risk of [Formula: see text] for arbitrary covariance matrix [Formula: see text] that generalizes the existing results for standard Gaussian design, i.e. [Formula: see text]. The results were derived from the non-rigorous replica method. We perform a higher-order analysis for LQLS in the small-error regime in which the first dominant term can be used to determine the phase transition behavior of LQLS. Our results show that the first dominant term does not depend on the covariance structure of [Formula: see text] in the cases [Formula: see text] and [Formula: see text] which indicates that the correlations among predictors only affect the phase transition curve in the case [Formula: see text] a.k.a. LASSO. To study the influence of the covariance structure of [Formula: see text] on the performance of LQLS in the cases [Formula: see text] and [Formula: see text], we derive the explicit formulas for the second dominant term in the expansion of the asymptotic risk in terms of small error. Extensive computational experiments confirm that our analytical predictions are consistent with numerical results.

Non-Cascaded and Crosstalk-Free Multi-Image Encryption Based on Optical Scanning Holography Using 2D Orthogonal Compressive Sensing.

We propose a non-cascaded and crosstalk-free multi-image encryption method based on optical scanning holography and 2D orthogonal compressive sensing. This approach enables the simultaneous recording and encryption of multiple plaintext images without mechanical scanning, while allows for independent retrieval of each image with exceptional quality and no crosstalk. Two features would bring about more substantial security and privacy. The one is that, by employing a sequence of pre-designed structural patterns as encryption keys at the pupil, multiple samplings can be achieved and ultimately the holographic cyphertext can be obtained. These patterns are generated using a measurement matrix processed with the generalized orthogonal one. As a result, one can accomplish the differentiation of images prior to the recording and thus neither need to pretreat the pending images nor to suppress the out-of-focus noise in the decrypted image. The other one is that, the non-cascaded architecture ensures that different plaintexts do not share sub-keys. Meanwhile, compared to 1D orthogonal compressive sensing, the 2D counterpart makes the proposed method to synchronously deal with multiple images of more complexity, while acquire significantly high-quality decrypted images and far greater encryption capacity. Further, the regularities of conversion between 1D and 2D orthogonal compressive sensing are identified, which may be instructive when to manufacture a practical multi-image cryptosystem or a single-pixel imaging equipment. A more general method or concept named synthesis pupil encoding is advanced. It may provide an effective way to combine multiple encryption methods together into a non-cascaded one. Our method possesses nonlinearity and it is also promising in multi-image asymmetric or public key cryptosystem as well as multi-user multiplexing.

A hardware friendly and meaningful image encryption strategy based on a binary measurement matrix and de Bruijn sequence

A hardware friendly and meaningful image encryption strategy based on a binary measurement matrix and de Bruijn sequence

Block Sparse Recovery With Redundant Measurement Matrices and Its Application in Frequency Agile Radar

Block Sparse Recovery With Redundant Measurement Matrices and Its Application in Frequency Agile Radar

Self-Adaptive Measurement Matrix Design and Channel Estimation in Time-Varying Hybrid MmWave Massive MIMO-OFDM Systems

Self-Adaptive Measurement Matrix Design and Channel Estimation in Time-Varying Hybrid MmWave Massive MIMO-OFDM Systems

Computational ghost imaging encryption using RSA algorithm and discrete wavelet transform

Ghost imaging technology has been widely used in the field of optical image encryption owing to its unique non-local imaging characteristics. However, there are some problems such as long encryption and decrypting time, poor reliability and large number of keys. To solve these problems, this paper proposed a computational ghost imaging encryption scheme based on RSA algorithm and wavelet transform. Firstly, the representation relationship between measurement matrix and random integer sequence is established to reduce the transmission of key quantity. Secondly, RSA encryption algorithm is used to improve the security of the system. Finally, using wavelet decomposition for packet transmission. In addition, the cake cutting matrix is used as the measurement matrix to reduce the sampling times and improve the quality of reconstructed images. The simulation results show that the encryption system has strong information transmission security and good robustness. It provides some reference for image encryption and information security transmission.

Real Aperture Radar Angular Super-Resolution Imaging Using Modified Smoothed L0 Norm with a Regularization Strategy

Restricted by the ill-posed antenna measurement matrix, the conventional smoothed L0 norm algorithm (SL0) fails to enable direct real aperture radar angular super-resolution imaging. This paper proposes a modified smoothed L0 norm (MSL0) algorithm to address this issue. First, as the pseudo-inverse of the ill-posed antenna measurement matrix is required to set the initial values and calculate the gradient projection, a regularization strategy is employed to relax the ill-posedness. Based on the regularization strategy, the proposed MSL0 algorithm can avoid noise amplification when faced with the ill-posed antenna measurement matrix of real aperture radar. Additionally, to prevent local minima problems, we introduce a hard thresholding operator, based on which the proposed MSL0 algorithm can accurately reconstruct sparse targets. Simulations and experimental results verify the performance of the proposed MSL0 algorithm.

Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka–Volterra systems

This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory. The AMP algorithms studied in this part are those where the measurement matrix has independent elements, up to the symmetry constraint when this matrix is symmetric, with a variance profile that can be sparse. The AMP problem is solved by adapting the approach of Bayati, Lelarge, and Montanari (2015) to this matrix model.The Lotka–Volterra (LV) model is the standard model for studying the dynamical behavior of large dimensional ecological food chains. The second part of this paper is focused on the study of the statistical distribution of the globally stable equilibrium vector of a LV system in the situation where the random symmetric interaction matrix among the living species is sparse, and in the regime of large dimensions. This equilibrium vector is the solution of a Linear Complementarity Problem, which distribution is shown to be characterized through the AMP approach developed in the first part. In the large dimensional regime, this distribution is close to a mixture of a large number of truncated Gaussians.

Mixed gray-color images encryption algorithm based on a memristor chaotic system and 2D compression sensing

Multi-image encryption has attracted great interest in the era of secret communication, however, the mixed encryption of gray and color images has been reported rarely. Meanwhile, the security of image encryption based on chaos system depends heavily on the performance of pseudo randomness and sensibility. Thus, a four-dimensional chaotic system is improved by introducing a memristor, which has good nonlinear characteristic and can enhance chaotic property. It is found that this new system possesses larger chaotic scope and exhibits a coexistence phenomenon, all of which reveal the intricate nature and underlying application. After the verification of spectral entropy and circuit simulations of the new system, a mixed-image encryption algorithm based on two-dimension compression sensing (2DCS) is designed innovatively. To achieve the target of compression and encryption, the image set is first preprocessed and varied utilizing DWT, and then is sampled by measurement matrix in two-dimension. Next, the pixels of compressed image set are diffused by employing DNA coding. The accuracy of reconstruction image is closely related to the randomness and sparsity of the measurement matrix. Chaotic system with pseudo-randomness can be fully exploited to fabric a measurement matrix. Hence the Toeplitz cyclic chaos matrix is conceived and the reconstruction accuracy does have better results. In addition, this method can not only encrypt multiple mixed images with grey and color simultaneously, but also compress them with different sizes and less storage space. At last, the reliability of the novel algorithm is assessed through a series of reconstruction and security performance tests. The results indicate that the encryption scheme has a better effect than encrypting one kind of image, and prove that the algorithm has high reconstruction accuracy and security.

Lexicostatistical Studies of the Connection of Buryat-Evenki Toponyms of the Irkutsk Region with the Russian Language

Lexicostatistical studies of the connection between the Buryat-Evenki toponyms of the Irkutsk region and the Russian language have been carried out. The study used a method of a matrix of proximity measures between the list of toponyms and the list of Russian words from the frequency Russian-Buryat dictionary, which are translated into consonantal classes according to A. Dolgopolsky. Closeness measures between two words composed of consonantal classes are described using the Ratcliffe — Oberschelp numerical metric. A matrix of word proximity measures has been calculated, numbering about 800,000 elements. The averages of the maximum measures in rows and columns and the average measure over the entire field of the matrix are found. Statistical studies show the historical connection of a group of toponyms with the Russian language at the level of 85 %. The meaning of some Buryat-Evenki toponyms in the Russian language has been restored.

Analysis of the Security of Internet of Multimedia Things in Wireless Environment

The Internet of Things (IoT) and real-time flexibility improve people’s lives, and IoT applications rely heavily on multimedia sensors and devices. An interconnected network of IoT multimedia devices has made the Internet of Medical Things (IoMT). It creates massive data distinct from what the Internet of Things (IoT) produced. Smart traffic monitoring and smart hospitals are only a few examples of real-time deployment applications. IoMT data and decision-making must be made quickly since it directly impacts human life. The security heterogeneity of optimization issues is a significant challenge for enabling multimedia applications on the IoT. The IoMT has difficulty achieving low-cost data collecting while maintaining data security. An Internet of Multimedia Things in a wireless environment (IoMT-WE) system decreases the bandwidth and privacy risk caused by the revocation list, ensures the integrity of batch verification information, and corresponds with Vehicular ad hoc network (VANET) security performance. The proposed method uses random subsampling and chaotic convolution to collect numerous images. The sampling method is safe since the measurement matrix is controlled by chaos. As part of the IoMT architecture, wireless multimedia sensor nodes can be more easily deployed over the long term for real-time multimedia. The Wireless Multimedia Sensor Network (WMSN) comprises nodes that can capture both multimedia and non-multimedia data. The ioMT-WE system has been tested and found to be secure and effective.

A new working reference material for cassiterite oxygen isotope microanalysis

Cassiterite is the principal ore mineral for tin, and its oxygen isotope is a promising proxy to trace the origin and evolution of ore‐forming fluids, which requires precise and accurate oxygen isotopic analysis. Secondary ion mass spectrometry (SIMS) is a powerful tool for oxygen isotope analysis, especially when samples bear complicated textures, but matrix‐matched reference materials are critical for accurate microanalysis. The only available matrix‐matched reference material for cassiterite oxygen isotope analysis is Yongde‐Cst, and more reference materials are required. Here, we report Piaotang‐Cst as a potential working reference material for cassiterite oxygen isotope microanalysis. Our extensive SIMS microanalysis confirmed that Piaotang‐Cst is relatively homogeneous, with an average two standard deviations (2SD) of 0.49‰ (n = 626). The δ18OVSMOW value of Piaotang‐Cst is 5.33 ± 0.07‰ (2SD, n = 5) as determined by a conventional fluorination isotope ratio mass spectrometer. We also demonstrated that there is no measurable matrix effect caused by the variable contents of trace elements for cassiterite oxygen isotope microanalysis. We proposed that the Piaotang‐Cst can be used as a working reference material for monitoring the external reproducibility and accuracy of SIMS analysis.

Cross-Layer RF Distance Bounding Scheme for Passive and Semi-passive Ubiquitous Computing Systems

Distance Bounding protocols have surfaced as an appealing security measure in ubiquitous computing systems with access control provisions whereby the physical proximity of a user becomes significantly important for its explicit privileges and assurances. These systems employ cryptographic protocols to ensure security. However, security vulnerabilities have been demonstrated that exploit not only the cryptographic protocol but the physical implementation of the protocol itself. Distance Bounding resolves this problem by tightly integrating cryptographic security with the physical layer through a cross-layer security design. The core idea is to employ physical proximity as a security fingerprint to ensure that the legitimate entity (namely ‘prover’) lies within an agreed spatial range of another entity (‘verifier’). While a large number of Distance Bounding protocols have been proposed in the past, they mainly focus on designing a secure authentication scheme integrated with a suitable distance measurement approach, disregarding multiple concerns in the practical realization of these protocols – which we termed as a cross-layer problem. Only a few practical Distance Bounding realizations have been demonstrated which however focus on some selected cross-layer design parameters. As a result, either these protocols are impractical as a realizable system, or in most cases, an attacker can easily exploit cross-layer vulnerabilities especially if the prover is a resource-constrained entity such as a fully passive or battery-assisted access control token. This requires formulation of a careful prover design while ensuring that secure authentication and precise ranging are tightly integrated in a cross-layer manner for a realizable system. To resolve these issues, we first present a holistic approach to designing a secure Distance Bounding system by identifying essential cross-layer parameters. While analyzing the salient Distance Bounding realizations, we observe them to be designed for a single-bit communication channel. We optimize the communication bit rate by incorporating a high-order modulation technique in our proposed scheme to achieve higher date rates while ensuring the overall integrity of cross-layer design parameters. Besides, we specifically analyze the effects of the prover's impedance mismatch on link efficacy and security. This is a significant factor which depicts the allowable tolerances in the prover's impedance from design to manufacturing phases. Lastly, we present a comparison between prior approaches and our proposed scheme while introducing Qualitative Measure Matrix (QMM-I) and Quantitative Measure Matrix (QMM-II), which are devised from cross-layer design parameters for a secure Distance Bounding realization.

Graph Neural Network-Based Distribution System State Estimators

State estimation is an essential tool for situational awareness and control to ensure safe operation. While current state-of-the-art techniques, such as model-based sparsity-aware state estimators, provide superior performance over conventional approaches, they have poor scalability and require large computational times. These limitations can be overcome by utilizing deep learning models such as deep neural networks (DNNs). However, DNNs are prone to over-fitting and cannot incorporate structural information of networks. Furthermore, current model-based approaches require detailed knowledge of network parameters that may be unavailable in large systems. Therefore, new models with comparable performance are desired that either do not require network parameters or that can work using partial knowledge of these parameters. Recently, graph neural networks (GNNs) have become popular deep learning models that extend neural models to graph structures and incorporate structural information of the networks through graph structures. Therefore, this article proposes GNN-based state estimators by modeling the state estimation problem in distribution systems as node-level prediction problems on their graph representations with state measurement matrices and tensors as input features. Feature scaling and pseudo-measurement generation phases are introduced to enhance their performance. These approaches are evaluated on the IEEE 33, 37-node systems, and an unbalanced three-phase 559-node system. The proposed approaches provide comparable performance to sparsity-aware state estimators while using significantly lower computational times. The GNN-based approaches produce state estimates conforming to the power flow constraints without prior knowledge of the network parameters, thus suggesting that the proposed models can learn the system's underlying physical flows.

Optimization of Bipolar Toeplitz Measurement Matrix Based on Cosine-Exponential Chaotic Map and Improved Abolghasemi Algorithm

Optimization of Bipolar Toeplitz Measurement Matrix Based on Cosine-Exponential Chaotic Map and Improved Abolghasemi Algorithm

Research on data-driven low-sampling-rate single-pixel imaging method.

Single-pixel imaging requires only a unit detector with no spatial resolution capability to acquire spatial information of the target and reconstruct the image. However, the quality of reconstructing images strongly depends on measurement matrices and their number of samples, making it challenging to achieve high-quality imaging with fewer samples. In this Letter, a dataset-driven low-sampling-rate single-pixel imaging method is proposed. It utilizes a network model driven by the image datasets to directly extract target feature information from a small number of samples and reconstruct the image. Experimental results demonstrate that, compared to traditional single-pixel imaging methods, this method no longer depends strongly on the relationship between the measurement matrices and the samples, and it can achieve an ideal imaging effect with a structural similarity of 90.20% at low sampling rates.