Measurement Matrix Research Articles

A High-Resolution Imaging Method for Multiple-Input Multiple-Output Sonar Based on Deterministic Compressed Sensing.

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit-receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches.

Black carbon instrument responses to laboratory generated particles

Accurate measurement of black carbon (BC) particles is vital for climate models as well as air quality assessments. While the need for BC particle measurement has been recognized, standardization of instruments and procedures for ambient measurement is still underway. In this study, we used laboratory generated soot particles to assess nine instruments targeting BC mass concentration measurement. The measurement matrix included different BC concentrations (ranging from atmospheric levels to combustion emission levels), different particle coatings, two particle sources (gas burner and spark generator) and two dilution methods. The nine instruments included six different models: aethalometers AE33 and MA200, thermo-optical OC-EC analysis, multi-angle absorption photometer MAAP 5012, photoacoustic instrument MSS, and soot particle aerosol mass spectrometer SP-AMS. The main discrepancy we observed was that the SP-AMS results were systematically lower, approximately only half of the BC measured by other instruments. A portion of this is explained by particle losses in the aerodynamic lens of the SP-AMS and the parameters used in the data analysis. Some smaller discrepancies were identified for the other instruments, but overall, the median values from were within 25 % of each other. Instruments’ operation principles and covered concentration ranges need to be carefully considered especially in emission measurements where the aerosols can have high temporal variation as well as high BC concentrations. In general, the results can decrease the uncertainties in climate and air quality studies by providing tools for more accurate and comparable BC measurements and when the existing BC data is interpreted.

Evaluation of students’ environmental attitude instruments: exploratory and confirmatory factor analysis

One’s environmental attitude can predict human behavior toward the environment. This study aimed to validate the environmental attitude instrument with the science, technology, engineering, and mathematics in ethnoscience-integrated (Ethno-STEM) approach. The questionnaire consisted of 16 items and was tested on 159 eighth-grade students. Data were analyzed using exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). The communality value of three instrument items was less than 0.5, so they were excluded in EFA stage 1. The EFA stage 2 test results showed that the 13 instrument items had a factor loading of more than 0.5 and were categorized into five factors. The CFA stage 1 was conducted using linear structural relations (LISREL) and obtained thet-value for all items in factors 1-4 more than the t-table, so they were declared valid. Factor 5 was omitted in CFA test stage 2 due to invalid items. The CFA test results showed that the t-count of the four factors was more than the t-table. Based on the goodness of fit value, the model and measurement matrices were the same (model fit). Thus, the environmental attitude instrument items are declared valid, and the model is fit. The instrument can be used to measure environmental attitudes.

Emission Ghost Imaging: reconstruction with data augmentation.

Ghost Imaging enables 2D reconstruction of an object even though particles transmitted or emitted by the object of interest are detected with a single pixel detector without spatial resolution. This is possible because for the particular implementation of ghost imaging presented here, the incident beam is spatially modulated with a non-configurable attenuating mask whose orientation is varied (e.g. via transverse displacement or rotation) in the course of the ghost imaging experiment. Each orientation yields a distinct spatial pattern in the attenuated beam. In many cases, ghost imaging reconstructions can be dramatically improved by factoring the measurement matrix which consists of measured attenuated incident radiation for each of many orientations of the mask at each pixel to be reconstructed as the product of an orthonormal matrix and an upper triangular matrix provided that the number of orientations of the mask () is greater than or equal to the number of pixels () reconstructed. For the case, we present a data augmentation method that enables QR factorization of the measurement matrix. To suppress noise in the reconstruction, we determine the Moore-Penrose pseudoinverse of the measurement matrix with a truncated singular value decomposition approach. Since the resulting reconstruction is still noisy, we denoise it with the Adaptive Weights Smoothing method. In simulation experiments, our method outperforms a modification of an existing alternative orthogonalization method where rows of the measurement matrix are orthogonalized by the Gram-Schmidt method. We apply our ghost imaging methods to experimental X-ray fluorescence data acquired at Brookhaven National Laboratory.

Optimal Dynamic Relative Performance Evaluation

ABSTRACT The theoretical prediction of a negative coefficient on positively correlated peer performance underlies much of the empirical literature on relative performance evaluation. This prediction is commonly obtained from a single period model where the variance–covariance matrix of available performance measures is exogenously restricted to be independent of the evaluee’s action. Using the dynamic approach of Holmström and Milgrom (1987), I study the properties of contracts that optimally condition an agent’s compensation both on his own performance and on how well he fares relative to a peer (group) when these restrictions are not imposed. I show that if the covariance is nonzero, the optimal contract is linear in own and peer performance as well as in their correlation. Significantly, and in line with the preponderance of the empirical evidence, in its simplest and perhaps most reasonable form, the model predicts that the expected coefficient on peer performance is exactly zero.

Single-pixel Fresnel incoherent correlation holography for 3D imaging

Fresnel incoherent correlation holography (FINCH) is an incoherent, non-scanning, and high-precision 3D imaging technique, but its area imaging characteristics limit the application of FINCH to some extent. Accordingly, we developed a single-pixel imaging method based on FINCH to realize 3D imaging. We utilized spatial light modulators (SLM) and loaded a measurement matrix on a digital micromirror array (DMD), thereby achieving phase modulation and compressed encoding simultaneously; one-dimensional data acquisition was achieved using a single-pixel camera. Finally, we combined the single-pixel reconstruction and phase-shifting algorithm to achieve incoherent correlation holography imaging with subsampling. The experimental results demonstrated that the proposed method could achieve comparable quality results at a sampling rate of 20 % compared to a 100 % sampling rate, and the method had good noise immunity. This not only avoided the limitations of area array sensors but also enabled high-fidelity imaging with a small data volume, which broadened the scope of research on the application of FINCH in the field of 3D imaging.

Establishing Quality and Outcome Measures for Recovery Housing: A Tiered Approach Supporting Service Evolution.

With over one-hundred thousand drug overdose deaths in 2021, substance use disorder (SUD) is a public health crisis in the United States. Medical stabilization has been the predominant focus of SUD interventions despite low levels of retention. Consequently, national quality measures for SUD care outside the clinical continuity of care are limited. The expansion of recovery support services addressing social drivers of health outside clinical settings is needed. The current SUD quality measures are not applicable nor feasible for recovery support service providers with limited resource capacities, like the estimated 17,900 recovery housing providers nationwide. Despite widespread support for recovery housing and its documented effectiveness, no universal set of measures has been developed for widespread adoption. In this brief, a matrix of quality measures are proposed to meet the needs of recovery housing providers with various capacities to support service evolution and improve equitable SUD treatment and recovery care.

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

Verifiable visually meaningful image encryption algorithm based on compressive sensing and (t, n)-threshold secret sharing

Abstract A verifiable visually meaningful image encryption algorithm based on compressive sensing and (t, n)-threshold secret sharing is proposed. Firstly, the plain image is compressed and encrypted by 2D block compressive sensing to obtain the pre-encrypted image. During this process, the enhanced logistic map and the enhanced tent map are used to generate the measurement matrix and the permutation sequence, respectively. Secondly, multiple shadow images of the pre-encrypted image are generated by using the (t, n)-threshold secret sharing scheme, and then each shadow image is further encrypted by using the encryption matrix generated by the chaotic system. Meanwhile, the signatures of the shadow images are obtained by using RSA signature algorithm. Finally, the shadow images and their corresponding signatures are embedded into the carrier image to generate the cipher image with high visual quality by using the LSB method. Additionally, the present algorithm can resist known-plaintext and chosen-plaintext attacks by incorporating the hash value of the plain image as part of the key. Meanwhile, the use of 2D block compressive sensing significantly reduces the reconstruction time. Simulation results demonstrate that the proposed algorithm achieves excellent decryption quality and operational efficiency.

High-capacity medical information hiding scheme with P-tensor product secret image sharing for wireless body area networks

Given the escalating demand for information transmission in the resource-restricted wireless body area networks (WBANs), securing medical data and minimizing energy consumption are paramount. We present an innovative information hiding scheme that employs P-tensor product secret image sharing (PTP-SIS) and multiple information-hiders for WBANs. Considering the remarkable compression performance demonstrated by compressed sensing (CS), as well as its link to Shamir's (k, n) secret sharing method, using CS rather than traditional secret sharing techniques for image processing purposes could potentially help alleviate transmission burden of sensor nodes. However, utilizing CS to process high-dimensional signals poses a significant challenge due to the large dimensionality of the measurement matrix. The P-tensor product (PTP) is a tool that offers outstanding universality and can overcome the dimension limitations of traditional matrix multiplication, it is applied in the secret sharing stage. Moreover, applying the ideas of secret sharing leads to less stress on an individual device as well as lower communication spending, and multiple hiders have the ability to independently embed additional secrets into shadow images for efficient information backup. Theoretical analysis and experiments validate that the proposed scheme ensures information security and transmission efficiency while achieving superior image recovery performance and higher information embedding rates compared to other approaches.

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.