•Proposing a new sparsity measure using the concept of energy distribution that satisfies the six criteria mathematically.•Introducing two new statistic metrics for a more accurate evaluation of the ...sparsity measures using Monte-Carlo simulation.•Providing comprehensive analysis.
Sparsity has long been a theoretical and practical signal property in applied mathematics and is utilized as a crucial concept in signal/image processing applications such as compression, source separation, sampling theory, signal recovery, and feature extraction. However, many previously proposed sparsity measures are often application-dependent, in this article, we present a new sparsity measure that is appropriate for all applications. This sparsity measure is called the counter of the sparsity of the components based on energy distribution (CSCE). It is proved mathematically that the CSCE satisfies six criteria that are necessary for the measurement of sparsity. Then, sparsity measures are evaluated using statistical analysis. Accordingly, new statistic metrics named resolution and robustness of sparsity measures are presented for statistical analysis. Finally, we analyze diverse synthetic statistical data and various signals and images for a comprehensive evaluation. The metrics and extensive experimental results have demonstrated the major effectiveness and adequacy of our proposed approach compared with the most common methods in the sparsity measure.
Speckle suppression is a prerequisite for many synthetic aperture radar (SAR) image-processing tasks. Previously, we introduced a Bayesian-based speckle-suppression method that employed the 2-D ...generalized autoregressive conditional heteroscedasticity (2D-GARCH) model for wavelet coefficients of log-transformed SAR images. Based on this method, we propose two new Bayesian speckle-suppression approaches in this paper. In the first approach, we introduce a new heteroscedastic model, i.e., the 2D-GARCH Mixture (2D-GARCH-M) model, as an extension of the 2D-GARCH model. This new model can capture the characteristics of wavelet coefficients. Also, the 2D-GARCH-M model introduces additional flexibility in the model formulation in comparison with the 2D-GARCH model, which results in better characterization of SAR image subbands and improved restoration in noisy environments. Then, we design a Bayesian estimator for estimating the clean-image wavelet coefficients based on 2D-GARCH-M modeling. In the second approach, the logarithm of an image is analyzed by means of the curvelet transform instead of wavelet transform. Then, we study the statistical properties of curvelet coefficients, and we demonstrate that the 2D-GARCH model can capture the characteristics of curvelet coefficients, such as heavy tailed marginal distribution, and the dependences among them. Consequently, under the 2D-GARCH model, we design a Bayesian estimator for estimating the clean-image curvelet coefficients. Finally, we compare these methods with other denoising methods applied on artificially speckled and actual SAR images, and we verify the performance improvement in utilizing the new strategies.
The purpose of this work is to investigate the synchro spline-kernelled chirplet extracting transformation (SSCET) method for defect detection in the nonlinear ultrasonic wave modulation (NUWM) ...method. To implement the NUWM method using only one piezoelectric transducer, the self-sensing method is used. Self-sensing has many advantages, but it is sensitive to temperature changes. To reduce the temperature effects, a novel circuit has been designed and implemented. A sandwich beam with bolt loosening and an aluminum beam with boundary loosening damages are used to test the results of the SSCET method on the signal received from the self-sensing circuit. First, an aluminum beam with a loosened boundary is modeled based on beam theory including self-sensing circuits with temperature effects. In this study, SSCET results are compared with those of other time–frequency methods for the detection of the loosened boundary. Based on the temperature effects, the theoretical results are compared with the experimental results of the circuit. To quantify defect detection, a damage index calculated based on instantaneous frequency is provided. Three piezoelectric configurations are also compared with the self-sensing method damage index results. SSCET is then used to check bolt loosening in a sandwich beam for further investigation. The proposed method is compared to a previous self-sensing temperature compensation method. Based on the SSCET method, the severity of the bolt loosening is determined.
The aim of this paper is to deal with the problem of conditional heteroscedastic noise in multivariate systems. In this regard, a new multivariate equation-error system with colored noise is ...introduced, in which the noise conditional variance varies with time and the noise exhibits a GARCH process. Thus, in this our new approach, both the time dependency and probability distribution of noise samples shall be identified. Based on the maximum likelihood principle and orthogonality of parameters, the problem of multivariate system identification is reduced into two separate maximum likelihood problems. An iterative algorithm is proposed, which can efficiently estimate the problem parameters based on gradient reduction and nonlinear optimization. Besides, a bootstrap algorithm is applied for assessing the accuracy of estimators. Also, some asymptotic result of proposed method in large sample size is provided. According to bootstrap simulation results, the proposed algorithm can effectively estimate the parameters of the system with conditional heteroscedastic noise and provides more accurate parameter estimates with a much lower confidence interval, compared to the least square method.
In this paper, we propose a new adaptive single model to track a maneuvering target with abrupt accelerations. We utilize the stochastic differential equation to model acceleration of a maneuvering ...target with stochastic volatility (SV). We assume the generalized autoregressive conditional heteroscedasticity (GARCH) process as the model for the tracking procedure of the SV. In the proposed scheme, to track a high maneuvering target, we modify the Kalman filtering by introducing a new GARCH model for estimating SV. The proposed tracking algorithm operates in both the non‐maneuvering and maneuvering modes, and, unlike the traditional decision‐based model, the maneuver detection procedure is eliminated. Furthermore, we stress that the improved performance using the GARCH acceleration model is due to properties inherent in GARCH modeling itself that comply with maneuvering target trajectory. Moreover, the computational complexity of this model is more efficient than that of traditional methods. Finally, the effectiveness and capabilities of our proposed strategy are demonstrated and validated through Monte Carlo simulation studies.
We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of ...the signal. Our proposed method leaves the space for unavailability of an accurate signal attenuation model in the environment by considering the model as an unknown function with reasonable prior assumptions about its functional space. Such approach is capable of enhancing the localization performance compared with only utilizing the signal attenuation information or the time delays. In this article, the localization problem is modeled as a cost function in terms of the source locations, attenuation model parameters, and the multi-path parameters. To globally perform the minimization, we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm. Besides the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided. Finally, the validity of the proposed method is examined in several localization scenarios, taking into account the noise in the environment, the multi-path phenomenon and considering the sensors being not synchronized.
•Symbolic filtering as a robust method was applied for wireless positioning.•HSDF uses the CRP process to eliminate the offline phase in positioning methods.•Online learning of RSSI data deals with ...indoor environments’ dynamical behavior.•Dirichlet-multinomial distribution was used to cluster short epochs of RSSI data.
Hierarchical symbolic dynamic filtering (HSDF) is used in literature for anomaly detection by unsupervised classification of time series data. This paper proposes a novel wireless positioning method based on the HSDF concept. This approach aims to tackle the main problems in fingerprinting-based localization methods by eliminating the offline phase, which is the most time-consuming part of a fingerprinting localization. Online learning of Received Signal Strength Indicator (RSSI) time series data causes this method to be efficient in dealing with indoor environments’ dynamical behavior, which is another problem in the localization methods domain. Due to SDF (symbolic dynamic filtering)-based structure, it shows robustness to noise and multipath effect. This paper demonstrates these achievements by results obtained from both simulation of noisy datasets and real-time positioning in an indoor testbed.
•We propose a wavelet domain scaling watermarking method.•We design an ML detector and analyze its performance analytically.•We use L-curve method to find tradeoff between imperceptibility and ...robustness.•Experimental results demonstrate the high performance of the proposed method.
In this paper, we propose a novel scaling watermarking scheme in which the watermark is embedded in the low-frequency wavelet coefficients to achieve improved robustness. We demonstrate that these coefficients have significantly non-Gaussian statistics that are efficiently described by Gaussian Mixture Model (GMM). By modeling the coefficients using the GMM, we calculate the distribution of watermarked noisy coefficients analytically and we design a Maximum Likelihood (ML) watermark detector using channel side information. Also, we extend the proposed watermarking scheme to a blind version. Consequently, since the efficiency of the proposed method is dependent on the good selection of the scaling factor, we propose L-curve method to find the tradeoff between the imperceptibility and robustness of the watermarked data. Experimental results demonstrate the high efficiency of the proposed scheme and the performance improvement in utilizing the new strategy in comparison with the some recently proposed techniques.
Functional magnetic resonance imaging a neuroimaging technique which is used in brain disorders and dysfunction studies, has been improved in recent years by mapping the topology of the brain ...connections, named connectopic mapping. Based on the fact that healthy and unhealthy brain regions and functions differ slightly, studying the complex topology of the functional and structural networks in the human brain is too complicated considering the growth of evaluation measures. One of the applications of irregular graph deep learning is to analyze the human cognitive functions related to the gene expression and related distributed spatial patterns. Since a variety of brain solutions can be dynamically held in the neuronal networks of the brain with different activity patterns and functional connectivity, both node-centric and graph-centric tasks are involved in this application. In this study, we used an individual generative model and high order graph analysis for the region of interest recognition areas of the brain with abnormal connection during performing certain tasks and resting-state or decompose irregular observations. Accordingly, a high order framework of Variational Graph Autoencoder with a Gaussian distributer was proposed in the paper to analyze the functional data in brain imaging studies in which Generative Adversarial Network is employed for optimizing the latent space in the process of learning strong non-rigid graphs among large scale data. Furthermore, the possible modes of correlations were distinguished in abnormal brain connections. Our goal was to find the degree of correlation between the affected regions and their simultaneous occurrence over time. We can take advantage of this to diagnose brain diseases or show the ability of the nervous system to modify brain topology at all angles and brain plasticity according to input stimuli. In this study, we particularly focused on Alzheimer’s disease.
Source localization is an important field of research with numerous applications in signal processing and wireless communications. In this paper, we present a received signal strength difference ...(RSSD) based method to localize a source with unknown transmit power in the presence of sensor position uncertainty. It is an efficient low complexity technique which does not require transmit power estimation as with other approaches. This eliminates the uncertainty due to signal propagation parameter variations. A constrained adaptive weighted least squares technique is presented to obtain a least squares initial estimate (LSIE) of the source location. Then, this estimate is improved using a computationally efficient modified Newton method (MNM) with adaptive weights. The bias of the proposed LSIE-MNM method and the Cramér-Rao lower bound (CRLB) of the RSSD based measurement model are derived to determine the effect of sensor position uncertainties on the source location estimate. Results are presented which show that the proposed method achieves the CRLB when the SNR is sufficiently high.
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