Search Results (62)

The article presents Modified Scaled Adaptive Daqrouq Wavelet (MSADW) as an autonomous wavelet framework to overcome the analysis obstacles of traditional wavelets (Morlet and Daubechies) for signals with non-stationary characteristics. MSADW adjusts its waveform shape and frequency in real time based on the specific characteristics of the signal, allowing it to outperform conventional wavelet methods. The system reaches adaptability through three core methods featuring gradient-dependent scale adjustments for fast transient detection and smooth regions, and instantaneous frequency monitoring achieved by a combination of STFT and Hilbert transforms and an iterative error reduction process using gradient descent and genetic algorithms. Continuous Wavelet Transform (CWT) combined with Discrete Wavelet Transform (DWT) extracts features from ECG and speech signals. Throughout this process, MSADW maintains great time precision to detect transients as well as maintain sensitivity for the audio’s base stability. Testing MSADW in practical use reveals its superior performance because it detects R-peaks accurately within 0.01 s through zero-crossing methods, which combine P/T-wave detection with effective ECG signal segmentation and noise-free reconstructed speech ($\mathit{MSE:} 1.17\times {10}^{-31}$). The localized parameterization framework of MSADW, enabled by feedback refinement, fulfills missing aspects in biomedical signal evaluation and creates space for low-cost real-time evaluation methods for medical devices and arrhythmia and ischemic detection platforms. The theoretical backbone for MSADW establishes itself because this work shows how wavelet analysis can transition toward managing non-stationary and noise-prone domains. Full article

This paper presents a novel non-uniform, non-stationary Loop subdivision that directly interpolates arbitrary initial triangular meshes. This subdivision is derived by assigning distinct parameters for “vertex-point” and “edge-point” generation within the stencils of a uniform, non-stationary Loop subdivision. This underlying uniform, non-stationary scheme is obtained based on a suitably chosen iterative process. Crucially, we derive the limit positions of the initial points under this non-uniform scheme and decrease the assigned parameters to a single shape parameter when interpolating the initial mesh. Compared with the existing methods interpolating the initial mesh using approximating subdivision, this new one achieves interpolation in finite steps and without any additional adjustment to the initial mesh or subdivision rules. Several numerical examples are given to show the scheme’s interpolation accuracy and shape control capabilities. Full article

Object detection in single synthetic aperture radar (SAR) imagery has always been essential for SAR interpretation. Over the years, the saliency-based detection method is considered as a strategy that can overcome some inherent deficiencies in traditional SAR detection and arouses widespread attention. Considering that the conventional saliency method usually suffers performance loss in saliency map generation from lacking specific task priors or highlighted non-object regions, this paper is devoted to achieving excellent salient object detection in single SAR imagery via a two-channel framework integrating Bayesian inference and adaptive iteration. Our algorithm firstly utilizes the two processing channels to calculate the object/background prior without specific task information and extract four typical features that can enhance the object presence, respectively. Then, these two channels are fused to generate an initial saliency map by Bayesian inference, in which object areas are assigned with high saliency values. After that, we develop an adaptive iteration mechanism to further modify the saliency map, during which object saliency is progressively enhanced while the background is continuously suppressed. Thus, in the final saliency map, there will be a distinct difference between object components and the background, allowing object detection to be realized easily by global threshold segmentation. Extensive experiments on real SAR images from the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset and SAR Ship Detection Dataset (SSDD) qualitatively and quantitatively demonstrate that our saliency map is superior to those of four classical benchmark methods, and final detection results of the proposed algorithm present better performance than several comparative methods across both ground and maritime scenarios. Full article

Effective noise elimination is essential for ensuring data reliability in high-accuracy measurement systems. However, selecting the optimal denoising strategy for diverse and non-stationary signal types remains a major challenge. This study presents a wavelet-based denoising optimization framework that systematically identifies and applies the most suitable noise reduction model for each signal segment. By evaluating multiple wavelet types and thresholding strategies, the proposed method enables adaptive and automated selection tailored to the specific characteristics of each signal. The framework was validated using synthetic, open-access, and experimentally acquired signals in both reference-based and reference-free scenarios. Extensive testing covered signals from power quality disturbance (PQD) events, electrocardiogram (ECG) data, and electroencephalogram (EEG) recordings, all of which represent critical applications where signal integrity under noise is essential. The method achieved optimal model selection in 22.15 s (across 4558 iterations) on a standard PC, with an average denoising time of 4.86 ms per signal window. These results highlight its potential for real-time and embedded applications, including smart grid monitoring systems, wearable health devices, and automated biomedical diagnostic platforms, where adaptive, fast, and reliable denoising is vital. The framework’s versatility makes it highly relevant for deployment in smart grid monitoring systems and intelligent energy infrastructures requiring robust signal conditioning. Full article

The Engel algorithm was created to solve chip-firing games and can be used to find the stationary distribution for absorbing Markov chains. Kaushal et al. developed a matlab-based version of the generalized Engel algorithm based on Engel’s probabilistic abacus theory. This paper introduces a modified version of the generalized Engel algorithm, which we call the modified Engel algorithm, or the mEngel algorithm for short. This modified version is designed to address issues related to non-absorbing Markov chains. It achieves this by breaking down the transition matrix into two distinct matrices, where each entry in the transition matrix is calculated from the ratio of the numerator and denominator matrices. In a nested iteration setting, these matrices play a crucial role in converting non-absorbing Markov chains into absorbing ones and then back again, thereby providing an approximation of the solutions of non-absorbing Markov chains until the distribution of a Markov chain converges to a stationary distribution. Our results show that the numerical outcomes of the mEngel algorithm align with those obtained from the power method and the canonical decomposition of absorbing Markov chains. We provide an example, Torrence’s problem, to illustrate the application of absorbing probabilities. Furthermore, our proposed algorithm analyzes the Monopoly transition matrix as a form of non-absorbing probabilities based on the rules of the Monopoly game, a complete information dynamic game, particularly the probability of landing on the Jail square, which is determined by the order of the product of the movement, Jail, Chance, and Community Chest matrices. The Long Jail strategy, the Short Jail strategy, and the strategy for getting out of Jail by rolling consecutive doubles three times have been formulated and tested. In addition, choosing which color group to buy is also an important strategy. By comparing the probability distribution of each strategy and the profit return for each property and color group of properties, and the color group property, we find which one should be used when playing Monopoly. In conclusion, the mEngel algorithm, implemented using R codes, offers an alternative approach to solving the Monopoly game and demonstrates practical value. Full article

Compressive sensing in the ambiguity domain facilitates high-performance reconstruction of time-frequency distributions (TFDs) for non-stationary signals. However, identifying the optimal regularization parameter in the absence of prior knowledge remains a significant challenge. The Rényi entropy-based two-step iterative shrinkage/thresholding (RTwIST) algorithm addresses this issue by incorporating local component estimates to guide adaptive thresholding, thereby improving interpretability and robustness. Nevertheless, RTwIST may struggle to accurately isolate components in cases of significant amplitude variations or component intersections. In this work, an enhanced RTwIST framework is proposed, integrating the random sample consensus (RANSAC)-based refinement stage that iteratively extracts individual components and fits smooth trajectories to their peaks. The best-fitting curves are selected by minimizing a dedicated objective function that balances amplitude consistency and trajectory smoothness. Experimental validation on both synthetic and real-world electroencephalogram (EEG) signals demonstrates that the proposed method achieves superior reconstruction accuracy, enhanced auto-term continuity, and improved robustness compared to the original RTwIST and several state-of-the-art algorithms. Full article

The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components, we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals, struggle with non-stationary datasets and they require the selection of predefined basis functions. In contrast, the empirical mode decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective non-linear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that varies simultaneously in space and time, like the ones sampled using sensor arrays. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate non-stationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines. Full article

The study of the process of laser action on powder materials requires the construction of mathematical models of the interaction of laser radiation with powder particles that take into account the features of energy supply and are applicable in a wide range of beam parameters and properties of the particle material. A model of the interaction of pulsed or pulse-periodic laser radiation with a spherical metal particle is developed. To find the temperature distribution in the particle volume, the non-stationary three-dimensional heat conductivity equation with a source term that takes into account the action of laser radiation is solved. In the plane normal to the direction of propagation of laser radiation, the change in the radiation intensity obeys the Gaussian law. It is possible to take into account changes in the intensity of laser radiation in space due to its absorption by the environment. To accelerate numerical calculations, a computational algorithm is used based on the use of vectorized data structures and parallel implementation of operations on general-purpose graphics accelerators. The features of the software implementation of the method for solving a system of difference equations that arises as a result of finite-volume discretization of the heat conductivity equation with implicit scheme by the iterative method are presented. The model developed describes the heating and melting of a spherical metal particle exposed by multi-pulsed laser radiation. The implementation of the computational algorithm developed is based on the use of vectorized data structures and GPU resources. The model and calculation results are of interest for constructing a two-phase flow model describing the interaction of test particles with laser radiation on the scale of the entire calculation domain. Such a model is implemented using a discrete-trajectory approach to modeling the motion and heat exchange of a dispersed admixture. Full article

A novel random coefficient autoregressive model is proposed, and a feature of the model is the non-stationarity of the state equation. The autoregressive coefficient is an unknown function with an unobservable state variable, which can be estimated by the local linear regression method. The iterative algorithm is constructed to estimate the parameters based on the ordinary least squares method. The ordinary least squares residuals are used to estimate the variances of the errors. The Kalman-smoothed estimation method is used to estimate the unobservable state variable because of its ability to deal with non-stationary stochastic processes. These methods allow deriving the analytical solutions. The performance of the estimation methods is evaluated through numerical simulation. The model is validated using actual time series data from the S&P/HKEX Large Cap Index. Full article

The detection of adverse events—for example, convulsive epileptic seizures—can be critical for patients suffering from a variety of pathological syndromes. Algorithms using remote sensing modalities, such as a video camera input, can be effective for real-time alerting, but the broad variability of environments and numerous nonstationary factors may limit their precision. In this work, we address the issue of adaptive reinforcement that can provide flexible applications in alerting devices. The general concept of our approach is the topological reinforced adaptive algorithm (TOREADA). Three essential steps—embedding, assessment, and envelope—act iteratively during the operation of the system, thus providing continuous, on-the-fly, reinforced learning. We apply this concept in the case of detecting convulsive epileptic seizures, where three parameters define the decision manifold. Monte Carlo-type simulations validate the effectiveness and robustness of the approach. We show that the adaptive procedure finds the correct detection parameters, providing optimal accuracy from a large variety of initial states. With respect to the separation quality between simulated seizure and normal epochs, the detection reinforcement algorithm is robust within the broad margins of signal-generation scenarios. We conclude that our technique is applicable to a large variety of event detection systems. Full article

Following the work on non-stationary fractal interpolation (Mathematics 7, 666 (2019)), we study non-stationary or statistically self-similar fractal interpolation on the Sierpiński gasket (SG). This article provides an upper bound of box dimension of the proposed interpolants in certain spaces under suitable assumption on the corresponding Iterated Function System. Along the way, we also prove that the proposed non-stationary fractal interpolation functions have finite energy. Full article

The research on how to effectively extract the instantaneous characteristic components of non-stationary signals continues to be both a research hotspot and a very challenging topic. In this paper, a new method of multi-component decomposition is proposed to decompose a signal into finite mono-component signals and extract their Instantaneous Amplitude (IA), Instantaneous Phase (IP), and Instantaneous Frequency (IF), which is called Sinusoidal Fitting Decomposition (SFD). The proposed method can ensure that the IA extracted from the given signal must be positive, the IP is monotonically increasing, and the signal synthesized by both IA and IP must be mono-componential and smooth. It transforms the decomposition process into a synthesis iterative process and does not rely on any dictionary or basis function space or carry out the sifting operation. In addition, the proposed method can describe the instantaneous-frequency-amplitude characteristics of the signal very well on the time-frequency plane. The results of numerical simulation and the qualitative analysis of the amount of calculation show that the proposed method is effective. Full article

Sea level monitoring is of great significance to the life safety and daily production activities of coastal residents. In recent years, GNSS interferometric reflectometry (GNSS-IR) has gradually developed into a powerful complementary technique for sea level monitoring, with the advantages of wide signal spatial coverage and lower maintenance cost. However, GNSS-IR-retrieved sea level estimates suffer from a prominent error source, referred to as the dynamic height error due to the nonstationary sea level. In this study, the tidal analysis method, least squares method and cubic spline fitting method are used to correct the dynamic height error, and their performances are analyzed. These three methods are applied to multi-system and multi-frequency data from three coastal GNSS stations, MAYG, SC02 and TPW2, for three years, and the retrievals are compared and analyzed with the in situ measurements from co-located tide gauges to explore the applicability of the three methods. The results show that the three correction methods can effectively correct the sea level dynamic height error and improve the accuracy and reliability of the GNSS-IR sea level retrievals. The tidal analysis method shows the best correction performance, with an average reduction of 39.3% (10.7 cm) and 37.6% (6.7 cm) in RMSE at the MAYG and TPW2 stations, respectively. At station SC02, the cubic spline fitting method performs the best, with the RMSE reduced by an average of 39.3% (5.5 cm) after correction. Furthermore, the iterative process of the tidal analysis method is analyzed for the first time. We found the tidal analysis method could significantly remove the outliers and correct the dynamic height error through iterations, generally superior to the other two correction methods. With the dense preliminary GNSS-IR sea level retrievals, the smaller window length of the least squares method can yield more corrected retrievals and better correction performance. The least squares method and cubic spline fitting method, especially the former, are highly dependent on the amount of daily GNSS-IR sea level retrievals, but they are more suitable for dynamic height correction in storm events than the tidal analysis method. Full article

An extremely large-scale antenna array (ELAA) can potentially provide significantly increased spatial multiplexing and beamforming gains, as well as enhanced localization capability. While presenting new potential, its near-field propagation and spatial non-stationary properties also impose a great challenge on the receiver design. This paper focuses on the receiver design in an uplink orthogonal frequency-division multiplexing system with a planar ELAA deployed at the base station. To solve the challenging problem of 3D user localization and channel estimation with the planar ELAA, a space-frequency user localization and channel reconstruction (SF-ULCR) receiver is proposed. Under the Bayesian framework, an extended probability model is first established, to capture the channel structural information comprehensively, based on which an iterative receiver consisting of three modules is derived: element-wise line spectrum estimation (ELSE), distance parameter estimation (DPE), and near-field localization (NFL). In particular, the ELSE module handles the line spectrum relationships among multiple subcarriers in the frequency domain, the DPE module extracts and integrates the distance information from the line spectrum parameters, and the NFL module utilizes the messages of distances for user localization based on near-field spatial characteristics. Our numerical results demonstrate that the proposed SF-ULCR algorithm outperforms existing baselines in terms of channel estimation and localization performance, and that it approaches the Cramèr–Rao bound. Full article

Aiming at tracking sharply maneuvering targets, this paper develops novel variational adaptive state estimators for joint target state and process noise parameter estimation for a class of linear state-space models with abruptly changing parameters. By combining variational inference with change-point detection in an online Bayesian fashion, two adaptive estimators—a change-point-based adaptive Kalman filter (CPAKF) and a change-point-based adaptive Kalman smoother (CPAKS)—are proposed in a recursive detection and estimation process. In each iteration, the run-length probability of the current maneuver mode is first calculated, and then the joint posterior of the target state and process noise parameter conditioned on the run length is approximated by variational inference. Compared with existing variational noise-adaptive Kalman filters, the proposed methods are robust to initial iterative value settings, improving their capability of tracking sharply maneuvering targets. Meanwhile, the change-point detection divides the non-stationary time sequence into several stationary segments, allowing for an adaptive sliding length in the CPAKS method. The tracking performance of the proposed methods is investigated using both synthetic and real-world datasets of maneuvering targets. Full article