Hard Thresholding Research Articles

Developing analytical models for the post‐detection SINR of TSVD‐based techniques with imperfect CSI

SummaryIn massive multiple input multiple output (m‐MIMO) uplink, the performance gap between zero forcing (ZF) or direct pseudo‐inverse and minimum mean square error (MMSE) detection schemes increases with an increase in the load factor. To report this issue, truncated singular value decomposition (TSVD) is used in both ZF and direct pseudo‐inverse detection techniques using dynamic threshold. Moreover, the analytical models for the post‐detection signal‐to‐interference‐plus‐noise ratio (PDSINR) of TSVD‐based detection schemes are derived with imperfect channel state information (CSI), and subsequently, bit error rate (BER) is evaluated. Later, an optimum hard threshold for the TSVD‐based detection schemes is deduced from the empirical analysis. Further, the tightness of the analysis is verified through Monte Carlo trails. The simulation result shows that at lower values of average signal‐to‐noise ratio (SNR), TSVD‐based detection schemes with imperfect CSI offer comparable performance and low complexity when compared with the MMSE technique. However, the BER of TSVD‐based detection schemes decreases and gets saturated with an increase in the average SNR, whereas the BER of the MMSE detection scheme increases and approaches the BER of ZF or direct pseudo‐inverse detection schemes.

Decision analysis framework for predicting no-shows to appointments using machine learning algorithms

BackgroundNo-show to medical appointments has significant adverse effects on healthcare systems and their clients. Using machine learning to predict no-shows allows managers to implement strategies such as overbooking and reminders targeting patients most likely to miss appointments, optimizing the use of resources.MethodsIn this study, we proposed a detailed analytical framework for predicting no-shows while addressing imbalanced datasets. The framework includes a novel use of z-fold cross-validation performed twice during the modeling process to improve model robustness and generalization. We also introduce Symbolic Regression (SR) as a classification algorithm and Instance Hardness Threshold (IHT) as a resampling technique and compared their performance with that of other classification algorithms, such as K-Nearest Neighbors (KNN) and Support Vector Machine (SVM), and resampling techniques, such as Random under Sampling (RUS), Synthetic Minority Oversampling Technique (SMOTE) and NearMiss-1. We validated the framework using two attendance datasets from Brazilian hospitals with no-show rates of 6.65% and 19.03%.ResultsFrom the academic perspective, our study is the first to propose using SR and IHT to predict the no-show of patients. Our findings indicate that SR and IHT presented superior performances compared to other techniques, particularly IHT, which excelled when combined with all classification algorithms and led to low variability in performance metrics results. Our results also outperformed sensitivity outcomes reported in the literature, with values above 0.94 for both datasets.ConclusionThis is the first study to use SR and IHT methods to predict patient no-shows and the first to propose performing z-fold cross-validation twice. Our study highlights the importance of avoiding relying on few validation runs for imbalanced datasets as it may lead to biased results and inadequate analysis of the generalization and stability of the models obtained during the training stage.

Hard threshold acceleration algorithms for sparse signal recovery

Hard threshold acceleration algorithms for sparse signal recovery

Partial discharge de-noising based on hybrid particle swarm optimization SWT adaptive threshold

A hybrid particle swarm optimization stationary wavelet adaptive threshold denoising (HPO-SWT-ATD) method was proposed to improve the adaptive ability of wavelet transform in partial discharge signal denoising. In the proposed method, the partial discharge signal is decomposed by stationary wavelet transform(SWT) and the multiorder differentiable function based on the Stein unbiased likelihood estimate (SURE) is used as the denoising threshold function. In threshold selection, the improved particle swarm optimization algorithm is used for global adaptive search to select the optimal denoising threshold. The de-noising experiments are carried out on the simulated partial discharge signals and the measured partial discharge signals.The experiment results show that, compared with the hard threshold method, particle swarm optimization threshold method, genetic algorithm optimization threshold method, Wiener filter method and modal decomposition method, the proposed method can better remove the white noise in the PD signal, and the denoising signal distortion degree is smaller.

Discrete wavelet transform based processing of embroidered textile-electrode electromyography signal acquired with load and pressure effect

The diagnosis of neuromuscular diseases is complicated by overlapping symptoms from other conditions. Textile-based surface electromyography (sEMG) of skeletal muscles, offer promising potential in diagnosis, treatment, and rehabilitation of various neuromuscular disorders. However, it is important to consider the impact of load and pressure on EMG signals, as this can significantly affect the signal’s accuracy. This study seeks to investigate the influence of load and pressure on EMG signals and establish a processing framework for these signals in the diagnosis of neuromuscular diseases. The sEMG data were collected from healthy subjects using a textile electrode developed from polyester multi-filament conductive hybrid thread (CleverTex). The textrode was embroidered directly on an elastic bandage (Velcro® strap) placed on volunteer’s muscles while different activities were performed with varying loads and pressure. The collected data were pre-processed using standard techniques of the discrete wavelet transform to remove noise and artifacts. The performance of the proposed denoising algorithm was evaluated using the signal-to-noise ratio (SNR), percentage root mean square difference (PRD), and root mean square error (RMSE). Various signal processing approaches (filters) were considered and the results were compared with the proposed EMG noise reduction algorithms. Based on the experimental results, the fourth level of decomposition for the sym5 wavelets with the Rigrsure threshold method achieved the highest signal-to-noise ratio (SNR) values of 16.69 and 21.91, for soft and hard thresholding functions, respectively. The SNR values of 22.11, 21.54, and 2.78 at three different pressure levels 5 mmHg, 10 mmHg, and 20 mmHg, respectively, indicate the superior performance of wavelet multiresolution filter in de-noising applications. The results of this study suggest that our methodology is effective, precise, and reliable for analysing sEMG data and provide insights into both physiological and pathological neuromuscular conditions.

Iterative singular tube hard thresholding algorithms for tensor recovery

Iterative singular tube hard thresholding algorithms for tensor recovery

Maintenance optimization of multi-unit balanced systems using deep reinforcement learning

Balanced systems are extensively utilized in various engineering fields. However, the study of maintenance optimization for balanced systems under dependent competing risks is very limited, and the existing method for orthodox multi-unit systems cannot solve the maintenance problem of balanced systems. Thus, we present a novel maintenance optimization method for systems with multiple balanced units. The units in the system are assumed to experience multiple failure processes due to continuous degradation and external shock damage. The system failure occurs in the following situations: (1) the deterioration levels of units on the symmetric positions exceed critical thresholds. (2) the deterioration level of any unit reaches the failure threshold. (3) the shock magnitude is greater than the hard failure threshold. By employing a customized deep reinforcement learning algorithm, we derive the optimal maintenance policy under a fixed planning horizon. Notably, our approach differs from previous research on maintenance optimization for balanced systems, the proposed method avoids the discretizing of the deterioration state. This significantly enhances computational efficiency, particularly when applied to multi-unit balanced systems. Numerous numerical studies illustrate the effectiveness of our proposed maintenance optimization method for multi-unit balanced systems.

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.

Reliability Analysis and Preventive Maintenance Strategy for Competitive Failure Process of Wind Turbine Blade with Hard Failure-Caused Threshold Variation

During the operation of wind turbines, various failure forms are often caused by the interaction of their own performance degradation and external shocks due to the complexity of the operating environment and the form of the load. Whereas these failures are not obvious, improvement of life cycle and reduction of maintenance cost can be realized by identifying potential failures using a sound maintenance strategy and inspecting each system. In this study, we further extend the applicability of the competitive failure model by considering the existence of multiple shock types in the degradation process based on the competitive failure model of threshold variation caused by hard failure. We discuss two different cases of varying failure thresholds due to the multiple shock types. In case 1, cumulative degradation causes the system to fail at less than a predetermined failure threshold and with the presence of multiple shock types. In case 2, the cumulative degradation of the system reaches a predetermined failure threshold but is less than or equal to the set maximum failure threshold under multiple shock types. Finally, the validation is performed by two special cases. A status maintenance model based on preventive maintenance state thresholds is investigated to ensure that the system works properly under different degradation stages and to obtain the optimal preventive replacement threshold based on minimizing the desired cost rate. At last, the feasibility of the method was verified by reliability assessment and sensitivity analysis of wind turbine blade.

Neutron image denoising method based on adaptive new wavelet threshold function

Neutron radiography is an important nondestructive testing technique in the industrial field. Due to the influence of various factors in the neutron imaging process, the image quality will be reduced. Aiming at the Gaussian-Poisson mixed noise in neutron images, an adaptive new wavelet threshold function denoising method is proposed to reduce the influence of noise on neutron images. The basic idea is to transform the Gaussian-Poisson mixed noise into a noise that approximately follows the Gaussian distribution by generalized Anscombe transformation, and then use Particle Swarm Optimization (PSO) algorithm and wavelet threshold function denoising method to remove the mixed noise in the image. The new wavelet threshold function overcomes the problems of discontinuity in the traditional hard threshold function and fixed deviation in the wavelet coefficient of the traditional soft threshold function, and has the adjustment factor, which can combine the advantages of the traditional soft and hard threshold functions. PSO algorithm is used to find the optimal adjustment factor for image denoising. In addition, the new wavelet threshold function is continuous and smooth at the threshold, avoiding excessive strangulation of wavelet coefficients. By analyzing the fixed threshold defect, a threshold selection formula that decreases with the number of decomposition layers is proposed. The results of Matlab software experiments show that the new method can significantly improve the Peak Signal-to-Noise Ratio (PSNR) and reduce the Mean Square Error (MSE) of noisy images compared with the other four methods in removing Gaussian-Poisson mixed noise. Therefore, the new method can retain more image details and effectively improve the quality of neutron images.

Gravity inversion using L0 norm for sparse constraints

SUMMARY Gravity surveys constitute an important method for investigating the Earth's interior based on density contrasts related to Earth material differentials. Because lithology depends on the environment and the period of formation, there are generally clear boundaries between rocks with different lithologies. Inversions with convex functions for approximating the L0 norm are used to detect boundaries in reconstructed models. Optimizations can easily be found because of the convex transformations; however, the volume of the reconstructed model depends on the weighting parameter and the density constraint rather than the model sparsity. To determine and adapt the modelling size, a novel non-convex framework for gravity inversion is proposed. The proposed optimization aims to directly reduce the L0 norm of the density matrix. An improved iterative hard thresholding algorithm is developed to linearly reduce the L0 penalty during the inner iteration. Accordingly, it is possible to determine the modelling scale during the iteration and achieve an expected scale for the reconstructed model. Both simple and complex model experiments demonstrate that the proposed method efficiently reconstructs models. In addition, granites formed during the Yanshanian and Indosinian periods in the Nanling region, China, are reconstructed according to the modelling size evaluated in agreement with the magnetotelluric profile and density statistics of rock samples. The known ores occur at the contact zones between the sedimentary rocks and the reconstructed Yanshanian granites. The ore-forming bodies, periods, and processes are identified, providing guidance for further deep resource exploration in the study area.

Sparse Diffusion Least Mean-Square Algorithm with Hard Thresholding over Networks

This paper proposes a distributed estimation technique utilizing the diffusion least mean-square (LMS) algorithm, specifically designed for sparse systems in which many coefficients of the system are zeros. To efficiently utilize the sparse representation of the system and achieve a promising performance, we have incorporated L0-norm regularization into the diffusion LMS algorithm. This integration is accomplished by employing hard thresholding through a variable splitting method into the update equation. The efficacy of our approach is validated by comprehensive theoretical analysis, rigorously examining the mean stability as well as the transient and steady-state behaviors of the proposed algorithm. The proposed algorithm preserves the behavior of large coefficients and strongly enforces smaller coefficients toward zero through the relaxation of L0-norm regularization. Experimental results show that the proposed algorithm achieves superior convergence performance compared with conventional sparse algorithms.

An adaptive data compression technique based on optimal thresholding using multi-objective PSO algorithm for power system data

The widespread development of monitoring devices in power system has indeed led to the generation of large amounts of power consumption data. Storing and transmitting this enormous volume of data has become a significant challenge for power system operators and researchers. Although high data rates are available for transmission, data compression is still necessary for power system applications to lessen the load of data transmission and storage. The wavelet transform plays an important role in data compression for power system applications. This paper presents an adaptive data compression algorithm based on the discrete wavelet transform (DWT) for power system applications. In general, some wavelet coefficients are neglected to produce DWT-based data compression by using hard or soft thresholds. But the volume of compressed data differs for various threshold values. In this context, selecting an optimal threshold is a challenging task in power system data compression. This paper proposes a multi-objective particle swarm optimisation (MO-PSO) for optimal threshold selection. The proposed approach is tested using IEEE power quality wave data sets and Dutch Residential Energy Datasets (DRED). The proposed MO-PSO algorithm finds the global optimum threshold, and it outperforms the other existing algorithms. The proposed algorithm efficiently compresses the test dataset with a maximum compression ratio (CR) of 2.07.

Recovery of Sparse Signals via Modified Hard Thresholding Pursuit Algorithms

In this paper, we propose a modified version of the hard thresholding pursuit algorithm, called modified hard thresholding pursuit (MHTP), using a convex combination of the current and previous points. The convergence analysis, finite termination properties, and stability of the MHTP are established under the restricted isometry property of the measurement matrix. Simulations are performed in noiseless and noisy environments using synthetic data, in which the successful frequencies, average runtime, and phase transition of the MHTP are considered. Standard test images are also used to test the reconstruction capability of the MHTP in terms of the peak signal-to-noise ratio. Numerical results indicate that the MHTP is competitive with several mainstream thresholding and greedy algorithms, such as hard thresholding pursuit, compressive sampling matching pursuit, subspace pursuit, generalized orthogonal matching pursuit, and Newton-step-based hard thresholding pursuit, in terms of recovery capability and runtime.

An improved wavelet threshold denoising approach for surface electromyography signal

BackgroundThe surface electromyography (sEMG) signal presents significant challenges for the dynamic analysis and subsequent examination of muscle movements due to its low signal energy, broad frequency distribution, and inherent noise interference. However, the conventional wavelet threshold filtering techniques for sEMG signals are plagued by the Gibbs-like phenomenon and an overall decrease in signal amplitude, leading to signal distortion.PurposeThis article aims to establish an improved wavelet thresholding method that can filter various types of signals, with a particular emphasis on sEMG signals, by adjusting two independent factors. Hence, it generates the filtered signal with a higher signal-to-noise ratio (SNR), a lower mean square error (MSE), and better signal quality.ResultsAfter denoising Doppler and Heavysine signals, the filtered signal exhibits a higher SNR and lower MSE than the signal generated from traditional filtering algorithms. The filtered sEMG signal has a lower noise baseline while retaining the peak sEMG signal strength.ConclusionThe empirical evaluation results show that the quality of the signal processed by the new noise reduction algorithm is better than the traditional hard thresholding, soft thresholding, and Garrote thresholding methods. Moreover, the filtering performance on the sEMG signal is improved significantly, which enhances the accuracy and reliability of subsequent experimental analyses.

Compressed sensing photoacoustic imaging based on the gradient projection Newton pursuit algorithm

Photoacoustic imaging (PAI) is a unique non-invasive biomedical imaging technique that illuminates biological tissue with short-pulsed laser light. This process generates acoustic waves, which in turn enable high-resolution and high-contrast imaging of deep tissue. However, the complexity of PAI imaging data presents challenges in achieving rapid and optimal reconstruction results due to the time and resource demands of traditional Nyquist sampling. On the contrary, compressive sensing (CS) overcomes the limitations of Nyquist sampling by recovering the original signal with a lower amount of sampled data, resulting in significant cost savings in signal transmission and processing. Additionally, CS-based hard-thresholding iterative algorithms possess various advantages in sparse optimization, including sparsity control and fast computation. Moreover, the assumptions of the Gradient Projection Newton Pursuit (GPNP) for CS problems are relatively weaker compared to many state-of-the-art algorithms. Therefore, we investigated the performance of the GPNP algorithm in PAI. We compared our algorithm with improved iterative hard thresholding (IIHT), conjugate gradient iterative hard thresholding (CGIHT), compressive sampling matching pursuit (CoSaMP), SPGL1, SALSA and elastic net algorithms using phantom, Vasculature, and SGERF simulation images. The simulation results demonstrate that the GPNP algorithm achieves excellent image reconstruction performance when evaluating both the quality of reconstruction and the reconstruction time. Taking the simulation results of Vasculature with a noise level of 40 dB and 40 channels as an example, the PNSR index of GPNP has improved by 4.09, 11.03, 12.89, 13.14, 13.15, and 11.75 compared to IIHT, CGIHT, elastic net algorithms, SPGL1, SALSA and CoSaMP, respectively.

Chromatography Denoising with Improved Wavelet Thresholding Based on Modified Genetic Particle Swarm Optimization

The wavelet threshold functions are widely used in oil chromatography denoising because high-quality signals are the basis for Dissolved Gas Analysis (DGA), which determines the accuracy of transformer fault monitoring. However, there are certain limitations of the wavelet threshold functions, such as the Pseudo-Gibbs phenomenon and improper threshold selection. To this purpose, a modified genetic particle swarm optimization-based improved threshold function denoising method (MGPSO-ITF) is proposed. Specifically, the method constructs a new parametric threshold function that possesses high-order derivability and a small constant deviation. To obtain optimal values for the tunable parameters, MGPSO is employed, which outperforms other methods in identifying the optimum and achieving fast convergence. The simulation results demonstrate that the enhanced thresholding function yields a higher Signal-to-Noise Ratio (SNR), higher Noise Suppression Ratio (NSR), and smaller Root Mean Square Error (RMSE) compared to prior methods. Specifically, for the originally relatively smooth signal, MGPSO-ITF does not over-correct it to cause distortion. Furthermore, experiments on measured signals illustrate that the MGPSO-ITF is highly effective at denoising and preserving the original signal properties. Particularly in cases where peak deformation is prominent, the algorithm outperforms both hard and soft thresholding methods, achieving a reduction of 2.934% and 1.029% in peak area error, respectively.

Roughness evaluation of turned composite surfaces by analysis of the shape of autocorrelation function

In this paper, the application of an Autocorrelation Function for the characterisation of surface topography was validated. The roughness evaluation of turned composite surfaces was supported by sophisticated studies of the Autocorrelation Function properties, considering especially the shape of the function. Details were measured with the optical method. The selection of the surface roughness evaluation procedures was carried out based on the Autocorrelation Function for both profile and areal analyses. Moreover, the application of various types of regular analysis methods, proposed in commercial software, like regular Gaussian regression and robust Gaussian functions, median de-noising, regular isotropic Spline, and fast Fourier transform filters, was proposed for the evaluation of surface topography parameters from the ISO 25178 standards. It was found that many common techniques, like commonly used filters, spectral analysis, and characterisation of texture direction, were supported by the proposed Autocorrelation Function studies. Moreover, the hard thresholding technique was found to be valuable in the comprehensive noise-suppression analysis.

Guided block matching and 4-D transform domain filter projection denoising method for dynamic PET image reconstruction

PurposeDynamic PET is an essential tool in oncology due to its ability to visualize and quantify radiotracer uptake, which has the potential to improve imaging quality. However, image noise caused by a low photon count in dynamic PET is more significant than in static PET. This study aims to develop a novel denoising method, namely the Guided Block Matching and 4-D Transform Domain Filter (GBM4D) projection, to enhance dynamic PET image reconstruction.MethodsThe sinogram was first transformed using the Anscombe method, then denoised using a combination of hard thresholding and Wiener filtering. Each denoising step involved guided block matching and grouping, collaborative filtering, and weighted averaging. The guided block matching was performed on accumulated PET sinograms to prevent mismatching due to low photon counts. The performance of the proposed denoising method (GBM4D) was compared to other methods such as wavelet, total variation, non-local means, and BM3D using computer simulations on the Shepp–Logan and digital brain phantoms. The denoising methods were also applied to real patient data for evaluation.ResultsIn all phantom studies, GBM4D outperformed other denoising methods in all time frames based on the structural similarity and peak signal-to-noise ratio. Moreover, GBM4D yielded the lowest root mean square error in the time-activity curve of all tissues and produced the highest image quality when applied to real patient data.ConclusionGBM4D demonstrates excellent denoising and edge-preserving capabilities, as validated through qualitative and quantitative assessments of both temporal and spatial denoising performance.

Bivariate retrieval from intensity of cross-correlation

Pulse characterization in ultra-fast optics presents a powerful motivation to study phase retrieval problems of high order. Frequency- and time-resolved techniques for pulse characterization both construct measurements that depend on the intensity of the cross-correlation between two unknown signals undergoing known modulations. The problem of recovering these signals has been traditionally studied and solved with alternating minimization, but recently Wirtinger gradient techniques were demonstrated to invert frequency-resolved measurements on a symmetric signal pair (Pinilla et al., 2019). In this paper, we construct a generalized Wirtinger gradient and Hessian to solve a wide breadth of problems including signal recovery from time- and frequency-resolved measurements. We further demonstrate that both measurement paradigms are special cases of low-rank phase retrieval but with a special structure that disrupts spectral initializers. To combat this problem, we present a tensor-based iterative hard thresholding initializer that, when paired with a Wirtinger gradient descent, is capable of recovering unknown signals with fewer measurements than matrix-based alternating minimization or spectral initialization methods. Finally, we employ Wirtinger gradient descent to recover signals from real-world DSCAN (Wilhelm et al., 2021) measurements and compare results with the existing state-of-the-art.