Hard Thresholding Method Research Articles

Confidence based compressed sensing approach with QoS differentiation for reliable grant-free access

With the rapid development of 5G technology, numerous intelligent terminals can be successively connected to a network. This brings significant challenges to existing network access because it increases the collision probability. It is essential for Grant-free random access (GF-RA) to ensure low delay and reliable transmission. Due to multiuser interference and varying environments, user detection can be complicated, which leads to unreliable transmission. To address the limitations above, research on the GF-RA method based on compressed sensing is carried out and it includes the following: (1) The confidence-weighted orthogonal matching pursuit method is used for estimating the number of active users and overcomes the constraint of sparse condition. (2) The confidence-weighted simultaneous hard thresholding (SHT) method is used for active user detection (AUD), which can improve the performance of the SHT algorithm. (3) We conduct collision probability analysis to not only provide the performance upper bound using the multiple preambles method but also infer the collision probability relationship with different priorities. This is helpful to realize diverse quality of service requirements. The numerical results prove that the proposed method is valid for non sparse signals and can realize a high success access rate.

Results of an Artificial Intelligence-Based Image Review System to Detect Patient Misalignment Errors in a Multi-institutional Database of Cone Beam Computed Tomography-Guided Radiation Therapy

PurposePresent knowledge of patient setup and alignment errors in image-guided radiotherapy (IGRT) relies on voluntary reporting, which is thought to underestimate error frequencies. A manual retrospective patient-setup misalignment error search is infeasible due to the bulk of cases to be reviewed. We applied a deep learning-based misalignment error detection algorithm (EDA) to perform a fully-automated retrospective error search of clinical IGRT databases and determine an absolute gross patient misalignment error rate. MethodsThe EDA was developed to analyze the registration between planning scans and pre-treatment CBCT scans, outputting a misalignment score ranging from 0 (most unlikely) to 1 (most likely). The algorithm was trained using simulated translational errors on a dataset obtained from 680 patients treated at two radiotherapy clinics between 2017 and 2022. A receiver operating characteristic analysis was performed to obtain target thresholds. A DICOM Query and Retrieval software was integrated with the EDA to interact with the clinical database and fully automate data retrieval and analysis during a retrospective error search from 2016-2017 and 2021-2022 for the two institutions, respectively. Registrations were flagged for human review using both a hard-thresholding method and a prediction trending analysis over each individual patient's treatment course. Flagged registrations were manually reviewed and categorized as errors (>1cm misalignment at the target) or non-errors. ResultsA total of 17,612 registrations were analyzed by the EDA, resulting in 7.7% flagged events. Three previously reported errors were successfully flagged by the EDA and four previously-unreported vertebral body misalignment errors were discovered during case reviews. False positive cases often displayed substantial image artifacts, patient rotation, and soft-tissue anatomy changes. ConclusionOur results validated the clinical utility of the EDA for bulk image reviews, and highlighted the reliability and safety of IGRT, with an absolute gross patient misalignment error rate of 0.04% ± 0.02% per delivered fraction.

Cardinality-Constrained Multi-objective Optimization: Novel Optimality Conditions and Algorithms

In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective optimization, we define the concept of L-stationarity and we analyze its relationships with other existing conditions and Pareto optimality concepts. We then propose two novel algorithmic approaches: the first one is an iterative hard thresholding method aiming to find a single L-stationary solution, while the second one is a two-stage algorithm designed to construct an approximation of the whole Pareto front. Both methods are characterized by theoretical properties of convergence to points satisfying necessary conditions for Pareto optimality. Moreover, we report numerical results establishing the practical effectiveness of the proposed methodologies.

Compressive Perception Image Reconstruction Technology for Basic Mixed Sparse Basis in Metal Surface Detection

<p>Applying Compressed Sensing (CS) technology to robot vision image transmission, an effective method for image reconstruction in robot imaging is proposed to improve the accuracy of reconstruction. Reconstructing images using a mixed sparse representation of DCT and circularly symmetric contour wave transform, the basic algorithm used is the Smoothed Projection Landweber (SPL) algorithm, which optimizes the coefficients under different sparse transformations by incorporating hard thresholding and binary thresholding methods for different sparse bases during iterations. The experiment shows that compared with single sparse base image reconstruction, the proposed reconstruction method has improved reconstruction accuracy.</p> <p> </p>

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.

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.

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.

The application of iterative hard threshold algorithm based on nonlinear optimal compression sensing and electronic information technology in the field of automatic control

Abstract To improve the accuracy effect of the iterative hard threshold, an improved iterative hard threshold (IHT) method is proposed. The specific contents of this method include the principle of an IHT algorithm based on compression sensing (nonlinear optimization), weighted least squares improvement, the establishment of an IHT algorithm model based on weighted least squares improvement, and the experimental research of traditional algorithms and improved algorithms on one-dimensional signal reconstruction. The results show that the improved IRLSIHT algorithm takes 8.37, 29.63, and 30.86 s when the sampling rate is 0.2, 0.5, and 0.8, respectively, and the signal-to-noise ratio is 20.11, 27.47, and 31.82 dB, respectively. Compared with the traditional IHT algorithm, it takes a long time, which is a deficiency, but the signal-to-noise ratio is the largest, and the improved algorithm improves the accuracy. It has been proven that combining the method proposed in this article with automatic control can significantly save time and increase industrial output.

Evaluation of threshold selection methods for adaptive wavelet quantile density estimation in the presence of bias

In this paper, the estimation of the quantile density function based on i.i.d biased observations is investigated. The bias function is assumed to be positive and bounded. Of the various smoothing methods for selecting the model parameters, hard and block thresholding methods are proposed and two adaptive estimators based on them are constructed. We evaluate these theoretical performances via the minimax approach over Besov balls. We show that these estimators obtain near-optimal and optimal convergence rates under some mild assumptions. Finally, with a simulation study and application on a real set of data, the performance quality of these estimators will be compared to other wavelet methods.

Hybrid Threshold Denoising Framework Using Singular Value Decomposition for Side-Channel Analysis Preprocessing.

The traces used in side-channel analysis are essential to breaking the key of encryption and the signal quality greatly affects the correct rate of key guessing. Therefore, the preprocessing of side-channel traces plays an important role in side-channel analysis. The process of side-channel leakage signal acquisition is usually affected by internal circuit noise, external environmental noise, and other factors, so the collected signal is often mixed with strong noise. In order to extract the feature information of side-channel signals from very low signal-to-noise ratio traces, a hybrid threshold denoising framework using singular value decomposition is proposed for side-channel analysis preprocessing. This framework is based on singular value decomposition and introduces low-rank matrix approximation theory to improve the rank selection methods of singular value decomposition. This paper combines the hard threshold method of truncated singular value decomposition with the soft threshold method of singular value shrinkage damping and proposes a hybrid threshold denoising framework using singular value decomposition for the data preprocessing step of side-channel analysis as a general preprocessing method for non-profiled side-channel analysis. The data used in the experimental evaluation are from the raw traces of the public database of DPA contest V2 and AES_HD. The success rate curve of non-profiled side-channel analysis further confirms the effectiveness of the proposed framework. Moreover, the signal-to-noise ratio of traces is significantly improved after preprocessing, and the correlation with the correct key is also significantly enhanced. Experimental results on DPA v2 and AES_HD show that the proposed noise reduction framework can be effectively applied to the side-channel analysis preprocessing step, and can successfully improve the signal-to-noise ratio of the traces and the attack efficiency.

Robust and efficient subsampling algorithms for massive data logistic regression

Datasets that are big with regard to their volume, variety and velocity are becoming increasingly common. However, limitations in computer processing can often restrict analysis performed on them. Nonuniform subsampling methods are effective in reducing computational loads for massive data. However, the variance of the estimator of nonuniform subsampling methods becomes large when the subsampling probabilities are highly heterogenous. To this end, we develop two new algorithms to improve the estimation method for massive data logistic regression based on a chosen hard threshold value and combining subsamples, respectively. The basic idea of the hard threshold method is to carefully select a threshold value and then replace subsampling probabilities lower than the threshold value with the chosen value itself. The main idea behind the combining subsamples method is to better exploit information in the data without hitting the computation bottleneck by generating many subsamples and then combining estimates constructed from the subsamples. The combining subsamples method obtains the standard error of the parameter estimator without estimating the sandwich matrix, which provides convenience for statistical inference in massive data, and can significantly improve the estimation efficiency. Asymptotic properties of the resultant estimators are established. Simulations and analysis of real data are conducted to assess and showcase the practical performance of the proposed methods.

Fuzzy line enhancement scheme of computer art image based on DRL algorithm

In this study, a new blurred line enhancement scheme of computer art image based on Deep Reinforcement Learning (DRL) algorithm was proposed. The hard threshold method is adopted to remove the noise of computer art images and the blurred lines are extracted by texture separation method. Based on the line extraction results, the Deep Q-Network (DQN) model was built with DRL algorithm, and the sample images were input into the model, and the fuzzy line enhancement results of computer art images were obtained in the output layer. The proposed method exhibits excellent noise reduction effect, and the fuzzy line enhancement quality of computer art image is good. The average enhancement time is 0.58 s, and the practical application effect is good.

OutSingle: a novel method of detecting and injecting outliers in RNA-Seq count data using the optimal hard threshold for singular values.

Finding outliers in RNA-sequencing (RNA-Seq) gene expression (GE) can help in identifying genes that are aberrant and cause Mendelian disorders. Recently developed models for this task rely on modeling RNA-Seq GE data using the negative binomial distribution (NBD). However, some of those models either rely on procedures for inferring NBD's parameters in a nonbiased way that are computationally demanding and thus make confounder control challenging, while others rely on less computationally demanding but biased procedures and convoluted confounder control approaches that hinder interpretability. In this article, we present OutSingle (Outlier detection using Singular Value Decomposition), an almost instantaneous way of detecting outliers in RNA-Seq GE data. It uses a simple log-normal approach for count modeling. For confounder control, it uses the recently discovered optimal hard threshold (OHT) method for noise detection, which itself is based on singular value decomposition (SVD). Due to its SVD/OHT utilization, OutSingle's model is straightforward to understand and interpret. We then show that our novel method, when used on RNA-Seq GE data with real biological outliers masked by confounders, outcompetes the previous state-of-the-art model based on an ad hoc denoising autoencoder. Additionally, OutSingle can be used to inject artificial outliers masked by confounders, which is difficult to achieve with previous approaches. We describe a way of using OutSingle for outlier injection and proceed to show how OutSingle outperforms its competition on 16 out of 18 datasets that were generated from three real datasets using OutSingle's injection procedure with different outlier types and magnitudes. Our methods are applicable to other types of similar problems involving finding outliers in matrices under the presence of confounders. The code for OutSingle is available at https://github.com/esalkovic/outsingle.

Uji Kinerja Sistem Denoising Sinyal Jantung atau EKG dengan Menggunakan Algoritma Empirical Mode Decomposition (EMD)

Electrocardiograms (EKGs) are signals created by the electrical activity of the heart muscle and displayed on the EKG device's monitor. Using the EKG recording, the primary characteristics for diagnosing the status of the human heart can be determined. The death rate of heart patients can be reduced through early identification of cardiac problems. In ECG readings, it is frequently affected by several disruptions caused by muscle contractions and electrode movement. Numerous investigations on ECG signal denoising techniques have been undertaken earlier. This article examines the testing of the performance of EKGs using the denoising technique based on the Empirical Mode Decomposition (EMD) algorithm. In this work, many metrics were utilized to evaluate the ECG signal denoising technique: mean square error (MSE), mean absolute error (MAE), and signal-to-noise ratio (SNR). In this investigation, the ECG data was contaminated with noise from muscle artifacts (MA), additive Gaussian white noise (AWGN), electrode movement (EM), and baseline wander (BW). The noise-contaminated ECG signal is subsequently subjected to the denoising process. Calculate the MSE, MAE, and SNR values of the signal after it has been denoised. This study includes a scenario for testing three thresholding techniques with four distinct types of noise. The performance of the hard thresholding method is superior for all types of noise. MSE is produced by AWGN, which is 0.15, 0.28, and 9.9 dB. MA noise generates MSE, MAE, and SNR values of 0.4, 0.033, and 41.0 dB, respectively. The EM noise has an MSE of 0.010, an MAE of 0.04, and an SNR of 30.8 dB. The MSE produced by BW noise is 0.008; the MAE and SNR values were 0.0356 and 28.5, respectively.

Matrix Completion via Successive Low-rank Matrix Approximation

In this paper, a successive low-rank matrix approximation algorithm is presented for the matrix completion (MC) based on hard thresholding method, which approximate the optimal low-rank matrix from rank-one matrix step by step. The algorithm enables the distance between the matrix with the observed elements and the projection on low-rank manifold to be minimum. The optimal low-rank matrix with observed elements is obtained when the distance is zero. In theory, convergence and convergent error of the new algorithm are analyzed in detail. Furthermore, some numerical experiments show that the algorithm is more effective in CPU time and precision than the orthogonal rank-one matrix pursuit(OR1MP) algorithm and the augmented Lagrange multiplier (ALM) method when the sampling rate is low.

RobustIV and controlfunctionIV: Causal Inference for Linear and Nonlinear Models with Invalid Instrumental Variables

Abstract: We present R software packages RobustIV and controlfunctionIV for causal inference with possibly invalid instrumental variables. RobustIV focuses on the linear outcome model. It implements the two-stage hard thresholding method to select valid instrumental variables from a set of candidate instrumental variables and make inferences for the causal effect in both low- and high-dimensional settings. Furthermore, RobustIV implements the high-dimensional endogeneity test and the searching and sampling method, a uniformly valid inference method robust to errors in instrumental variable selection. controlfunctionIV considers the nonlinear outcome model and makes inferences about the causal effect based on the control function method. Our packages are demonstrated using two publicly available economic data sets together with applications to the Framingham Heart Study.

Adaptive iterative hard thresholding for low-rank matrix recovery and rank-one measurements

In low-rank matrix recovery, many kinds of measurements fail to meet the standard restricted isometry property (RIP), such as rank-one measurements, that is, [A(X)]i=〈Ai,X〉 with rank(Ai)=1, i=1,...,m. Historical iterative hard thresholding sequence for low-rank matrix recovery and rank-one measurements was taken as Xn+1=Ps(Xn−μnPt(A⁎sign(A(Xn)−y))), which introduced the “tail” and “head” approximations Ps and Pt, respectively. In this paper, we remove the term Pt and provide a new iterative hard thresholding algorithm with adaptive step size (abbreviated as AIHT). The linear convergence analysis and stability results on AIHT are established under the ℓ1/ℓ2-RIP. Particularly, we discuss the rank-one Gaussian measurements under the tight upper and lower bounds on E‖A(X)‖1, and provide better convergence rate and sampling complexity. Besides, several empirical experiments are provided to show that AIHT performs better than the historical rank-one iterative hard thresholding method.

An adaptive noise removal method for EEG signals

EEG signals are the response to the electrophysiological activity of brain nerve cells in the cerebral cortex, but the collected EEG signal generally contains noise. In order to effectively remove the noise and retain useful information, after research and analysis, this paper proposes an improved EEG noise-removing algorithm based on the threshold method where wavelet contraction is used. The improved adaptive threshold selection algorithm makes it possible that the threshold changes with the number of layers of decomposed signal, so it can be applied flexibly in practice. The wavelet transform is used to decompose the EEG signal into multiple layers of high- and low-frequency coefficients. Adaptive threshold processing is then applied to the wavelet coefficients in accordance with the various decomposition levels, and the scaled wavelet coefficients are then reconstituted to produce the denoised EEG signal. Using the Root Mean Square Error (RMSE) and Signal Noise Ratio (SNR) as quantitative measures of the denoising effect Through trials, the improved threshold method, hard and soft threshold method, and adaptive threshold method were contrasted. The experimental findings demonstrate that the wavelet shrinkage-based improved threshold approach has a better denoising effect than the other three threshold methods.

Efficient Gradient Support Pursuit With Less Hard Thresholding for Cardinality-Constrained Learning.

Recently, stochastic hard thresholding (HT) optimization methods [e.g., stochastic variance reduced gradient hard thresholding (SVRGHT)] are becoming more attractive for solving large-scale sparsity/rank-constrained problems. However, they have much higher HT oracle complexities, especially for high-dimensional data or large-scale matrices. To address this issue and inspired by the well-known Gradient Support Pursuit (GraSP) method, this article proposes a new Relaxed Gradient Support Pursuit (RGraSP) framework. Unlike GraSP, RGraSP only requires to yield an approximation solution at each iteration. Based on the property of RGraSP, we also present an efficient stochastic variance reduction-gradient support pursuit algorithm and its fast version (called stochastic variance reduced gradient support pursuit (SVRGSP+). We prove that the gradient oracle complexity of both our algorithms is two times less than that of SVRGHT. In particular, their HT complexity is about κ∧s times less than that of SVRGHT, where κ∧s is the restricted condition number. Moreover, we prove that our algorithms enjoy fast linear convergence to an approximately global optimum, and also present an asynchronous parallel variant to deal with very high-dimensional and sparse data. Experimental results on both synthetic and real-world datasets show that our algorithms yield superior results than the state-of-the-art gradient HT methods.

A Weak SNR Signal Extraction Method for Near-Bit Attitude Parameters Based on DWT

In practice, the near-bit signals are usually accompanied by noises generated by drilling tool vibration and high-speed rotary. This study introduces discrete wavelet transform to a well drilling area and presents a new weal signal extraction algorithm, which can eliminate the vibration and rotary noises effectively and obtain the useful gravity attitude signals based on the discrete wavelet transform through a hard threshold method. The effectiveness and usefulness of our method are verified via Matlab simulation and actual drilling data.