Iterative Thresholding Research Articles

Convolutional sparse coding network for sparse seismic time-frequency representation

Seismic time-frequency (TF) transforms are essential tools in reservoir interpretation and signal processing, particularly for characterizing frequency variations in non-stationary seismic data. Recently, sparse TF transforms, which leverage sparse coding (SC), have gained significant attention in the geosciences due to their ability to achieve high TF resolution. However, the iterative approaches typically employed in sparse TF transforms are computationally intensive, making them impractical for real seismic data analysis. To address this issue, we propose an interpretable convolutional sparse coding (CSC) network to achieve high TF resolution. The proposed model is generated based on the traditional short-time Fourier transform (STFT) transform and a modified UNet, named ULISTANet. In this design, we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm (LISTA) blocks, a specialized form of CSC. The LISTA block, which evolves from the traditional iterative shrinkage thresholding algorithm (ISTA), is optimized for extracting sparse features more effectively. Furthermore, we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet. Finally, the proposed method's performance is subsequently validated using both synthetic and field data, demonstrating its potential for enhanced seismic data analysis.

Application of simplifying jacobian matrix and introducing iterative threshold to improve newton-raphson method in three-phase power flow calculation

Abstract With the expansion of the scale and complexity of the power system, traditional three-phase power flow calculation methods are facing dual challenges of computational efficiency and accuracy. Power flow calculation is a mathematical method for analyzing the power flow of an electrical system. And the Newton-Raphson (NR) method is an effective algorithm for solving nonlinear problems. However, updating the Jacobian matrix in the NR method can take a lot of time. Based on the asymmetry in three-phase power systems and the time-consuming nature of the NR method, an enhanced version of the NR method is proposed in this paper that improves the efficiency of power flow calculations by simplifying the Jacobian matrix and optimizing the iteration speed. Furthermore, in order to minimize the number of iterations in the NR method, it is proposed to use the PO method to determine the ideal iteration threshold.

3D Seismic Data Reconstruction based on Weighted Fast Iterative Shrinkage Thresholding algorithm

3D Seismic Data Reconstruction based on Weighted Fast Iterative Shrinkage Thresholding algorithm

Bearing fault diagnosis by sparse frequency spiral spectrum driven NAF-LDM under strong noise and small samples

Abstract The complexity of background noise and the scarcity of real fault samples seriously affect the diagnostic accuracy of the model. To address this, a noise-robust two-dimensional feature map, the sparse frequency spiral spectrum (SFSM), based on sparse representation theory, is proposed. A bridge penalty coefficient is applied to the sparse representation model to accurately select impact components, and the fast iterative shrinkage threshold algorithm is used to solve for sparse representation coefficients. Sparse reconstructed signals are obtained by convolving the impact patterns with these coefficients, leading to a sparse reconstruction algorithm with reduced computational complexity. Furthermore, the novel non-linear activation-free blocks (NAF Blocks) are embedded into the latent diffusion model to augment small samples, significantly improving image generation speed and quality. The integration of the Swin transformer for feature extraction and classification further enhances diagnostic performance. The superiority of this method is validated on the XJTU-SY dataset, a bearing experimental platform dataset, and enterprise engineering dataset. Experimental results demonstrate that the structural and generalization advantages of NAF Blocks are crucial for improving image quality and inference speed. The noise suppression capability of the proposed method, facilitated by the SFSM feature processing technique, is confirmed through ablation and noise robustness tests. Finally, the Swin transformer’s excellent feature extraction and classification capabilities for SFSM are verified. The proposed method achieves diagnostic accuracies of 99.10% and 98.7% on the XJTU-SY and experimental platform datasets, respectively.

Deep Learning-Based Approximated Observation Sparse SAR Imaging via Complex-Valued Convolutional Neural Network

Sparse synthetic aperture radar (SAR) imaging has demonstrated excellent potential in image quality improvement and data compression. However, conventional observation matrix-based methods suffer from high computational overhead, which is hard to use for real data processing. The approximated observation sparse SAR imaging method relieves the computation pressure, but it needs to manually set the parameters to solve the optimization problem. Thus, several deep learning (DL) SAR imaging methods have been used for scene recovery, but many of them employ dual-path networks. To better leverage the complex-valued characteristics of echo data, in this paper, we present a novel complex-valued convolutional neural network (CNN)-based approximated observation sparse SAR imaging method, which is a single-path DL network. Firstly, we present the approximated observation-based model via the chirp-scaling algorithm (CSA). Next, we map the process of the iterative soft thresholding (IST) algorithm into the deep network form, and design the symmetric complex-valued CNN block to achieve the sparse recovery of large-scale scenes. In comparison to matched filtering (MF), the approximated observation sparse imaging method, and the existing DL SAR imaging methods, our complex-valued network model shows excellent performance in image quality improvement especially when the used data are down-sampled.

Adaptive iterative thresholding segmentation method guided by optical prior water body information in extracting urban flood inundation areas of synthetic aperture radar images

Adaptive iterative thresholding segmentation method guided by optical prior water body information in extracting urban flood inundation areas of synthetic aperture radar images

High dynamic range land wavefield reconstruction from randomized acquisition

Compressive sensing (CS) is an alternative to regular Shannon sampling that captures similar information from reduced measurements. It relies on randomized sampling patterns and a sparse data representation to reconstruct the regularly sampled object. CS is an important ingredient in affordable seismic acquisition, which can lead to improvements in the near-surface mapping and noise suppression for land data. However, the near surface traps most of the source-generated energy, resulting in data that are rich in high-wavenumber content and have amplitudes spanning several orders of magnitude. When dealing with such high dynamic range nonstationary data, the Fourier domain is not optimal for providing a sparse representation — a necessary condition for successful application of CS. In contrast, a discrete complex wavelet transform can localize high-energy features, has good directional selectivity, and is near-shift invariant. Combined, these properties allow complex wavelets to represent detail-rich wavefields in a compact form. To leverage these features and achieve good CS reconstructions, we develop a scale- and orientation-dependent iterative soft thresholding (IST) scheme for reconstructing high dynamic range wavefields. Our approach requires little parameterization, is easy to implement, and is robust to reconstructed wavefield sampling grid and dynamic range. We test IST on different wavefields with randomly missing traces and compare the data reconstructions with the spectral projected gradient solver and projection onto convex sets. We quantify the reconstructions by a direct comparison of Fourier coefficients between fully sampled and reconstructed wavefields. Taking log10 of Fourier coefficients prior to computing the quality metric deemphasizes the importance of magnitude match while highlighting Fourier coefficient support accuracy, which usually translates into good structural fidelity of reconstructed data. We find that IST performs consistently among all examples, yielding good phase match while performing gentle denoising.

A Fast iterative shrinkage and threshold algorithm-based least-squares deconvolution technique with application to bearing fault signals

Bearings are commonly subjected to load, transmission, and impact during operation, resulting in bearing failure that ultimately leads to mechanical breakdown. The low energy level of fault-induced impulsive signals, however, renders it vulnerable to being masked by environmental noise and other disturbances present in the vibration signal. To cope with this issue, this paper investigates the application of the finite impulse response (FIR) filter for bearing fault detection. In this work, the estimation of the FIR is formulated as a least squares optimization problem, aiming to minimize the l 2 norm of the FIR and effectively suppress noise and interference sources. The solutions of the least squares optimization problem are obtained using the fast iterative shrinkage–thresholding (FISTA) algorithm. Furthermore, to better select the regularization parameter in our method, an improved gray wolf optimizer (I–GWO) is employed to conduct the parameter selection. Based on these improvements, the proposed FISTA–LSD technique enables rapid and precise detection of fault characteristics upon their occurrence, thereby mitigating the propagation of faults and preventing accidents from happening. Furthermore, with this automated selection process, engineers can save valuable time that would otherwise be spent on trial-and-error approaches. Through its rapid response capabilities and precise fault detection abilities enabled by the FISTA–LSD technique along with I–GWO integration for automatic parameter selection; this FISTA–LSD technique greatly enhances its practical value. The proposed technique is validated through the utilization of both numerical and experimental data.

Sparse recovery using expanders via hard thresholding algorithm

Expanders play an important role in combinatorial compressed sensing. Via expanders measurements, we propose the expander normalized heavy ball hard thresholding algorithm (ENHB-HT) based on expander iterative hard thresholding (E-IHT) algorithm. We provide convergence analysis of ENHB-HT, and it turns out that ENHB-HT can recover an s-sparse signal if the measurement matrix A∈{0,1}m×n satisfies some mild conditions. Numerical experiments are simulated to support our two main theorems which describe the convergence rate and the accuracy of the proposed algorithm. Simulations are also performed to compare the performance of ENHB-HT and several existing algorithms under different types of noise, the empirical results demonstrate that our algorithm outperform a few existing ones in the presence of outliers.

Off-Grid Underwater Acoustic Source Direction-of-Arrival Estimation Method Based on Iterative Empirical Mode Decomposition Interval Threshold.

To solve the problem that the hydrophone arrays are disturbed by ocean noise when collecting signals in shallow seas, resulting in reduced accuracy and resolution of target orientation estimation, a direction-of-arrival (DOA) estimation algorithm based on iterative EMD interval thresholding (EMD-IIT) and off-grid sparse Bayesian learning is proposed. Firstly, the noisy signal acquired by the hydrophone array is denoised by the EMD-IIT algorithm. Secondly, the singular value decomposition is performed on the denoised signal, and then an off-grid sparse reconstruction model is established. Finally, the maximum a posteriori probability of the target signal is obtained by the Bayesian learning algorithm, and the DOA estimate of the target is derived to achieve the orientation estimation of the target. Simulation analysis and sea trial data results show that the algorithm achieves a resolution probability of 100% at an azimuthal separation of 8° between adjacent signal sources. At a low signal-to-noise ratio of -9 dB, the resolution probability reaches 100%. Compared with the conventional MUSIC-like and OGSBI-SVD algorithms, this algorithm can effectively eliminate noise interference and provides better performance in terms of localization accuracy, algorithm runtime, and algorithm robustness.

Construction of uniform designs for high-dimensional screening via an adjusted multiple quadrupling algorithm

One of the most common strategies to achieve optimum designs for physical and computer high-dimensional experiments with no model pre-specification and limited budget is to uniformly spread the design points over the experimental domain, which are called uniform designs. A uniform design provides good design space coverage (space-filling), resulting in more accurate estimates using fewer points. Algorithmic search is commonly used for finding such designs, but this approach becomes ineffective for large problems. Though the construction of uniform designs theoretically is challenging, intriguing and encouraging findings have recently been accomplished for highly specialized cases. This paper gives a new theoretical construction method for high-dimensional experiments with a mixture of four-level and sixteen-level factors via an adjusted version of the multiple quadrupling algorithm (Elsawah, Communication in Mathematics and Statistics 10:623-652, 2022). The new technique (called AMQA) is simple to use since it only needs small suitable four-level designs, which may be easily generated theoretically or by algorithmic search. The quality of the small designs ensures the quality of the large designs. The effectiveness of the AMQA is investigated both theoretically and computationally. The main findings demonstrate that, compared with other widely used techniques, the AMQA provides more accurate results for high-dimensional screening using a variety of models, including polynomial, spline, and kriging models, as well as variable selection techniques, including AIC, BIC, RIC, SCAD, and LASSO. To further improve performance, a hybrid algorithm that combines the AMQA with the iterative threshold accepting algorithm is proposed.

PET radiomics-based lymphovascular invasion prediction in lung cancer using multiple segmentation and multi-machine learning algorithms.

The current study aimed to predict lymphovascular invasion (LVI) using multiple machine learning algorithms and multi-segmentation positron emission tomography (PET) radiomics in non-small cell lung cancer (NSCLC) patients, offering new avenues for personalized treatment strategies and improving patient outcomes. One hundred and twenty-six patients with NSCLC were enrolled in this study. Various automated and semi-automated PET image segmentation methods were applied, including Local Active Contour (LAC), Fuzzy-C-mean (FCM), K-means (KM), Watershed, Region Growing (RG), and Iterative thresholding (IT) with different percentages of the threshold. One hundred five radiomic features were extracted from each region of interest (ROI). Multiple feature selection methods, including Minimum Redundancy Maximum Relevance (MRMR), Recursive Feature Elimination (RFE), and Boruta, and multiple classifiers, including Multilayer Perceptron (MLP), Logistic Regression (LR), XGBoost (XGB), Naive Bayes (NB), and Random Forest (RF), were employed. Synthetic Minority Oversampling Technique (SMOTE) was also used to determine if it boosts the area under the ROC curve (AUC), accuracy (ACC), sensitivity (SEN), and specificity (SPE). Our results indicated that the combination of SMOTE, IT (with 45% threshold), RFE feature selection and LR classifier showed the best performance (AUC = 0.93, ACC = 0.84, SEN = 0.85, SPE = 0.84) followed by SMOTE, FCM segmentation, MRMR feature selection, and LR classifier (AUC = 0.92, ACC = 0.87, SEN = 1, SPE = 0.84). The highest ACC belonged to the IT segmentation (with 45 and 50% thresholds) alongside Boruta feature selection and the NB classifier without SMOTE (ACC = 0.9, AUC = 0.78 and 0.76, SEN = 0.7, and SPE = 0.94, respectively). Our results indicate that selection of appropriate segmentation method and machine learning algorithm may be helpful in successful prediction of LVI in patients with NSCLC with high accuracy using PET radiomics analysis.

Reduction Accelerated Adaptive Step‐Size FISTA Based Smooth‐Lasso Regularization for Fluorescence Molecular Tomography Reconstruction

ABSTRACTIn this paper, a reduced accelerated adaptive fast iterative shrinkage threshold algorithm based on Smooth‐Lasso regularization (SL‐RAFISTA‐BB) is proposed for fluorescence molecular tomography (FMT) 3D reconstruction. This method uses the Smooth‐Lasso regularization to fuse the group sparse prior information which can balance the relationship between the sparsity and smoothness of the solution, simplifying the process of calculation. In particular, the convergence speed of the FISTA is improved by introducing a reduction strategy and Barzilai‐Borwein variable step size factor, and constructing a continuation strategy to reduce computing costs and the number of iterations. The experimental results show that the proposed algorithm not only accelerates the convergence speed of the iterative algorithm, but also improves the positioning accuracy of the tumor target, alleviates the over‐sparse or over‐smooth phenomenon of the reconstructed target, and clearly outlines the boundary information of the tumor target. We hope that this method can promote the development of optical molecular tomography.

Noise Reduction Using Sparsity Constrained and Regularized Iterative Thresholding Algorithm and Dictionary

Dictionary-based methods are recognized for their ability to estimate clear speech from speech contaminated with noise. However, these techniques face a limitation in distinguishing between speech and noise components. The presented algorithm addresses this challenge by introducing an innovative solution through an iterative thresholding method. In this method, the thresholding is based on noise characteristics and remains independent of variations in noise power. To determine the stopping criteria for thresholding, the algorithm leverages the structure of the speech signal in time–frequency domains using the Gini Index. Remarkably, this technique adeptly extracts reliable signal components from a noisy time–frequency magnitude spectrum, performing well under non-varying and varying Signal-to-Noise Ratio (SNR) conditions. Importantly, it achieves this without the need for mask functions, voice activity detection techniques, noise or mixture dictionaries, or SNR information, which are essential components in other dictionary-based methods. Following the thresholding process, the clean speech is assessed using a dictionary-based approach to restore perceptual loss. In evaluating its performance, the algorithm is compared with traditional enhancement techniques concerning perceptual evaluation of speech quality and short-time objective intelligibility. The assessment is conducted under various background noise conditions, including babble, white, factory, and Volvo noises. The proposed algorithm exhibits superior performance, particularly in low and varying SNR scenarios.

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

In the construction process of radial basis function (RBF) networks, two common crucial issues arise: the selection of RBF centers and the effective utilization of the given source without encountering the overfitting problem. Another important issue is the fault tolerant capability. That is, when noise or faults exist in a trained network, it is crucial that the network’s performance does not undergo significant deterioration or decrease. However, without employing a fault tolerant procedure, a trained RBF network may exhibit significantly poor performance. Unfortunately, most existing algorithms are unable to simultaneously address all of the aforementioned issues. This paper proposes fault tolerant training algorithms that can simultaneously select RBF nodes and train RBF output weights. Additionally, our algorithms can directly control the number of RBF nodes in an explicit manner, eliminating the need for a time-consuming procedure to tune the regularization parameter and achieve the target RBF network size. Based on simulation results, our algorithms demonstrate improved test set performance when more RBF nodes are used, effectively utilizing the given source without encountering the overfitting problem. This paper first defines a fault tolerant objective function, which includes a term to suppress the effects of weight faults and weight noise. This term also prevents the issue of overfitting, resulting in better test set performance when more RBF nodes are utilized. With the defined objective function, the training process is designed to solve a generalized M-sparse problem by incorporating an ℓ0-norm constraint. The ℓ0-norm constraint allows us to directly and explicitly control the number of RBF nodes. To address the generalized M-sparse problem, we introduce the noise-resistant iterative hard thresholding (NR-IHT) algorithm. The convergence properties of the NR-IHT algorithm are subsequently discussed theoretically. To further enhance performance, we incorporate the momentum concept into the NR-IHT algorithm, referring to the modified version as “NR-IHT-Mom”. Simulation results show that both the NR-IHT algorithm and the NR-IHT-Mom algorithm outperform several state-of-the-art comparison algorithms.

Binary Iterative Hard Thresholding Converges with Optimal Number of Measurements for 1-Bit Compressed Sensing

Binary Iterative Hard Thresholding Converges with Optimal Number of Measurements for 1-Bit Compressed Sensing

Simultaneous seismic data de‐aliasing and denoising with a fast adaptive method based on hybrid wavelet transform

AbstractMissing data and random noise are prevalent issues encountered during the processing of acquired seismic data. Interpolation and denoising represent economical solutions to address these limitations. Recovering regularly missing traces is challenging because of the spatial aliasing, and the extra difficulty is compounded by the presence of noise. Hence, developing an effective approach to realize denoising and anti‐aliasing is important. Projection onto convex sets is an effective method for recovering missing seismic data that is typically used for processing data with a good signal‐to‐noise ratio. The computational attractiveness of the projection onto convex sets reconstruction approach is compromised by its slow convergence rate. In this study, we aimed to efficiently implement simultaneous seismic data de‐aliasing and denoising. We combined a discrete wavelet transform with a seislet transform to construct a hybrid wavelet transform. A new fast adaptive method based on the fast projection onto convex sets method was proposed to recover the missing data and remove random noise. This approach adjusts the projection operator and iterative shrinkage threshold operator. The result is influenced by the threshold value. We enhanced the processing accuracy by adopting an optimal threshold strategy. Synthetic and field data tests indicate the effectiveness of the proposed method.

SNR Based Adaptive Quantized Iterative Thresholding for Sparse Approximation

SNR Based Adaptive Quantized Iterative Thresholding for Sparse Approximation

Quantitative detection and sorting of broken kernels and chalky grains in milled rice using computer vision algorithms

The milled rice industry faces challenges in effectively detecting and sorting broken kernels and chalky grains. This paper presents a computer vision approach to detect and characterize broken kernels and chalky grains in three milled rice varieties (HM105, WYD4, and JH6). Broken kernel sorting was validated against an ISO-derived recognition method, while the identification of chalky grains was validated using a DSC to assess thermal behavior. The logistic regression showed a strong discriminatory ability in identifying broken kernels. Unlike the ISO method, logistic regression achieved high sorting accuracy for HM105, WYD4, and JH6. The iterative threshold segmentation algorithm also accurately segmented chalky regions in milled rice grains. Regression analysis revealed a significant positive correlation (R2 ≥ 0.94) between the chalky region area and ΔH values. Therefore, this study introduces a robust and rapid methodology for quantitatively detecting milled rice, with the potential for automation and intelligentization in rice-based food processes.

Advanced enhancement technique for infrared images of wind turbine blades utilizing adaptive difference multi-scale top-hat transformation

Enhancing infrared images is essential for detecting wind turbine blades using infrared technology. This paper introduces an Infrared Image Enhancement Method based on Adaptive Iterative Cutoff Threshold Difference Multi-Scale Top-Hat Transformation (AICT-DMTH) to address the challenge of low image clarity in infrared detection. The method involves performing a black-white difference top-hat transformation by utilizing structural elements of varying scales for dilation and erosion. Additionally, an iterative threshold method is applied to extract more detailed image features, followed by setting a cutoff constant to determine the final scale of the structural element. The effectiveness of the proposed method is evaluated both qualitatively and quantitatively, with infrared images from laboratory and wind farm settings enhanced and compared against existing methods. The experimental results indicate that the proposed method significantly improves the clarity of infrared images, demonstrating robustness in enhancing images from various environments.