Iterative Thresholding Method Research Articles

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.

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.

Sparse Identification of Fractional Chaotic Systems based on the time-domain data

The complexity inherent in defining and computing fractional derivatives renders the development of a data-driven modeling framework for fractional-order systems more formidable than for their integer-order counterparts. This study introduces a methodology for sparsely identifying fractional chaotic systems by leveraging time-domain data to ascertain the system’s governing equations. Initially, we establish a sparse identification framework specifically tailored for fractional order systems and introduce a joint iterative thresholding method designed to identify these systems’ fractional and integer order components concurrently. Moreover, this study conducts a comparative analysis of two error criteria for model selection. It introduces a strategy predicated on minimizing the distance to balance sparsity and model fitting error optimally. To validate the efficacy and precision of the proposed methodology, numerical simulations were conducted on fractional order simplified Lorenz and Chua’s circuits, affirming the robustness and accuracy of our approach.

Defect imaging and identification in asphalt materials using coplanar capacitance sensors with single-pair electrodes

Coplanar capacitance imaging technology (CCIT) is a non-destructive method with intuitive and accurate identification. This paper aims to realize defect identification in asphalt materials based on the CCIT using coplanar single-pair electrode capacitance sensor (CSCS). Firstly, the Linear Back Projection (LBP) algorithm, the Landweber algorithm, and the Kalman-Filter (KF) algorithm, are compared and evaluated. Then, the principal component analysis (PCA) method is utilized to fuse the reconstructed images. In addition, the OTSU method, the iterative threshold (IT) method, and the genetic algorithm (OA) method, is compared and utilized to quantify the defective region. Finally, this investigation analyzes the reconstructed and segmented images of defects in asphalt materials. It is concluded that the KL algorithm is the most suitable algorithm to reconstruct the defective images. The PCA method improve the quality of the reconstructed defective images. The defective region is determined by the OTSU method, which is the most approximate imaging segment method. It is found that the CCIT can detect the invisible defect depth in asphalt materials. The different defect mediums in various asphalt materials can be identified by the CCIT. The segmented defective region error in asphalt materials is less than 13%, demonstrating that the CCIT is effective for the identification of defect shape details in asphalt materials. The segmented imaging precision of square defects in asphalt materials is the highest; circular defects are the next lowest; and triangular defects are the lowest. The outcomes of this research can assist engineers in realizing intuitive and high-accuracy identification of various invisible defects in shallow asphalt layers in bridge deck asphalt pavement utilizing the CCIT.

Distribution Characteristics and Influencing Factors of Sea Ice Leads in the Weddell Sea, Antarctica

The characteristics of sea ice leads (SILs) in the Weddell Sea are an important basis for understanding the mechanism of the atmosphere–ocean system in the Southern Ocean. In this study, we derived the sea ice surface temperature (IST) of the Weddell Sea from MODIS thermal images and then generated a daily SIL map for 2015 and 2022 by utilizing the iterative threshold method on the optimised MOD35 cloud-masked IST. The results showed that SIL variations in the Weddell Sea presented remarkable seasonal characteristics. The trend of the SIL area exhibited an initial rise followed by a decline from January to December, characterised by lower values in spring and summer and higher values in fall and winter. SILs in the Weddell Sea were predominantly concentrated between 70~78°S and 60~30°W. The coastal spatial distribution density of the SILs exceeded that of offshore regions, peaking near the Antarctic Peninsula and then near Queen Maud Land. The SIL variation was mainly influenced by dynamical factors, and there were strong positive correlations between the wind field, ocean currents, and sea-ice motion.

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.

An Iterative Thresholding Method for the Heat Transfer Problem

An Iterative Thresholding Method for the Heat Transfer Problem

An Iterative Thresholding Method for the Minimum Compliance Problem

An Iterative Thresholding Method for the Minimum Compliance Problem

Image-derived input functions from dynamic 15O–water PET scans using penalised reconstruction

BackgroundQuantitative positron emission tomography (PET) scans of the brain typically require arterial blood sampling but this is complicated and logistically challenging. One solution to remove the need for arterial blood sampling is the use of image-derived input functions (IDIFs). Obtaining accurate IDIFs, however, has proved to be challenging, mainly due to the limited resolution of PET. Here, we employ penalised reconstruction alongside iterative thresholding methods and simple partial volume correction methods to produce IDIFs from a single PET scan, and subsequently, compare these to blood-sampled input curves (BSIFs) as ground truth. Retrospectively we used data from sixteen subjects with two dynamic 15O-labelled water PET scans and continuous arterial blood sampling: one baseline scan and another post-administration of acetazolamide.ResultsIDIFs and BSIFs agreed well in terms of the area under the curve of input curves when comparing peaks, tails and peak-to-tail ratios with R2 values of 0.95, 0.70 and 0.76, respectively. Grey matter cerebral blood flow (CBF) values showed good agreement with an average difference between the BSIF and IDIF CBF values of 2% ± and a coefficient of variation (CoV) of 7.3%.ConclusionOur results show promising results that a robust IDIF can be produced for dynamic 15O–water PET scans using only the dynamic PET scan images with no need for a corresponding MRI or complex analytical techniques and thereby making routine clinical use of quantitative CBF measurements with 15O–water feasible.

An Image Denoising Model via the Reconciliation of the Sparsity and Low-Rankness of the Dictionary Domain Coefficients

Sparse coding has achieved great success in various image restoration tasks. However, if the sparse representation coefficients of the structure (low-frequency information) and texture (high-frequency information) components of the image are under the same penalty constraint, the restoration effect may not be ideal. In this paper, an image denoising model combining mixed norm and weighted nuclear norm as regularization terms is proposed. The proposed model simultaneously exploits the group sparsity of the high frequency and low-rankness of the low frequency in dictionary-domain. The mixed norm is used to constrain the high frequency part and the weighted nuclear norm is used to constrain the low frequency part. In order to make the proposed model easy to solve under the framework of alternative direction multiplier method (ADMM), iterative shrinkage threshold method and weighted nuclear norm minimization method are used to solve the two sub-problems. The validity of the model is verified experimentally through comparison with some state-of-the-art methods.

A Hybrid Iterative Thresholding Method for Solving Sparsity-Regularized Linear Inverse Problems and Its Application in Seismic Sparse-Spike Deconvolution

Sparsity-regularized linear inverse problem has been served as the base in many disciplines, such as remote sensing imaging, image processing and analysis, seismic deconvolution, compressed sensing, medical imaging, and so forth. Iterative hard thresholding algorithm (IHTA) and iterative soft thresholding algorithm (ISTA) are two frequently used methods to solve sparsity-regularized linear inverse problems. They are also the basic unit of other more complex methods. IHTA and ISTA are derived under steepest descent method. I.e., iteratively perform gradient descent and thresholding shrinkage. Steepest descent method is a first order algorithm, which is a powerful way to solve optimization due to its relatively simple implementation. However, a known issue of first order method is possible poor convergence rate. Fast iterative thresholding-like algorithms have been proposed to overcome this issue in the existing literatures. In history, another alternative way is second order algorithms or quasi-second order algorithms. In this paper, we include a quasi-Newton’s method, i.e., DFP (Davidon-Fletcher-Powell) formulations in the framework of iterative thresholding-like algorithms to replace gradient descent to form a hybrid method to further increase convergence rate. The proposed method has been performed on two numerical examples and a real-life application in sparse-spike seismic deconvolution. The numerical examples and real-life application showed that it provides an effective alternative method to solve sparsity-regularized linear inverse problems.

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.

Automatic recognition and localization of underground pipelines in GPR B-scans using a deep learning model

Ground penetrating radar (GPR) is a popular non-destructive method for detecting and locating underground pipelines. However, manual interpretation of a large number of GPR B-scan images is time-consuming, and the results highly relies on the practitioner’s experience and the priori information at hands. An automatic GPR method for recognition and localization of underground pipelines is proposed based on a deep learning model in the paper. Firstly, a dataset containing 3,824 real GPR B-scans of pipelines is established. Secondly, a You Only Look Once version 3 (YOLOv3) model is trained to recognize the regions of the underground pipelines in a GPR image. Thirdly, the hyperbolic response of a pipeline is focused by migration, and transformed into a binary image by an iterative thresholding method. Finally, the apex of the hyperbola is employed to estimate both the horizontal position and the buried depth of the pipeline. Field experiments validated that the absolute errors of the estimated depths are less than 0.04 m and the average relative error is lower than 4 %. It is demonstrated that the proposed method is automatic, high-speed, and reliable for recognition and localization of underground pipelines in urban area.

Cascaded Hough Transform-Based Hair Mask Generation and Harmonic Inpainting for Automated Hair Removal from Dermoscopy Images.

Restoring information obstructed by hair is one of the main issues for the accurate analysis and segmentation of skin images. For retrieving pixels obstructed by hair, the proposed system converts dermoscopy images into the L*a*b* color space, then principal component analysis (PCA) is applied to produce grayscale images. Afterward, the contrast-limited adaptive histogram equalization (CLAHE) and the average filter are implemented to enhance the grayscale image. Subsequently, the binary image is generated using the iterative thresholding method. After that, the Hough transform (HT) is applied to each image block to generate the hair mask. Finally, the hair pixels are removed by harmonic inpainting. The performance of the proposed automated hair removal was evaluated by applying the proposed system to the International Skin Imaging Collaboration (ISIC) dermoscopy dataset as well as to clinical images. Six performance evaluation metrics were measured, namely the mean squared error (MSE), the peak signal-to-noise ratio (PSNR), the signal-to-noise ratio (SNR), the structural similarity index (SSIM), the universal quality image index (UQI), and the correlation (C). Using the clinical dataset, the system achieved MSE, PSNR, SNR, SSIM, UQI, and C values of 34.7957, 66.98, 42.39, 0.9813, 0.9801, and 0.9985, respectively. The results demonstrated that the proposed system could satisfy the medical diagnostic requirements and achieve the best performance compared to the state-of-art.

Riemannian thresholding methods for row-sparse and low-rank matrix recovery

In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular, a Riemannian version of IHT is considered which significantly reduces computational cost of the gradient projection in the case of rank-one measurement operators, which have concrete applications in blind deconvolution. Experimental results are reported that show near-optimal recovery for Gaussian and rank-one measurements, and that adaptive stepsizes give crucial improvement. A Riemannian proximal gradient method is derived for the special case of unknown sparsity.

Stochastic privacy-preserving methods for nonconvex sparse learning

Sparse learning is essential in mining high-dimensional data. Iterative hard thresholding (IHT) methods are effective for optimizing nonconvex objectives for sparse learning. However, IHT methods are vulnerable to adversary attacks that infer sensitive data. Although pioneering works attempted to relieve such vulnerability, they confront the issue of high computational cost for large-scale problems. We propose two differentially private stochastic IHT: one based on the stochastic gradient descent method (DP-SGD-HT) and the other based on the stochastically controlled stochastic gradient method (DP-SCSG-HT). The DP-SGD-HT method perturbs stochastic gradients with small Gaussian noise rather than full gradients, which are computationally expensive. As a result, computational complexity is reduced from O(nlog(n)) to a lower O(blog(n)), where n is the sample size and b is the mini-batch size used to compute stochastic gradients. The DP-SCSG-HT method further perturbs the stochastic gradients controlled by large-batch snapshot gradients to reduce stochastic gradient variance. We prove that both algorithms guarantee differential privacy and have linear convergence rates with estimation bias. A utility analysis examines the relationship between convergence rate and the level of perturbation, yielding the best-known utility bound for nonconvex sparse optimization. Extensive experiments show that our algorithms outperform existing methods.

Federated Optimization of ℓ0-norm Regularized Sparse Learning

Regularized sparse learning with the ℓ0-norm is important in many areas, including statistical learning and signal processing. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex-constrained sparse learning due to their capability of recovering true support and scalability with large datasets. The current theoretical analysis of IHT assumes the use of centralized IID data. In realistic large-scale scenarios, however, data are distributed, seldom IID, and private to edge computing devices at the local level. Consequently, it is required to study the property of IHT in a federated environment, where local devices update the sparse model individually and communicate with a central server for aggregation infrequently without sharing local data. In this paper, we propose the first group of federated IHT methods: Federated Hard Thresholding (Fed-HT) and Federated Iterative Hard Thresholding (FedIter-HT) with theoretical guarantees. We prove that both algorithms have a linear convergence rate and guarantee for recovering the optimal sparse estimator, which is comparable to classic IHT methods, but with decentralized, non-IID, and unbalanced data. Empirical results demonstrate that the Fed-HT and FedIter-HT outperform their competitor—a distributed IHT, in terms of reducing objective values with fewer communication rounds and bandwidth requirements.

Huber inversion-based reverse-time migration with de-primary imaging condition and curvelet-domain sparse constraint

Least-squares reverse-time migration (LSRTM) formulates reverse-time migration (RTM) in the least-squares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist: (1) inversion can be dominated by strong events in the residual; (2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results; (3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Huber-norm as the objective function to emphasize the weak reflectors during the inversion; secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient; thirdly, we apply the L 1 -norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L 1 -norm, we use a modified iterative soft thresholding (IST) method to update along the Polak-Ribière conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient (PNCG) method. The numerical examples, especially the Sigsbee2A model, demonstrate that the Huber inversion-based RTM can generate high-quality images by mitigating migration artifacts and improving the contribution of weak reflection events.

A Fourier Transform-Based Calculation Method of Wilting Index for Soybean Canopy Using Multispectral Image

The growth process of soybean plants needs a lot of water. The rapid detection of canopy wilting of soybean under drought stress is of great significance for soybean variety breeding, cultivation regulation and fine management. Aiming at the problems of cumbersome and time-consuming when the traditional chemical technology was used to determine soybean wilting index, a calculation method of wilting index for soybean canopy was proposed in this study based on multispectral images’ Fourier transform. Suinong 26, a northeast soybean variety, was taken as the object. First, four kinds of soybean multispectral images of green, red, red-edge and near-infrared channels were acquired by a Sequoia multispectral camera. Second, based on the multispectral reflection image preprocessed by median filter and mean filter, the target area of a multispectral image of the soybean canopy was extracted by the iterative threshold method and affine transformation algorithm, and the effective segmentation rate was 97.02%. In addition, Fourier transform was used to analyze the spectrum characteristics of the soybean canopy’s multispectral image. When the spectrum radius of each channel was 50, the energy reached more than 98% and was concentrated in the low-frequency region of the spectrum center. Finally, according to the difference between the low-frequency DC component and the proportion of total energy in the spectral radius of the multispectral images under normal and drought treatment, a calculation model of the soybean wilting index was constructed based on the energy spectrum of Fourier transform. The results showed that the difference of the wilting index between normal and drought treatment for the four channels (green, near-infrared, red and red-edge) was 2.38, 3.11, 3.56 and 4.11, respectively. The effectiveness of the wilting index was verified and analyzed by using the average leaf inclination angle. The determination coefficient R2 of the four channels between the calculated wilting index and the average leaf inclination angle was more than 0.85. This calculation method can provide a quantitative basis and technical support for the scientific regulation of ecological and morphological phenotypic traits of soybean plants under drought stress.

Underwater Image Enhancement by Attenuated Color Channel Correction and Detail Preserved Contrast Enhancement

An underwater image often suffers from quality degradation issues, such as color deviations, low contrast, and blurred details, due to the absorption and scattering of light. In this article, we propose to address the aforementioned degradation issues via attenuated color channel correction and detail preserved contrast enhancement. Concretely, we first propose an underwater image color correction method. Considering the differences between superior and inferior color channels of an underwater image, the inferior color channels are compensated via especially designed attenuation matrices. We then employ a dual-histogram-based iterative threshold method and a limited histogram method with Rayleigh distribution to improve the global and local contrast of the color-corrected image, thus achieving a global contrast-enhanced version and a local contrast-enhanced version, respectively. To integrate the complementary merits between the global contrast-enhanced version and the local contrast-enhanced version, we adopt a multiscale fusion strategy to fuse them. Finally, we propose a multiscale unsharp masking strategy to further sharpen the fused image for better visual quality. Extensive experiments on four underwater image enhancement benchmark data sets demonstrate that our method effectively enhances underwater images qualitatively and quantitatively. Besides, our method also generalizes well to the enhancement of low-light images and hazy images.