Fast Iterative Shrinkage-thresholding Algorithm Research Articles

Automatic Modulation Recognition Based on a New Deep K-SVD Denoising Algorithm

Automatic modulation recognition has a wide range of applications in wireless communication. To solve the problem that the previous methods convert signal modulation recognition into image recognition, leading to increased time costs and information loss, an automatic modulation recognition approach consisting of the improved deep K-SVD denoising algorithm is suggested. First, the effectiveness of the model for random sine wave denoising is demonstrated by simulation. Second, the original I/Q signals are fed into the modified deep K-SVD model for denoising, skipping the complicated image processing steps. Finally, the noise-reduced signals are input into a multi-channel convolutional long short-term neural network to complete the modulation recognition. To solve the slow convergence problem of Iterative Shrinkage Thresholding Algorithms in sparse coding, the Fast Iterative Shrinkage Thresholding Algorithm is adopted to improve the computational efficiency and obtain a better denoising effect. The experiments show that the improved model has an average recognition accuracy of 91.26% at different SNRs from -2 dB to 18 dB, which is better than the state-of-the-art modulation recognition models.

FISTA-NET: Deep Algorithm Unrolling for Cerenkov luminescence tomography.

Cerenkov luminescence tomography (CLT) is a highly sensitive and promising imaging technique that can be used to reconstruct the three-dimensional distribution of radioactive probes in living animals. However, the accuracy of CLT reconstruction is limited by the simplified radiative transfer equation and ill-conditioned inverse problem. To address this issue, we propose a model-based deep learning network that combines the neural network with a model-based approach to enhance the performance of CLT reconstruction. The Fast Iterative Shrinkage Thresholding Algorithm (FISTA), a traditional model-based approach, is expanded into a deep network (known as FISTA-NET). Each layer in the network represents an iteration of the algorithm steps, and connecting these layers can form a deep neural network. In addition, different from the traditional FISTA, the key parameters in FISTA, such as gradient step size and threshold value, can be learned through training data without manual production. To evaluate the performance of FISTA-NET, numerical simulation experiments were conducted, which demonstrate its excellent positioning and shape recovery abilities.Clinical Relevance-This indicates that FISTA-NET strategy can significantly improve the quality of CLT reconstruction, which is further beneficial to the assessment of disease activity and treatment effect based on CLT.

Novel Approach-Based Sparsity for Damage Localization in Functionally Graded Material

Model-based approaches have been widely employed in damage detection and localization studies. However, alternative techniques, such as built-in online detection methods, hold promise for future advancements in structural health monitoring technologies. In this research paper, we present a dynamic algorithm specifically designed for accurate damage localization in functionally graded plates. The suggested method involves the creation of a grid matrix that captures the dynamic response of the structure over time. Subsequently, an optimization process is performed using a linear equation that incorporates the information contained within the grid, enabling the precise localization of damage. To address the inherent sparsity of the localization nature, we utilize the FISTA (fast iterative shrinkage-thresholding algorithm) as a problem solver. The effectiveness of our approach is evaluated through experimental tests on a functionally graded plate with clamped free boundary conditions. Multiple damage scenarios are investigated, including cases with damage signals on and off-the-grid. The results demonstrate that our proposed approach is capable of accurately predicting the position of damage, indicating its suitability for application in low-size data systems.

Numerical analysis of aerospace plate damage via 3D electrical impedance tomography.

The carbon fiber reinforced plastic (CFRP) is widely used in the aerospace industry due to its high strength and lightweight characteristics, making it crucial to ensure the reliability of these materials. This has led to an increasing focus on research on the health monitoring technologies of aerospace materials. Electrical impedance tomography (EIT) is a non-invasive and cost-effective technology that has the potential to realize real-time health monitoring of materials by measuring changes in electrical parameters. This paper investigates the application of EIT for direct 3D reconstruction of damage in CFRP laminates with significant conductivity anisotropy distribution. Based on the corrected sensitivity matrix formula, the direct 3D image reconstruction method combined with the fast iterative shrinkage-thresholding algorithm (FISTA) is proposed to achieve damage imaging of CFRP laminates in the inverse problem. The fast convergence of the FISTA makes it possible to solve complex inverse problems. The numerical simulation results indicate that, compared with 2D EIT, the proposed method is more capable of providing damage information, especially in the depth direction. This research plays a constructive role in realizing 3D image reconstruction of CFRP material damage and has significant implications for improving the reliability and safety of CFRP materials in aerospace applications.

Robust RFI Excision for Pulsar Signals by a Novel Nonlinear M-type Estimator with an Application to Pulsar Timing

Radio frequency interference (RFI) mitigation for pulsar signals is a long perplexing issue in astrophysical measurements. Linear mitigation methods are often criticized for limited RFI excision range and weakness of RFI modeling. Meanwhile, thresholding methods (e.g., the SumThreshold) suffer from empirical factors. In our opinion, the main defect of the current status is the lack of a concise definition to distinguish signals from RFI with the aid of certain techniques, e.g., sparse representation. This point is the root cause of these problems and also forms our motivation. This paper aims to expand the excision range (e.g., the on-pulse and quasiperiodic RFI) and cut down some empirical factors. The main contribution is that we give a definition and derive a widely practicable nonlinear framework for RFI excision. This framework can overcome the susceptibility of the least-square criterion to RFI, and excise almost all types of RFI once and for all. A robust LnCosh criterion based nonlinear maximum likelihood-type (M-type) penalized smoothing estimator is introduced. The novelty is that this estimator is first embedded into the iterative shrinkage-thresholding algorithm (ISTA) and the fast ISTA. Nonlinearity highlights this method. Curvelet sparsity gives satisfying approximation for pulsar signals containing dispersion feature. Finally, useful signal details will be retrieved from the excision residual by a morphological component analysis. This method is applied to the time-frequency signals collected by the Nanshan 26 m Radio Telescope. The numerical experiments can persuasively prove that it has desired application prospects.

An accelerated proximal gradient method for multiobjective optimization

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm, for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ( $$O(1 / k^2)$$ ), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments.

Broadband Acoustic Modal Identification by Array Nonsynchronous Measurements with One Reference

This paper proposes a broadband acoustic modal identification method based on nonsynchronous measurements from a microphone array, which overcomes the acoustic modal aliasing problem caused by a limited number of microphones. In the proposed method, the number of measurement points is augmented by sequentially rotating a circular microphone array that is circumferentially mounted in the wall of the compressor duct. This technique employs only one reference microphone to enhance the robustness of the cross-spectral matrix completion for nonsynchronous measurements. The fast iterative shrinkage threshold algorithm is adopted to iteratively complete the cross-spectral matrix of all measurement points for acoustic modal identification. The in-duct acoustic modal coefficients of the broadband noise are then determined using the least-squares method with the sound pressure vector recovered from the completed cross-spectral matrix. The accuracy of the cross-spectral matrix and the identified acoustic modals is verified through numerical simulations. The proposed method is validated by experimental results from an axial flow compressor. The results show that it can effectively suppress the modal aliasing problem and identify the azimuthal modes of compressor broadband noise.

The variant of the iterative shrinkage-thresholding algorithm for minimization of the ℓ1 over ℓ∞ norms

In this paper, we study minimization of the ratio of ℓ1 and ℓ∞ norms (ℓ1/ℓ∞) as a nonconvex and sparsity-promoting metric for solving the unconstrained compressed sensing problems. To design some efficient algorithms, we derive a closed-form solution to the proximal operator of the ℓ1/ℓ∞ function. With the newly variant of the shrinkage operator, we propose a novel variant of fast iterative shrinkage-thresholding algorithm (FISTA) and a specific variable-splitting scheme of the alternating direction method of multipliers (ADMM) which is guaranteed to have sub-sequential convergence. Experimentally, we construct extensive numerical simulations to demonstrate the efficiency of these two proposed approaches over the state-of-the-art algorithms in sparse recovery.

Wheel-rail force identification for high-speed railway based on a modified weighted l1-norm regularization with optimal strain sensors

Wheel-rail force identification is an important inverse problem for structural health monitoring of high-speed railway train-track-bridge system. It is widely used for dynamic response reconstruction of bridges and early safety warning of dynamic reduction rate of wheel weight for the train. It can also serve as a reference for the calibration of wheel-rail force model. This paper proposes a wheel-rail force identification method for high-speed railway based on a modified weighted l1-norm regularization. Based on numerical simulations, it is found that variations of dynamic component of wheel-rail forces are very small. Therefore, the problem is transformed into the identification of three categories of static wheel weights and two categories of average dynamic components, which greatly simplifies the degree of freedom of the solution compared to traditional methods, thereby improving the solution accuracy and saving the number of sensors needed. The wheel-rail forces are decomposed into the product of a series of redundant basis functions and corresponding coefficients. The fast iterative shrinkage threshold algorithm (FISTA) and the Bayesian information criterion (BIC) are used to seek the solution of l1-norm regularization and to select the optimal regularization coefficients, respectively. Since the number of sensors and their locations have a significant impact on the accuracy of reconstructed wheel-rail forces, they are optimized using a genetic algorithm (GA), aiming to accurately reconstruct the wheel-rail forces with the minimum number of sensors at corresponding optimal positions. Numerical simulation of a 32 m box girder standard beam for high-speed railway shows that the reconstructed wheel-rail forces are in good agreement with the simulated results, which verifies the accuracy of the proposed method. In addition, the results of dynamic load test indirectly demonstrate the effectiveness of the proposed method.

Tail-FISTA and applications

Inspired by the fast iterative shrinkage-thresholding algorithm (FISTA), a tail-FISTA method based on the tail-ℓ1 minimization is proposed and analyzed for sparse signal recoveries. Solutions using the profile and the direct methods are both derived. It is also shown that the tail-FISTA method has the convergence rate of O(1/n2) for a given support index T. The tail-FISTA is therefore a much more efficient technique solving the tail-ℓ1 minimization problem than the usual basis pursuit solutions. The superior performance is also demonstrated through extensive numerical simulations in comparison with state-of-the-art algorithms. As an example, for A∈R64×128, traditional algorithms may recovery signals up to sparsity s≤15, while the tail-FISTA can recovery signals with sparsity s≤25. An image restoration/deblurring application is also studied among other techniques to demonstrate the effectiveness of the tail-FISTA technique.

Corrigendum: Reconstruction of seismic data based on SFISTA and curvelet transform

In seismic data processing, the reconstruction and interpolation of missing traces are an essential task. To overcome the limitations of irregularly sampled seismic data, this paper proposes a seismic data interpolation method combining the smoothing fast iterative soft threshold algorithm (SFISTA) and Curvelet transform, this method uses Curvelet domain as sparse domain, for comparing, Contourlet transform is used for different sparse domain, and the fast iterative shrinkage-thresholding algorithm(FISTA) is used for different optimization algorithm. The numerical modeling and real data show that the SFISTA method in Curvelet domain can give better reconstruction effects and higher reconstruction accuracy than that of in Contourlet domain with the FISTA method, in addition, the SFISTA method in Curvelet domain can be used to reconstruct the missing traces of three-dimensionalseismic data.

HFIST-Net: High-throughput fast iterative shrinkage thresholding network for accelerating MR image reconstruction

Background and ObjectivesCompressed sensing (CS) is often used to accelerate magnetic resonance image (MRI) reconstruction from undersampled k-space data. A novelty deeply unfolded networks (DUNs) based method, designed by unfolding a traditional CS-MRI optimization algorithm into deep networks, can provide significantly faster reconstruction speeds than traditional CS-MRI methods while improving image quality. MethodsIn this paper, we propose a High-Throughput Fast Iterative Shrinkage Thresholding Network (HFIST-Net) for reconstructing MR images from sparse measurements by combining traditional model-based CS techniques and data-driven deep learning methods. Specifically, the conventional Fast Iterative Shrinkage Thresholding Algorithm (FISTA) method is expanded as a deep network. To break the bottleneck of information transmission, a multi-channel fusion mechanism is proposed to improve the efficiency of information transmission between adjacent network stages. Moreover, a simple yet efficient channel attention block, called Gaussian context transformer (GCT), is proposed to improve the characterization capabilities of deep Convolutional Neural Network (CNN,) which utilizes Gaussian functions that satisfy preset relationships to achieve context feature excitation. ResultsT1 and T2 brain MR images from the FastMRI dataset are used to validate the performance of the proposed HFIST-Net. The qualitative and quantitative results showed that our method is superior to those compared state-of-the-art unfolded deep learning networks. ConclusionsThe proposed HFIST-Net is capable of reconstructing more accurate MR image details from highly undersampled k-space data while maintaining fast computational speed.

Reconstruction of seismic data based on SFISTA and curvelet transform

In seismic data processing, the reconstruction and interpolation of missing traces are essential tasks. To overcome the limitations of irregularly sampled seismic data, this paper proposes a seismic data interpolation method combining the smoothing fast iterative soft threshold algorithm (SFISTA) and the curvelet transform; this method uses the curvelet domain as the sparse domain. For comparison, the contourlet transform is used for different sparse domains, and the fast iterative shrinkage-thresholding algorithm (FISTA) is used for different optimization algorithms. Numerical modeling and real data show that the SFISTA method in the curvelet domain can give better reconstruction effects and higher reconstruction accuracy than those in the contourlet domain with the FISTA method; in addition, the SFISTA method in the curvelet domain can be used to reconstruct the missing traces of three-dimensional seismic data.

Regularization Solver Guided FISTA for Electrical Impedance Tomography.

Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton-Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.

Linearly-Convergent FISTA Variant for Composite Optimization with Duality

Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage–thresholding algorithm (FISTA) have proven effective for numerous large composite models. In this paper, we present a new variation of FISTA, to be called C-FISTA, which obtains global linear convergence for a broader class of composite models than many of the latest FISTA variants. We demonstrate the versatility and effectiveness of C-FISTA through multiple numerical experiments on group Lasso, group logistic regression and geometric programming models. Furthermore, we utilize Fenchel duality to show C-FISTA can solve the dual of a finite sum convex optimization model.

DOA Estimation in Impulsive Noise Based on FISTA Algorithm

This paper investigates the challenging problem of direction-of-arrival (DOA) estimation in impulsive noise and presents a fast iterative shrinkage-thresholding algorithm (FISTA)-based approach to tackle the difficulty. More specifically, the underlying noise is modelled as the superposition of outliers in the white Gaussian noise. Leveraging on the spot-sparse characteristic of the outlier matrix, the FISTA is conducted on each snapshot of the array output. With the estimated outlier matrix and the coarse on-grid DOA estimates, an alternating optimization method is developed to retrieve the final off-grid DOA estimates. Simulation results show that the proposed method outperforms existing methods in terms of resolution capability and estimation accuracy especially in severe noise environments.

An Acoustic Localization Sensor Based on MEMS Microphone Array for Partial Discharge.

Partial discharge (PD) localization is important for monitoring and maintaining high-voltage equipment, which can help to prevent accidents. In this work, an acoustic localization sensor based on microelectromechanical system (MEMS) microphone array is proposed, which can detect and locate the partial discharge through a beam-forming algorithm. The MEMS microphone array consists of eight commercial MEMS microphones (SPV08A0LR5H-1, Knowles Electronics, IL, USA) with an aperture size of about 0.1 m × 0.1 m, allowing for a small hardware size and low cost. In order to optimize the acoustic performance of the array, a random array topology is designed. The simulation analysis indicates that the designed random topology is superior to several commonly used topologies. In terms of the localization algorithm, a deconvolution method called Fourier-based fast iterative shrinkage thresholding algorithm (FFT-FISTA) is applied. Simulation and experiment results demonstrate that FFT-FISTA used in the proposed acoustic localization sensor has significant advantages over the conventional beam-forming algorithm on spatial resolution and sidelobe suppression. Experimental results also show that the average localization error of the proposed scheme is about 0.04 m, which can meet the demands of practical application.

Speckle Removal Using Dictionary Learning and PnP-Based Fast Iterative Shrinkage Threshold Algorithm

Speckle is a multiplicative granular noise that naturally occurs in the images captured by coherent imaging sensors such as synthetic aperture radar (SAR). It visually degrades the underlying image information and has an impact on subsequent image analysis. This problem is addressed here by developing a sparse representation model and applying an alternating minimization scheme for SAR image despeckling. The proposed method directly deals with the multiplicative noise and the data model is formed by utilizing the speckle statistics. The similar patches are clustered together to adaptively learn the dictionary, and the sparse coefficients are updated using plug-and-play based fast iterative shrinkage threshold algorithm (PnP-FISTA). Finally, the clean image is estimated using Newton’s method. Experiments on simulated and practical SAR images signify that the proposed method performs better compared to the state-of-the-art methods in terms of performance metrics and visual assessment.

RDFNet: Regional Dynamic FISTA-Net for Spectral Snapshot Compressive Imaging

Deep convolutional neural networks have recently shown promising results in compressive spectral reconstruction. Previous methods, however, usually adopt a single mapping function for sparse representation. Considering that different regions have distinct characteristics, it is desirable to apply various mapping functions to adjust different regions' transformations dynamically. With this in mind, we first introduce a regional dynamic way of using Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) to exploit regional characteristics and derive dynamic sparse representations. Then, we propose to unfold the process into a hierarchical dynamic deep network, dubbed RDFNet. The network comprises multiple regional dynamic blocks and corresponding pixel-wise adaptive soft-thresholding modules, respectively in charge of region-based dynamic mapping and pixel-wise soft-thresholding selection. The regional dynamic block guides the network to adjust the transformation domain for different regions. Equipped with the adaptive soft-thresholding, our proposed regional dynamic architecture can also learn appropriate shrinkage scale in a pixel-wise manner. Extensive experiments on both simulated and real data demonstrate that our method outperforms prior state-of-the-arts.

Heart disease detection using inertial Mann relaxed $ CQ $ algorithms for split feasibility problems

<abstract><p>This study investigates the weak convergence of the sequences generated by the inertial relaxed $ CQ $ algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed $ CQ $ algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score.</p></abstract>