Shrinkage 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.

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.

A fast impact force identification method via constructing a dynamic reduced dictionary

Impact force identification is an important aspect of structural health monitoring for online assessment of the integrity of engineering structures. Increasing the number of monitoring positions is undoubtedly beneficial to accurate force localization, however, it may increase sharply the dimension of the transfer matrix and thus lead to a large-scale inverse problem. In this case, traditional methods, such as the Iterative Shrinkage Threshold algorithm (IST) and the Two-Step Iterative Shrinkage Thresholding algorithm (TwIST), suffer from low solving efficiency. In this paper, the dynamic reduced dictionary is firstly introduced according to the sparsity of impact force in both time and spatial domains so as to lower significantly the dimension of the transfer matrix. Then, a new reduced unconstrained optimization problem is established via the dynamic reduced dictionary for impact force identification. By integrating the reduced unconstrained optimization problem into each iteration step of IST/TwIST, two novel algorithms, which are the reduced Newton iteration shrinkage threshold algorithm (rNIST) and the reduced Newton two-step iteration shrinkage threshold algorithm (rNTwIST), are proposed to solve quickly the large-scale impact force identification problem using ℓ1-norm sparse regularization. Meanwhile, the adaptive setting of regularization parameters strategy is used to construct force more fast and accurately. The proposed algorithms are numerically and experimentally demonstrated through identifying impact forces at 16-point and 81-point distributions of a plate using one sensor response. The results show that rNIST/rNTwIST can more quickly and accurately identify impact forces under numerous monitoring points compared with other ℓ1-norm regularization methods and nonconvex sparse regularization methods. Moreover, the more the number of monitoring points, the more obvious the efficiency improvement of the impact force identification by rNIST/rNTwIST method.

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.

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.

A robust underwater polarization image recovery based on Angle of Polarization with low-rank and sparse decomposition

Underwater imaging method based on the Angle of Polarization (AoP) is extremely popular due to its ability to remove the backscattered light effectively. However, existing methods overlook a potentially important phenomenon: the AoP contains significant noise in the real world, which leads to inaccurate estimations of key parameters. In this study, we propose a novel robust underwater polarization image recovery method based on AoP with low-rank and sparse decomposition. Based on the analysis of polarization, the AoP of backscattering exhibits low-rank characteristics, whereas the AoP of noise and targets demonstrates sparsity. Considering different sparsity of AoP, we combine Robust Principal Component Analysis and Alternating Direction Multiplier Method (RPCA-ADMM) with an adaptive threshold shrinkage method for low-rank and sparse decomposition, the AoP of the backscattering is obtained. Moreover, according to the low-rank component of the AoP, the Degree of Linear Polarization (DoLP) of backscattering can be effectively and automatically estimated without considering whether the background region exists, relying on a frequency prior strategy. Finally, the degraded image is recovered utilizing underwater polarization imaging model. Extensive experimental results demonstrate that the recovered images from the proposed method have abundant detail, high contrast, and minimal color distortion, which is competitive with most state-of-the-art methods.

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.

Improved Analytic Learned Iterative Shrinkage Thresholding Algorithm and Its Application to Tomographic Synthetic Aperture Radar Building Object Height Inversion

Tomographic Synthetic Aperture Radar (TomoSAR) building object height inversion is a sparse reconstruction problem that utilizes the data obtained from several spacecraft passes to invert the scatterer position in the height direction. In practical applications, the number of passes is often small, and the observation data are also small due to the objective conditions, so this study focuses on the inversion under the restricted observation data conditions. The Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA) is a kind of deep unfolding network algorithm, which is a combination of the Iterative Shrinkage Thresholding Algorithm (ISTA) and deep learning technology, and it has the advantages of both. The ALISTA is one of the representative algorithms for TomoSAR building object height inversion. However, the structure of the ALISTA algorithm is simple, which has neither the excellent connection structure of a deep learning network nor the acceleration format combined with the ISTA algorithm. Therefore, this study proposes two directions of improvement for the ALISTA algorithm: firstly, an improvement in the inter-layer connection of the network by introducing a connection similar to residual networks obtains the Extragradient Analytic Learned Iterative Shrinkage Thresholding Algorithm (EALISTA) and further proves that the EALISTA achieves linear convergence; secondly, there is an improvement in the iterative format of the intra-layer iteration of the network by introducing the Nesterov momentum acceleration, which obtains the Fast Analytic Learned Iterative Shrinkage Thresholding Algorithm (FALISTA). We first performed inversion experiments on simulated data, which verified the effectiveness of the two proposed algorithms. Then, we conducted TomoSAR building object height inversion experiments on limited measured data and used the deviation metric P to measure the robustness of the algorithms to invert under restricted observation data. The results show that both proposed algorithms have better robustness, which verifies the superior performance of the two algorithms. In addition, we further analyze how to choose the most suitable algorithms for inversion in engineering practice applications based on the results of the experiments on measured data.

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

CTV-Net: Complex-Valued TV-Driven Network With Nested Topology for 3-D SAR Imaging.

The regularization-based approaches offer promise in improving synthetic aperture radar (SAR) imaging quality while reducing system complexity. However, the widely applied l1 regularization model is hindered by their hypothesis of inherent sparsity, causing unreal estimations of surface-like targets. Inspired by the edge-preserving property of total variation (TV), we propose a new complex-valued TV (CTV)-driven interpretable neural network with nested topology, i.e., CTV-Net, for 3-D SAR imaging. In our scheme, based on the 2-D holography imaging operator, the CTV-driven optimization model is constructed to pursue precise estimations in weakly sparse scenarios. Subsequently, a nested algorithmic framework, i.e., complex-valued TV-driven fast iterative shrinkage thresholding (CTV-FIST), is derived from the theory of proximal gradient descent (PGD) and FIST algorithm, theoretically supporting the design of CTV-Net. In CTV-Net, the trainable weights are layer-varied and functionally relevant to the hyperparameters of CTV-FIST, which aims to constrain the algorithmic parameters to update in a well-conditioned tendency. All weights are learned by end-to-end training based on a two-term cost function, which bounds the measurement fidelity and TV norm simultaneously. Under the guidance of the SAR signal model, a reasonably sized training set is generated, by randomly selecting reference images from the MNIST set and consequently synthesizing complex-valued label signals. Finally, the methodology is validated, numerically and visually, by extensive SAR simulations and real-measured experiments, and the results demonstrate the viability and efficiency of the proposed CTV-Net in the cases of recovering 3-D SAR images from incomplete echoes.

AN ENHANCED SHRINKAGE FUNCTION FOR DENOISING ECONOMIC TIME SERIES DATA USING WAVELET ANALYSIS

In the realm of economic (financial) time series analysis, accurate prediction holds paramount importance. However, these data often suffer from the presence of noise, particularly in highly random and non-stationary datasets like stock market data. Dealing with noisy data makes predicting noise-free economic models exceedingly challenging. This research paper introduces an innovative shrinkage (thresholding) function designed to improve the efficiency of wavelet shrinkage denoising in the context of financial time series data. The proposed function is constructed based on an arctangent model with adjustable parameters meticulously chosen to ensure the function maintains continuous differentiability. The application of this novel shrinkage function effectively reduces noise in stock data. Employing R program for data analysis and figure plotting, the performance of this approach is rigorously validated using closing price data from the Shanghai Composite Index, spanning the period from January 4, 2000 to August 28, 2023. The experimental results demonstrate that the proposed thresholding function outperforms classical shrinkage functions (hard, soft, and nonnegative garrote) in both continuous derivative property and denoising efficacy.

Migration through Resolution Cell Correction and Sparse Aperture ISAR Imaging for Maneuvering Target Based on Whale Optimization Algorithm-Fast Iterative Shrinkage Thresholding Algorithm.

Targets faced by inverse synthetic aperture radar (ISAR) are often non-cooperative, with target maneuvering being the main manifestation of this non-cooperation. Maneuvers cause ISAR imaging results to be severely defocused, which can create huge difficulties in target identification. In addition, as the ISAR bandwidth continues to increase, the impact of migration through resolution cells (MTRC) on imaging results becomes more significant. Target non-cooperation may also result in sparse aperture, leading to the failure of traditional ISAR imaging algorithms. Therefore, this paper proposes an algorithm to realize MTRC correction and sparse aperture ISAR imaging for maneuvering targets simultaneously named whale optimization algorithm-fast iterative shrinkage thresholding algorithm (WOA-FISTA). In this algorithm, FISTA is used to perform MTRC correction and sparse aperture ISAR imaging efficiently and WOA is adopted to estimate the rotational parameter to eliminate the effects of maneuvering on imaging results. Experimental results based on simulation and measured datasets prove that the proposed algorithm implements sparse aperture ISAR imaging and MTRC correction for maneuvering targets simultaneously. The proposed algorithm achieves better results than traditional algorithms under different signal-to-noise ratio conditions.

EIDNet: Extragradient-based iterative denoising network for image compressive sensing reconstruction

Compressive sensing (CS) is a kind of hardware-friendly technology in effective image reconstruction. Most of the existing CS reconstruction methods can be classified into model-driven iterative optimization methods and data-driven neural network methods. These two types of methods have their own problems with computational complexity and theoretical interpretability. Motivated by the deep unfolding theory, we develop the model-driven Extragradient-based Iterative Denoising Network, dubbed EIDNet, which is based on the denoising model of the iterative shrinkage threshold algorithm (ISTA). By unfolding the iterative denoising model into the deep learning network, EIDNet addresses the interpretability problem of neural network methods in CS reconstruction. Each denoising iteration of the optimization algorithm is mapped into one layer of the reconstruction network in EIDNet. The extragradient method is adopted to accelerate network convergence. In addition, we introduce a learning-based sampling and initialization network for adaptive sampling and initialization. Extensive experiments show that the proposed EIDNet can obtain better image CS reconstruction performance than other state-of-the-art CS methods while maintaining satisfactory reconstruction efficiency.

Robust treatment planning for small animal radio-neuromodulation using focused kV x-ray beams.

In preclinical radio-neuromodulation research, small animal experiments are pivotal for unraveling radiobiological mechanism, investigating prescription and planning techniques, and assessing treatment effects and toxicities. However, the target size inside a rat brain is typically in the order of sub-millimeters. The small target inside the visual cortex neural region in rat brain with a diameter of around 1mm was focused in this work to observe the physiological change of this region. Delivering uniform doses to the small target while sparing health tissues is challenging. Focused kV x-ray technique based on modern x-ray polycapillary focusing lens is a promising modality for small animal radio-neuromodulation. The current manual planning method could lead to sub-optimal plans, and the positioning uncertainties due to mechanical accuracy limitations, animal immobilization, and robotic arm motion are not considered. This work aims to design a robust inverse planning method to optimize the intensities of focused kV x-ray beams located in beam trajectories to irradiate small mm-sized targets in rat brains for radio-neuromodulation. Focused kV x-ray beams were generated through polycapillary x-ray focusing lenses on achieving small (≤0.3mm) focus perpendicular to the beam. The beam trajectories were manually designed in 3D space in scanning-while-rotating mode. Geant4 Monte Carlo (MC) simulation generated a dose calculation matrix for each focused kV x-ray beam located in beam trajectories. In the proposed robust inverse planning method, an objective function combining a voxel-wise stochastic programming approach and L1 norm regularization was established to overcome the positioning uncertainties and obtain a high-quality plan. The fast iterative shrinkage thresholding algorithm (FISTA) was utilized to solve the objective function and obtain the optimal intensities. Four cases were employed to validate the feasibility and effectiveness of the proposed method. The manual and non-robust inverse planning methods were also implemented for comparison. The proposed robust inverse planning method achieved superior dose homogeneity and higher robustness against positioning uncertainties. On average, the clinical target volume (CTV) homogeneity index (HI) of robust inverse plan improved to 13.3 from 22.9 in non-robust inverse plan and 53.8 in manual plan if positioning uncertainties were also present. The average bandwidth at D90 was reduced by 6.5Gy in the robust inverse plan, compared to 9.6Gy in non-robust inverse plan and 12.5Gy in manual plan. The average bandwidth at D80 was reduced by 3.4Gy in robust inverse plan, compared to 5.5Gy in non-robust inverse plan and 8.5Gy in manual plan. Moreover, the dose delivery time of manual plan was reduced by an average reduction of 54.7% with robust inverse plan and 29.0% with non-robust inverse plan. Compared to manual and non-robust inverse planning methods, the robust inverse planning method improved the dose homogeneity and delivery efficiency and was resistant to the uncertainties, which are crucial for radio-neuromodulation utilizing focused kV x-rays.

Improving noise characteristics using a modified image pyramid with guided filtering and Bayesian shrinkage threshold in low-dose animal radiography

Radiography is a commonly used diagnostic tool in animal practice to provide clinical information. The recent market for animal radiography is rapidly growing owing to the increasing awareness of the welfare of companion animals and the expansion of animal clinics. As the clinical use of radiography in animal hospitals has grown rapidly, radiologists continuously seek ways to reduce the radiation dose to animals. This study proposes an effective noise removal method using a modified image pyramid with guided filtering and Bayesian shrinkage threshold for low-dose animal radiography. This study aims to model a modified image pyramid-based denoising algorithm and to confirm its applicability in an animal radiographic system. We conducted an experiment on a companion dog and cat using a commercially-available veterinary radiographic system and quantitatively evaluated the image quality using the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). The PSNR and SSIM values measured in the denoised image of the dog using the proposed denoising algorithm were 39.54 and 0.96, respectively, which are improvements of approximately 11.3% and 5.5% of the values obtained in the original noisy image. Consequently, the proposed method is highly efficient in reducing image noise in animal radiography, thereby improving the image quality.

Impact load identification of high-speed train scale carbody based on multi-objective optimisation and TwIST sparse regularisation

ABSTRACT Effective identification of dynamic loads on vehicle systems is crucial for evaluating the structural integrity of railway vehicles. The inverse problem method has been proposed for dynamic load identification to determine the impact load on the carbody. Due to the sparse nature of the impact load, the combination of the l 1-norm and TwIST (two-step iterative threshold shrinkage method) methods is used to reconstruct the impact load, taking into account the influence of sensor placement on the identification results. The MOHBA (Multi-objective Optimisation Honey Badger Algorithm) was proposed to simultaneously select the regularisation and iteration parameters. This algorithm aims to improve the accuracy of subsequence load reconstruction by considering the influence of noise levels when selecting the measured data. The impact load experiment was conducted on the scale carbody, and the single-point impact load and multi-point impact load matched well with the actual load. Satisfactory load identification results can still be achieved when the noise level is within 15%. When arranging measurement points on the boundary of the vehicle body, satisfactory load identification results can also be achieved.

SWISTA-Nets: Subband-adaptive wavelet iterative shrinkage thresholding networks for image reconstruction

Robust and interpretable image reconstruction is central to imageology applications in clinical practice. Prevalent deep networks, with strong learning ability to extract implicit information from data manifold, are still lack of prior knowledge introduced from mathematics or physics, leading to instability, poor structure interpretability and high computation cost. As to this issue, we propose two prior knowledge-driven networks to combine the good interpretability of mathematical methods and the powerful learnability of deep learning methods. Incorporating different kinds of prior knowledge, we propose subband-adaptive wavelet iterative shrinkage thresholding networks (SWISTA-Nets), where almost every network module is in one-to-one correspondence with each step involved in the iterative algorithm. By end-to-end training of proposed SWISTA-Nets, implicit information can be extracted from training data and guide the tuning process of key parameters that possess mathematical definition. The inverse problems associated with two medical imaging modalities, i.e., electromagnetic tomography and X-ray computational tomography are applied to validate the proposed networks. Both visual and quantitative results indicate that the SWISTA-Nets outperform mathematical methods and state-of-the-art prior knowledge-driven networks, especially with fewer training parameters, interpretable network structures and well robustness. We assume that our analysis will support further investigation of prior knowledge-driven networks in the field of ill-posed image reconstruction.

A Fast Intersection of Confidence Intervals Method-Based Adaptive Thresholding for Sparse Image Reconstruction Using the Matrix Form of the Wavelet Transform

One of the frequently used classes of sparse reconstruction algorithms is based on the iterative shrinkage/thresholding procedure, in which the thresholding parameter controls a trade-off between the algorithm’s accuracy and execution time. In order to avoid this trade-off, we propose using a fast intersection of confidence intervals method in order to adaptively control the threshold value throughout the iterations of the reconstruction algorithm. We have upgraded the two-step iterative shrinkage thresholding algorithm with a such procedure, improving its performance. The proposed algorithm, denoted as the FICI-TwIST, along with a few selected state-of-the-art sparse reconstruction algorithms, has been tested on the classical problem of image recovery by emphasizing the image sparsity in the discrete cosine and the discrete wavelet domain. Furthermore, we have derived a single wavelet transformation matrix which avoids wrapping effects, thereby achieving significantly faster execution times as compared to a more traditional function-based transformation. The obtained results indicate the competitive performance of the proposed algorithm, even in cases where all algorithm parameters have been individually fine-tuned for best performance.

MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multiscale Dilated Convolution for Image Compressive Sensing (CS)

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation mechanisms into the ISTA block. This block serves as a deep equilibrium layer connected to a semi-tensor product network for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation tradeoffs. Additionally, the model benefits from multiscale dilated convolutions, further enhancing performance.