Sparse Reconstruction Research Articles

A modified PRP conjugate gradient method with inertial extrapolation for sparse signal reconstruction

It is widely known that the inertial technique of the heavy-ball method can accelerate its convergence speed. In this paper, by embedding the inertial technique in the famous PRP conjugate gradient method, we propose a modified PRP conjugate gradient method with inertial extrapolation (PRPCG-IE) for sparse signal reconstruction. Its direction satisfies the sufficient descent property, which is independent of any line search. Global convergence of PRPCG-IE is established under some standard conditions. PRPCG-IE is applied to two sparse signal reconstruction problems with noise, and preliminary experimental results demonstrate the effectiveness of PRPCG-IE.

Sparse Bayesian Learning Based Multi Trajectory Tracking Algorithm For Direction of Arrival Trajectory Estimation

One of the applications of sequential sparse signal reconstruction is multi-target Direction of Arrival (DoA) trajectory estimation. In fact, each member of the support set is equivalent to the DoA of a moving target at each time instant. There is a mapping between the indices of the sparse vector and DoA values in continuous angle space. The key idea of this paper is to use the dynamic information of the continuous angular space to more accurately track sparse vectors and estimate the DoA trajectories of moving sources with time-varying acceleration based on the Sparse Bayesian Learning (SBL) framework. For this purpose, the members of the estimated support set are mapped to the continuous angular space at each instant. Then, the obtained DoAs are assigned to the available DoA trajectories using the Predictive-Description-Length (PDL) algorithm. In the following, the DoA of each source is predicted for the next time using the Kalman filter. Finally, the predicted DoAs are mapped to a sparse vector. The obtained sparse vector is used as the prior information for SBL-based sparse reconstruction. Simulation results show that the proposed algorithm, which is called SBL-MTT (Multi Trajectory Tracking), leads to an accurate reconstruction of successive sparse vectors in application of DoA trajectory estimation of moving sources.

Sparsity-based direction-of-arrival estimation in the presence of near-field and far-field interferences for small-scale platform sonar arrays.

For the sonar arrays mounted on an unmanned underwater vehicle (UUV), the direction-of-arrival (DOA) estimation of the far-field (FF) weak sources is influenced by the near-field (NF) interferences generated from the radiated self-noise of the UUV and the FF interferences simultaneously. To address the problem, a sparsity-based DOA estimation method resistant to the NF and FF interferences is proposed in this paper. This method isolates the FF signals from the NF signals by sparse reconstruction. Additionally, subspace projection is applied to address the masking problem of the weak target signal by the strong interferences in the spatial domain, effectively enhancing the capacity of estimating the DOA of the weak target signal in the presence of strong interferences. Numerical simulations and experimental results demonstrate the effectiveness of the proposed method. Compared to other advanced DOA estimation methods, the proposed method exhibits better DOA estimation performance in the presence of strong NF and FF interferences.

Integrated top-down process and voxel-based microstructure modeling for Ti-6Al-4 V in laser wire direct energy deposition process

Laser-wire metal additive manufacturing (AM) is one of the ideal direct energy deposition (DED) processes for creating large-scale parts with a medium level of complexity. However, the DED process involves complex thermal signatures and wide length scales making the fabrication of realistic AM components and part qualification often reliant on experimental trial-and-error optimization. While experimental measurements over the full volume of a part are valuable and necessary, measuring the entire area of a part is significantly laborious and practically infeasible, particularly for large parts in terms of cost and rapid qualification. Therefore, in this work, we developed an effective thermal and microstructure modeling framework based on the Johnson–Mehl-Avrami-Kolmogorov (JMAK) and Koistinen & Marburger (KM) models through a top-down approach that considers plate distortion-affected thermal profiles. A voxel-by-voxel simulation method is used to predict individual phase fractions of Ti-6Al-4 V. The predicted results were validated through detailed metallurgical measurements. A combined voxel-by-voxel approach with a sparse data reconstruction technique produced a near-perfect reconstruction of the original data. This approach anticipates a significant reduction in data points and computation time and resources. Lastly, we conclude with potential extensions of this work to other modeling efforts.

Sparse Signal Reconstruction: Sequential Convex Relaxation, Restricted Null Space Property, and Error Bounds

Sparse Signal Reconstruction: Sequential Convex Relaxation, Restricted Null Space Property, and Error Bounds

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.

Research on a three-dimensional radiation field reconstruction algorithm based on an improved 3D CNN

This article investigates the application of an improved three-dimensional convolutional neural network (3D CNN) for sparse data-based reconstruction of radiation fields. Sparse radiation data points are consolidated into structured three-dimensional matrices and fed into a self-attention integrated CNN, enabling the network to interpolate and produce complete radiation distribution grids. The model’s validity is assessed through experiments with randomly sourced radiation in scenarios both with and without shielding, as well as in refined grid configurations. Results indicate that in unshielded environments, a mere 5%(15 points) sampling yields an average relative error of 4%, while in shielded settings, a 7% (21 points) sampling maintains the error around 11%. In refined grid contexts, a 2% sampling rate suffices to limit the error to 6.58%. Thus, the improved 3D CNN is demonstrated to be highly effective for precise three-dimensional radiation field reconstruction in sparse data scenarios.

Oracle-Net for Nonlinear Compressed Sensing in Electrical Impedance Tomography Reconstruction Problems

Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with learned support estimation for compressed sensing sparse reconstructions, where the available measurements are nonlinear and possibly corrupted by noise. A graph neural network, named Oracle-Net, is proposed to predict the support from the nonlinear measurements and is integrated into a regularized recovery model to enforce sparsity. The derived nonsmooth optimization problem is then efficiently solved through a constrained proximal gradient method. Error bounds on the approximate solution of the proposed Oracle-based optimization are provided in the context of the ill-posed Electrical Impedance Tomography problem (EIT). Numerical solutions of the EIT nonlinear inverse reconstruction problem confirm the potential of the proposed method which improves the reconstruction quality from undersampled measurements, under sparsity assumptions.

Broadband multi‐carrier linear frequency modulation signal reception with subcarrier frequency offset deramp processing

AbstractIn this paper, a broadband multi‐carrier linear frequency modulation (LFM) signal reception method with subcarrier frequency offset deramp processing is proposed and investigated. The proposed frequency offset deramp processing is implemented by mixing the multi‐carrier LFM radar echo with a multi‐carrier LFM reference that has a different subcarrier frequency interval. With this design, the sampling rate of the radar receiver is remarkably reduced and crosstalk‐free separation of different subcarrier signals is easily conducted in the frequency domain. To fuse the multiple subcarriers and fill the frequency gaps, a sparse reconstruction method is employed to obtain the broadband response, which is essential for achieving high range resolution detection. The effectiveness of the proposed method is validated through an experiment in which the reception of an 8‐carrier LFM signal is conducted and a total bandwidth of 6 GHz after multi‐carrier fusion is demonstrated. An inverse synthetic aperture radar imaging experiment is also conducted with the results verifying the good potential of the proposed method in practical applications.

FilterGNN: Image feature matching with cascaded outlier filters and linear attention

The cross-view matching of local image features is a fundamental task in visual localization and 3D reconstruction. This study proposes FilterGNN, a transformer-based graph neural network (GNN), aiming to improve the matching efficiency and accuracy of visual descriptors. Based on high matching sparseness and coarse-to-fine covisible area detection, FilterGNN utilizes cascaded optimal graph-matching filter modules to dynamically reject outlier matches. Moreover, we successfully adapted linear attention in FilterGNN with post-instance normalization support, which significantly reduces the complexity of complete graph learning from O(N2) to O(N). Experiments show that FilterGNN requires only 6% of the time cost and 33.3% of the memory cost compared with SuperGlue under a large-scale input size and achieves a competitive performance in various tasks, such as pose estimation, visual localization, and sparse 3D reconstruction.

Flowfield reconstruction in a supersonic isolator based on proper orthogonal decomposition and sensor compression coupling under variable Mach numbers

The supersonic inflow passes through the shock train in the isolator of the scramjet to complete deceleration and pressurization, followed by combustion and energy release, providing strong thrust. When the back pressure generated by combustion is disturbed forward, the location of shock train leading edge (STLE) will also change accordingly. Once it moves to the entrance of the isolator, it will cause unstart. Accurately detecting STLE in the isolator of a scramjet is crucial for controlling the shock train and preventing the inlet from unstart. Therefore, based on the sparse reconstruction of compressive sensing and sensor compression coupling, a supersonic flowfield reconstruction model (POD-STLE) based on proper orthogonal decomposition (POD) was constructed to reconstruct the supersonic flowfield and detect the location of STLE in the supersonic isolator. The experiments were conducted on the shock oscillation under variable Mach numbers and back pressures, to construct the experimental dataset. Combining supersonic flowfield reconstruction and matrix decomposition, different sensor layouts were constructed, which can ensure accuracy and stability while saving sensor resources. The POD-STLE was applied to the flowfield reconstruction of the supersonic isolator, and the location of STLE was detected under variable and constant conditions, ultimately achieving the expected reconstruction effect and detection accuracy. This study provides a new research method for detecting the location of STLE in the supersonic isolator of a scramjet and provides technical for exploring supersonic flowfield.

Reconstructing Multiphase Flow Fields with Limited Pressure Observations Based on an Improved Transformer Model

In practical applications, the implementation of active cavitation control can significantly enhance the hydrodynamic performance of underwater vehicles. However, the sparsity of sensor information poses a substantial challenge to acquiring flow field states. Recent advances in deep learning offer reliable solutions to this problem. Specifically, deep learning methods, through the construction of sparse reconstruction models, establish connections between sparse observational information and flow field states with minimal or no prior knowledge. To reconstruct multiphase flow fields from sparse pressure observations on the hydrofoil surface, this work proposes a Transformer-based sparse reconstruction model. Test results on cavitation datasets demonstrate that the model's predictions of cavity contours, cavity lengths, and cavity volumes are highly consistent with actual results during the sheet cavity growth and cavity shedding stages. However, due to the highly unsteady nature of cavitation flow and the lack of far-field information, the model's prediction performance is limited during the cloud cavity aggregation and collapse stages. This model exhibits potential in the sparse reconstruction of multiphase flow fields, providing support for the observation of flow field states and active cavitation control.

Research on the Depth Image Reconstruction Algorithm Using the Two-Dimensional Kaniadakis Entropy Threshold.

The photon-counting light laser detection and ranging (LiDAR), especially the Geiger mode avalanche photon diode (Gm-APD) LiDAR, can obtain three-dimensional images of the scene, with the characteristics of single-photon sensitivity, but the background noise limits the imaging quality of the laser radar. In order to solve this problem, a depth image estimation method based on a two-dimensional (2D) Kaniadakis entropy thresholding method is proposed which transforms a weak signal extraction problem into a denoising problem for point cloud data. The characteristics of signal peak aggregation in the data and the spatio-temporal correlation features between target image elements in the point cloud-intensity data are exploited. Through adequate simulations and outdoor target-imaging experiments under different signal-to-background ratios (SBRs), the effectiveness of the method under low signal-to-background ratio conditions is demonstrated. When the SBR is 0.025, the proposed method reaches a target recovery rate of 91.7%, which is better than the existing typical methods, such as the Peak-picking method, Cross-Correlation method, and the sparse Poisson intensity reconstruction algorithm (SPIRAL), which achieve a target recovery rate of 15.7%, 7.0%, and 18.4%, respectively. Additionally, comparing with the SPIRAL, the reconstruction recovery ratio is improved by 73.3%. The proposed method greatly improves the integrity of the target under high-background-noise environments and finally provides a basis for feature extraction and target recognition.

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.

Hybrid Transformer and Convolution for Image Compressed Sensing

In recent years, deep unfolding networks (DUNs) have received widespread attention in the field of compressed sensing (CS) reconstruction due to their good interpretability and strong mapping capabilities. However, existing DUNs often improve the reconstruction effect at the expense of a large number of parameters, and there is the problem of information loss in long-distance feature transmission. Based on the above problems, we propose an unfolded network architecture that mixes Transformer and large kernel convolution to achieve sparse sampling and reconstruction of natural images, namely, a reconstruction network based on Transformer and convolution (TCR-Net). The Transformer framework has the inherent ability to capture global context through a self-attention mechanism, which can effectively solve the challenge of long-range dependence on features. TCR-Net is an end-to-end two-stage architecture. First, a data-driven pre-trained encoder is used to complete the sparse representation and basic feature extraction of image information. Second, a new attention mechanism is introduced to replace the self-attention mechanism in Transformer, and a hybrid Transformer and convolution module based on optimization-inspired is designed. Its iterative process leads to the unfolding framework, which approximates the original image stage by stage. Experimental results show that TCR-Net outperforms existing state-of-the-art CS methods while maintaining fast computational speed. Specifically, when the CS ratio is 0.10, the average PSNR on the test set used in this paper is improved by at least 0.8%, the average SSIM is improved by at least 1.5%, and the processing speed is higher than 70FPS. These quantitative results show that our method has high computational efficiency while ensuring high-quality image restoration.

Omni-directional wavenumber dictionary modified imaging method for orthotropic composites damage detection using ultrasonic guided waves

The sparse reconstruction imaging method is promising for detecting damage in isotropic and quasi-isotropic materials. However, its effectiveness relies on an accurate dictionary. When applied to orthotropic materials without accounting for wavenumber directionality, the accuracy of the dictionary degrades, leading to inaccurate damage localization. To address this limitation, this paper presents an omnidirectional wavenumber dictionary modified imaging method for orthotropic composites damage detection. The omni-directional wavenumber dispersion curve of ultrasonic guided waves is calculated numerically by converting of elastic stiffness coefficient of orthotropic composites at various propagation angles. A modified propagation model, informed by the omni-directional wavenumber dispersion curve, enhances the precision of the acoustic field dictionary. Utilizing a coherent matched field processor, the method compares the scattered signal's envelope with the acoustic field dictionary's envelope to generate an ambiguity function, which in turn forms a damage image. Simulation and experimental results confirm the method's superiority in resolving damage localization inaccuracies and artifacts typically associated with orthotropic composites. The proposed method exhibits enhanced signal-to-noise ratio and lower positioning error, facilitating precise multi-damage detection in orthotropic composites compared to existing methods.

Time Series Forecasting for Sparse Ring-shaped Array Photoacoustic Imaging Reconstruction

Abstract Photoacoustic computed tomography (PACT), which provides high optical absorption contrast and deep acoustic penetration, plays an important role in non-invasive biomedical imaging area. As the decrease of array elements, the reconstructed image suffers from severe artifacts. Recent studies utilize deep learning methods to improve the imaging quality of PACT based on image network design, but few were reported with raw data. To address this issue, this paper proposes a Wave to Wave Convolution Gate Recurrent-Net (WWCG-Net) to reconstruct photoacoustic image based on time series acoustic signal prediction. Simulation and experiment results show the superiority of our method compared with linear interpolation (LI) and eXtreme Gradient Boosting (XGBoost) in term of suppress artifact and improve resolution.

Robust sensing matrix design for the Orthogonal Matching Pursuit algorithm in compressive sensing

In compressive sensing, Orthogonal Matching Pursuit (OMP) is a greedy algorithm used for recovering sparse signals from their incomplete linear measurements. Conventionally, the OMP algorithm relies on both the measurement matrix and the measurement signal to reconstruct sparse signals. A sensing matrix can be designed to have a small mutual coherence with respect to (w.r.t.) the measurement matrix, which is used to boost the performance of the OMP algorithm in sparse signal reconstruction. Nevertheless, sensing matrices designed by current methods are vulnerable to measurement noises. In this paper, we begin by examining the underlying cause of the non-robustness to measurement noises exhibited by these sensing matrices. Subsequently, we propose a novel approach to design a robust sensing matrix capable of withstanding the influence of measurement noises. Finally, we conduct numerical simulations to demonstrate the effectiveness and robustness of the sensing matrix designed by the proposed method.

SBL-LCGL: sparse Bayesian learning based on Laplace distribution for robust cone-beam x-ray luminescence computed tomography

Objective. To address the quality and accuracy issues in the distribution of nanophosphors (NPs) using Cone-beam x-ray luminescence computed tomography (CB-XLCT) by proposing a novel reconstruction strategy.Approach. This paper introduces a sparse Bayesian learning reconstruction method termed SBL-LCGL, which is grounded in the Lipschitz continuous gradient condition and the Laplace prior to overcome the ill-posed inverse problem inherent in CB-XLCT.Main results. The SBL-LCGL method has demonstrated its effectiveness in capturing the sparse features of NPs and mitigating the computational complexity associated with matrix inversion. Both numerical simulation andin vivoexperiments confirm that the method yields satisfactory imaging results regarding the position and shape of the targets.Significance. The advancements presented in this work are expected to enhance the clinical applicability of CB-XLCT, contributing to its broader adoption in medical imaging and diagnostics.

A New Perspective for Scientific Modelling: Sparse Reconstruction Based Approach for Learning Time-Space Fractional Differential Equations

Abstract This paper studies a sparse reconstruction based approach to learn time-space fractional differential equations, i.e. to identify parameter values and particularly the order of the fractional derivatives. The approach uses a generalized Taylor series expansion to generate, in every iteration, a feature matrix which is used to learn the fractional orders of both, temporal and spatial derivatives by minimizing the LASSO operator using Differential Evolution algorithm. To verify the robustness of the method, numerical results for time-space fractional diffusion equation, wave equation, and Burgers? equation at different noise levels in the data are presented. Finally, the methodology is applied to a realistic example where underlying fractional differential equation associated to published experimental data obtained from an in-vitro cell culture assay is learned.