Sparse Reconstruction Algorithm Research Articles

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 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.

2D DOA and Polarization Estimation Using Parallel Synthetic Coprime Array of Non-Collocated EMVSs

For target detection and recognition in a complicated electromagnetic environment, the two-dimensional direction-of-arrival and polarization estimation using a polarization-sensitive array has been receiving increased attention. To efficiently improve the performance of such multi-parameter estimation in practice, this paper proposes a parallel synthetic coprime array with reduced mutual coupling and hardware cost saving and then presents a dimension-reduction compressive sensing-based estimation method. For the proposed array, the polarization types, numbers, and positions of antennas in each subarray are jointly considered to effectively mitigate mutual coupling in the physical array domain and to both enhance degrees of freedom and extend the aperture in the difference coarray domain with the limited physical antennas. By exploring the array configuration, the parameter estimation can be formulated as a block-sparse signal reconstruction problem, and then the one-dimensional sparse reconstruction algorithm is only used once to achieve multi-parameter estimation with automatic pair-matching. The theoretical analysis and simulation results are provided to demonstrate the superior performance of the proposed array and method over the existing techniques.

An Extremely Sparse Tomography Reconstruction of a Multispectral Temperature Field without Any a Priori Knowledge.

When undertaking optical sparse projection reconstruction, the reconstruction of the tested field often requires the utilization of a priori knowledge to compensate for the lack of information due to the sparse projection angle. In order to reconstruct the radiation field of unknown materials or in situations where a priori knowledge cannot be obtained, this paper proposes an extremely sparse tomography multispectral temperature field reconstruction algorithm that analyzes the similarity (the similarity here compares and calculates the Euclidean distance of the spectral emissivity values at various wavelengths between different spectral curves) of radiation characteristics of materials under the same pressure and concentration but different temperature, describes the similarity between the radiation information of the tested field using the dynamic time warping (DTW) algorithm, and uses the similarity sum of the radiation information among the subregions of the temperature field as the optimization objective. This is combined with the equation-constrained optimization algorithm and multispectral thermometry to establish the statistical law between the missing information and finally realize the reconstruction of the temperature field. Simulation experiments show that, without any a priori knowledge, the method in this paper can realize reconstruction of the temperature field with an accuracy of 1.53-12.05% under two projection angles and has fewer projection angles and stronger robustness than other methods.

Time-varying neurodynamic optimization approaches with fixed-time convergence for sparse signal reconstruction

Convergence speed is one of the most considerable features for sparse signal reconstruction algorithms. This paper introduces several novel fast time-varying neurodynamic optimization approaches (TVNOAs) with fixed-time convergence for sparse signal reconstruction. It is demonstrated that these trajectories converge to solutions within a fixed-time from arbitrary initial conditions, exhibiting a faster convergence rate due to the selection of appropriate time-varying coefficients. The fixed-time convergence of the proposed TVNOAs is investigated using the Polyak–Lojasiewicz condition. Moreover, explicit upper bounds for the settling time of TVNOAs are provided. Additionally, the robustness under bounded noises is further examined. Numerical experiments on sparse signal reconstruction validate the superiority of the proposed neurodynamic approaches.

Directional TV algorithm for image reconstruction from sparse-view projections in EPR imaging

Objective. Electron paramagnetic resonance (EPR) imaging is an advanced in vivo oxygen imaging modality. The main drawback of EPR imaging is the long scanning time. Sparse-view projections collection is an effective fast scanning pattern. However, the commonly-used filtered back projection (FBP) algorithm is not competent to accurately reconstruct images from sparse-view projections because of the severe streak artifacts. The aim of this work is to develop an advanced algorithm for sparse reconstruction of 3D EPR imaging. Methods. The optimization based algorithms including the total variation (TV) algorithm have proven to be effective in sparse reconstruction in EPR imaging. To further improve the reconstruction accuracy, we propose the directional TV (DTV) model and derive its Chambolle–Pock solving algorithm. Results. After the algorithm correctness validation on simulation data, we explore the sparse reconstruction capability of the DTV algorithm via a simulated six-sphere phantom and two real bottle phantoms filled with OX063 trityl solution and scanned by an EPR imager with a magnetic field strength of 250 G. Conclusion. Both the simulated and real data experiments show that the DTV algorithm is superior to the existing FBP and TV-type algorithms and a deep learning based method according to visual inspection and quantitative evaluations in sparse reconstruction of EPR imaging. Significance. These insights gained in this work may be used in the development of fast EPR imaging workflow of practical significance.

A Reduced Sparse Dictionary Reconstruction Algorithm Based on Grid Selection

A sparse dictionary reconstruction algorithm based on grid selection is introduced to solve the grid mismatch when using the sparse recovery space time adaptive processing (SR-STAP) algorithm. First, the atom most closely related to clutter is selected from the traditional dictionary through the spectral value dimensionality reduction method. The local mesh is divided around the selected atoms to create mesh cells, and the mesh cells that are most likely to appear in the real clutter points are judged according to the local selection iteration criteria. In this way, the mesh spacing is refined, the local mesh selection is carried out step by step, and the optimal atoms in the local region are constantly adjusted and selected to narrow the search region until the iteration termination condition is met. Finally, the space-time plane is divided using a novel meshing technique that centers around the optimal atom. By removing atoms beyond the maximum range of spatial and Doppler frequencies, the simplified sparse dictionary can overcome the mesh mismatch problem. The simulation results demonstrate that the algorithm enhances the sparse recovery accuracy of clutter space-time spectrum, mitigates the mesh mismatch effect, and boosts STAP performance.

Investigation on uncertainty quantification of transonic airfoil using compressive sensing greedy reconstruction algorithms

Uncertainty quantification constructs the stochastic responses of system output under uncertainties. Traditional uncertainty quantification methods such as Monte Carlo and Full-Rank Polynomial Chaos Expansion need large amounts of samples. Compressive Sensing has the advantages of requiring few observation samples and sparse reconstruction. By combining Compressive Sensing with uncertainty quantification, the samples in demand can be reduced. Nevertheless, the sparse reconstruction algorithms directly affect predicting accuracy, especially in a practical aerodynamic scenario. To compare the effect of two l0-minimization based greedy reconstruction algorithms, Orthogonal Matching Pursuit and Subspace Pursuit, this study adopts them into uncertainty quantification of RAE2822 airfoil considering geometrical uncertainties. The Polynomial Chaos Expansion is used to realize sparse representation and Structured Random Observation Matrix is constructed by randomly selecting from Gaussian quadrature set. The two greedy reconstruction methods are compared to Monte Carlo and Full-Rank Probabilistic Collocations on convergence, required samples and accuracy. The results show that both methods could achieve similar accuracy as Monte Carlo with much fewer samples. Besides, Orthogonal Matching Pursuit is able to precisely reconstruct original signal with proper sparsity estimation, while Subspace Pursuit provides more robust prediction for different cases. This study presents an efficient approach that integrates compressive sensing into uncertainty quantification of airfoils.

Evaluation on improved sparse signal reconstruction algorithm for trusted AI and DCS technology

The improved Sparse Signal Reconstruction (SR) algorithm for Trusted Artificial Intelligence (AI) and Distributed Compressed Sensing (DCS) technology was thoroughly investigated. The study verified its effectiveness and advantages in trusted AI and DCS systems, which have significant implications for enhancing the credibility, security, and performance of signal processing and AI algorithms. The reconstruction performance was evaluated using Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP), and Least Absolute Shrinkage and Selection Operator (LASSO). The analysis primarily focused on runtime, refactoring errors, and the number of successful reconstruction attempts. When K = 4, K = 6, K = 8, and K = 10, OMP outperformed BP and LASSO in terms of successful reconstructions, demonstrating better performance and higher reconstruction precision.

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.

Inverse-free distributed neurodynamic optimization algorithms for sparse reconstruction

This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L1-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L1-minimization problem into a distributed optimization model. To tackle such model, a three-layer inverse-free distributed algorithm is proposed by using projection operator and derivative feedback, which enjoys global convergence. To simplify the structure of this three-layer distributed algorithm, a time-varying parameter-based two-layer inverse-free distributed algorithm is designed, which has global convergence. Moreover, to accelerate convergence and further simplify the structure of this two-layer distributed algorithm, we develop a Tikhonov-like regularization-based single-layer inverse-free distributed algorithm, which achieves consensus within finite time for any given initial point and possesses an O(1/ξ(t)) convergence rate of the linear-equality constraint function. Finally, experimental results on signal and image reconstruction are presented to illustrate the efficiency of our inverse-free distributed algorithms.

Mobile edge assisted multi-view light field video system: Prototype design and empirical evaluation

Metaverse is recently envisioned as the main driver for immersive multimedia in future networks. Light field video (LFV), considered an intermediate transition scheme towards the metaverse, is conducive to sensing and reconstructing realistic scenes in the digital twins. However, the research on LFV systems still lacks comprehensive investigation, impeding their practical application. This paper addresses major technical challenges involved in LFV delivery through mobile networks, showing a trade-off between equipment cost, calibration effort, and workflow simplicity. It also considers the balance of communications and computations latency when maintaining reconstruction performance. Leveraging edge and cloud infrastructure, a novel Mobile Edge Assisted Multi-view Light-field-video System (MEAMLS) is proposed, integrating LFV collection, volumetric video construction, and an immersive viewing scheme. A custom-made LFV capture array is designed to capture real-world scenes, while employing a learning method-integrated edge server to facilitate adaptive LFV coding. Moreover, a fast sparse reconstruction algorithm is established, leveraging edge–cloud collaboration to minimize computation latency during volumetric video construction. Intelligent service for users is deployed on edge to enable viewport-driven virtual reality viewing. By providing an immersive visual experience, the proposed MEAMLS bridges the physical world and its digital twins. The system is prototyped on a realistic 5G network to empirically validate the performance under static and dynamic circumstances. Experimental results yield fundamental insights for designing mobile edge networks-assisted LFV system from the perspective of transmission resource, adaptability, and deployment.

Sparse Microwave Imaging Algorithm Based on L1/2 Threshold Iteration and an Approximate Observation Operator

Aiming at the problems of synthetic-aperture radar (SAR), such as high sampling rate and vulnerability to noise interference in imaging, a sparse reconstruction algorithm based on approximate observation and L1/2 threshold iteration is proposed in this paper. To solve the problem of the large dimension and high computational complexity of the measurement matrix, a sparse reconstruction model based on approximate observation is constructed, and a threshold iterative algorithm to rapidly solve the L1/2 regularization problem is introduced, which can realize sparse signal reconstruction with fewer sampling data and quickly solve the problem. The simulation results of point targets and the measured data of spaceborne SAR show that compared with the traditional matched filtering algorithm and L1 threshold algorithm based on a two-step iteration, the proposed sparse reconstruction algorithm has a faster iteration speed and improves the image quality.

Adaptive milling chatter identification based on sparse dictionary considering noise estimation and critical bandwidth analysis

As one of the most unfavorable factors, chatter will seriously hinder the improvement of production efficiency. The weak chatter identification is an effective method for stable cutting. In this paper, a weak chatter identification method is developed using sparse dictionary on account of the milling dynamic responses. As the bases for chatter identification, chatter frequencies are calculated based on the milling dynamic equations. In order to decrease false alarm rate due to the measured background noise, the noise estimation based filtering is proposed. Besides, in consideration of the parameter uncertainty, an adaptive critical bandwidth analysis is implemented with the developed energy proportion index in case of missed alarm. Then, the sparse dictionary matrix is constructed based on the obtained chatter frequencies and critical bandwidth. Finally, the gradient projection for sparse reconstruction (GPSR) algorithm is adopted for chatter frequencies extraction. The proposed method can decrease the measured background noise, obtain critical chatter band and extract weak chatter frequencies accurately. Experimental results shows that the developed method can be successful in weak chatter identification.

Sparse reconstruction of EMT based on compressed sensing and Lp regularization with the split Bregman method

Electromagnetic tomography (EMT) is a promising tomographic method used to reconstruct the conductivity and permeability material owing to its contactless nature. However, the EMT inverse problem is ill-posed due to the soft-field characteristic and limited prior information, which will severely affect the imaging quality. To address the challenge, a novel sparse reconstruction algorithm is proposed in this article on the basis of compressed sensing (CS) and Lp regularization. The EMT inverse problem is converted into the L1 norm regularization problem using the advantages of the compressed sensing theory. To combine the merits of L1 and L2 regularization, Lp regularization is deployed as the regularizer taking the place of L1 norm, which can overcome the over-smoothing and over-sparsity of the reconstruction objects. A modified split Bregman (SB) method is exploited to effectively cope with the Lp regularization problem. An accelerating method is further applied to improve the reconstruction speed. The sensitivity matrix calculation is performed by the perturbation method. Simulation studies are implemented to show the superiority of the presented method in comparison with the classical methods. The effectiveness of the proposed method is further validated by the developed EMT system. Experimental results confirm that the proposed method has better imaging capability, which provides a great candidate for the practical application of EMT.

Sparse underwater acoustics signal reconstruction on shallow water and its performance evaluation

We performed a simple underwater acoustics signal transmission on an experimental pond and shallow water in Surabaya harbor. First, we tested the sparse reconstruction algorithm on the underwater signal transmitted in the experimental pond to evaluate the sparsity limit of reconstructed signal. The transmitted signal consisted of a train of sinusoidal and pure tone with variation of frequency and duration. From the results, it is concluded that the proposed algorithm performed well in our experimental pond. However, it performed poorly with respect to distance on a shallow water environment.

An edge-preserving total nuclear variation minimization algorithm in EPR image reconstruction

ObjectiveCurrently, slow scanning speed has become a technical bottleneck limiting the development of electron paramagnetic resonance imaging (EPRI), a novel oxygen imaging modality. Image reconstruction from sparse-view projections is an important imaging configuration to achieve fast scanning in EPRI. However, EPR images reconstructed from sparse-view projections using traditional analytic algorithms suffer from sparse artifacts, causing severe image degradation. In this work, we aim to use an optimization-based approach to achieve high-precision sparse reconstruction for EPRI. Methods. Inspired by the success of total nuclear variation (TVN) for denoising multi-channel spectral CT images and adaptive-weighted total variation (awTV) for improving the edge-preserving performance of TV, we proposed an edge-preserving total nuclear variation (EPTVN) minimization algorithm for sparse reconstruction in EPRI. The EPTVN combines the advantage of TVN in modelling structural similarity and low-rank prior between multi-channel images for denoising with the advantage of awTV for edge-preserving, which can better protect the edge structure of images while suppressing sparse artifacts. Results. We designed two numerical phantoms with different properties, a piecewise-constant phantom and a gradient phantom, and a physical phantom, and then performed inverse crime, simulation study and real-data study. Experimental results show that the EPTVN minimization algorithm can reconstruct more accurate EPR images from sparse-view projections for both the numerical and physical phantoms. Significance. The proposed method can effectively suppress sparse artifacts and protect edge structures of reconstructed images, thus achieving high-precision sparse-view reconstruction for EPRI. The insights of this work can also be applied to multi-channel image denoising tasks.

A novel method for noise reduction of blade tip timing signals based on sparse representation and dictionary learning

Blade Tip Timing Technology (BTT) is a new type of blade vibration measurement method with non-contact measurement capabilities, which is associated with high efficiency and convenience. However, due to under-sampling feature of the BTT signal, the method can only measure part of the vibration information. Therefore, various BTT spectral reconstruction algorithms have been developed based on the under-sampling feature and sparsity of the blade vibration spectrum. Because of the harsh working environment of the blades, BTT signal typically contains high-level Gaussian noise in actual measurement, which significantly reduces frequency-domain sparsity and even aliases the vibration modals, resulting in a decrease in the performance of sparse reconstruction algorithms. In this paper, a multi-sequences BTT signal noise reduction method is proposed, which is based on sparse representation to suppress Gaussian noise. Through appropriately modifying the constraint in the ℓ0 optimization problem, the method filters out the noise elements in the sparse vector of the BTT signal. Then, denoising is completed by sparse inverse transformation. Finally, a global average-based singular value decomposition dictionary learning algorithm (GA-K-SVD) is proposed to generate an over-complete sparse dictionary which is adaptable to the original signal, to increase the effectiveness of GA-K-SVD. At last, simulation and experience are carried out to verify the performance optimization effect for sparse reconstruction algorithm and the effectiveness of proposed noise reduction method.

Noise-suppression algorithm of GM-APD lidar based on Markov random field

Background light easily affects a Geiger-mode avalanche photodiode (GM-APD) laser imaging, detection, and ranging (Lidar), and its detection ability is significantly reduced in strong light environments. Improving imaging performance under a low signal-to-back ratio has become critical. A GM-APD lidar noise-suppression algorithm based on a Markov random field is proposed. The field objective function and prior model are established using similar centre and adjacent pixel features. Both enhance the feature difference between a strong background light and a weak echo signal and improve the ability of weak echo signal reconstruction under an ultra-low signal-to-background ratio (SBR). Imaging experiments of long-distance building targets under varying illumination verified the noise-suppression ability of the algorithm. When the SBR is 0.0055, target recovery can reach 19.40%, and recovery of the whole array image can reach 60.94%. Compared with the sparse Poisson intensity reconstruction algorithm, the image signal-to-noise ratio is improved by 83 dB, and the average depth error was reduced by 36.14 cm. The proposed algorithm improves the imaging performance under ultra-low SBR; it significantly promotes the development of GM-APD lidar all-time applications.

Improved sparse domain super-resolution reconstruction algorithm based on CMUT.

A novel breast ultrasound tomography system based on a circular array of capacitive micromechanical ultrasound transducers (CMUT) has broad application prospects. However, the images produced by this system are not suitable as input for the training phase of the super-resolution (SR) reconstruction algorithm. To solve the problem, this paper proposes an improved medical image super-resolution (MeSR) method based on the sparse domain. First, we use the simultaneous algebraic reconstruction technique (SART) with high imaging accuracy to reconstruct the image into a training image in a sparse domain model. Secondly, we denoise and enhance the contrast of the SART images to obtain improved detail images before training the dictionary. Then, we use the original detail image as the guide image to further process the improved detail image. Therefore, a high-precision dictionary was obtained during the testing phase and applied to filtered back projection SR reconstruction. We compared the proposed algorithm with previously reported algorithms in the Shepp Logan model and the model based on the CMUT background. The results showed significant improvements in peak signal-to-noise ratio, entropy, and average gradient compared to previously reported algorithms. The experimental results demonstrated that the proposed MeSR method can use noisy reconstructed images as input for the training phase of the SR algorithm and produce excellent visual effects.