Sparse Signal 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.

A D* orthogonal matching pursuit algorithm for time-varying channel estimation.

Orthogonal matching pursuit (OMP) combined with the A* search algorithm (A*OMP) exhibits robust reconstruction capabilities for synthesizing sparse data and signals, achieving relatively low reconstruction errors and a higher exact recovery ability than conventional OMP. However, A*OMP is only suitable for static channel estimation and cannot be applied to dynamic scenarios. This is because the channel delays for several consecutive orthogonal frequency-division multiplexing blocks per frame are similar and the path gains exhibit temporal correlation. This paper introduces a dynamic OMP approach (D*OMP) that employs a heuristic function of A*OMP and a unique reverse process, enabling sparse solutions to be identified in unknown and changing environments. The proposed method is highly practical for joint channel estimation across multiple blocks. Simulation and sea trial results indicate that D*OMP not only possesses superior channel recovery accuracy, but also has a more efficient channel reconstruction process, outperforming both A*OMP and conventional OMP.

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.

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

Hyperparameter free sparse estimation for wideband multiple‐input‐multiple‐output radar direction finding without secondary data

AbstractThe estimation of target directions of arrival (DOA) for wideband multiple‐input‐multiple‐output (MIMO) radar is investigated in this article. First, the authors establish a signal model for wideband MIMO radar systems. Then, an algorithm is proposed to estimate the target angles without secondary data (i.e. the training data from slow‐time is not required).The proposed algorithm unitises the spatial sparsity of target signals and it is derived under the Bayesian framework. It can estimate the spatial pseudo‐spectra of the targets through cyclic optimisation. Additionally, it is hyperparameter‐free and guarantees convergence. To analyse the performance of the proposed algorithm, the Cramér‐Rao bound (CRB) is derived for DOA estimation with wideband MIMO radar. Numerical examples demonstrate that even without secondary data, the proposed algorithm can accurately estimate the DOA of the targets.

New scheme of cooperative compressed spectrum sensing

Abstract This study addresses key challenges in sparse signal recovery and compressed spectrum sensing (CSS), focusing on low signal-to-noise ratios (SNR), and the computational complexity of cooperative systems. Motivated by the need for faster and more accurate recovery techniques, we first investigate and generalize the Reduced-Set Matching Pursuit (RMP) algorithm, which overcomes the speed and accuracy limitations of conventional greedy algorithms. Secondly, we propose a novel spatial averaging technique that enhances detection performance by exploiting data from multiple users to counteract low SNR. Lastly, we integrate cooperation into CSS, further improving the detection capabilities during the recovery process. Compared to existing techniques like Joint Sparse Recovery (JSR) and CoSaMP, which face computational and accuracy constraints in real-time applications, the RMP algorithm, combined with the Virtual method (data transformation) and AND fusion rule, delivers superior performance than JSR methods. Moreover, spatial averaging significantly increases the probability of cooperative detection Q d , with SNR increasing linearly by a factor of L − 1 per channel. The results are validated through the implementation of SDR. These findings demonstrate the potential of RMP and cooperation to overcome current limitations in CSS, advancing the state-of-the-art in spectrum sensing for collaborative networks.

SMAR: self-supervised mobile application recommendation based on graph convolutional networks

PurposeWith the exponential growth of mobile applications, recommending suitable mobile applications to users becomes a critical challenge. Although existing methods have made achievements in mobile application recommendation by leveraging graph convolutional networks (GCNs), they suffer from two limitations: the reliance on a singular acquisition path leads to signal sparsity, and the neighborhood aggregation method exacerbates the adverse impact of noisy interactions. This paper aims to propose SMAR, a self-supervised mobile application recommendation approach based on GCN, which is designed to overcome existing challenges by using self-supervised learning to create an auxiliary task.Design/methodology/approachIn detail, this method uses three distinct data augmentation techniques node dropout, edge dropout and random walk, which create varied perspectives of each node. Then compares these perspectives, aiming to ensure uniformity across different views of the same node while maintaining the differences between separate nodes. Ultimately, auxiliary task is combined with the primary supervised task using a multi-task learning framework, thereby refining the overall mobile application recommendation process.FindingsExtensive experiments on two real datasets demonstrate that SMAR achieves better Recall and NDCG performances than other strong baselines, validating the effectiveness of the proposed method.Originality/valueIn this paper, the authors introduce self-supervised learning into mobile application recommendation approach based on GCNs. This method enhances traditional supervised tasks by using auxiliary task to provide additional information, thereby improving signal accuracy and reducing the influence of noisy interactions in mobile application recommendations.

A Comprehensive Analysis of Traditional and Advanced Approaches of Image Restoration Techniques

Introduction: Tremendous developments in multimedia technology have promoted a massive amount of research in image and video processing. As imaging technologies are rapidly increasing, it is becoming essential to use images in almost every application in our day-today life. Materials and Method: This paper presents a comparative analysis of various image restoration approaches, ranging from fundamental methods to advanced techniques. These approaches aim to improve the quality of images that have been degraded during acquisition or transmission. A brief overview of the image restoration approaches is mentioned in the paper, which are as follows: Wiener Filter: The Wiener filter is a classical approach used for image restoration. It is a linear filter that minimizes the mean square error between the original image and the restored image. Inverse Filter: The inverse filter is another traditional restoration technique. It attempts to invert the degradation process to recover the original image. However, inverse filtering is highly sensitive to noise and tends to amplify noise artifacts. Linear and Nonlinear Filtering: These methods involve applying linear or nonlinear filters to the degraded image to enhance its quality. Linear filters, such as Gaussian filters, can effectively reduce noise but may blur the image. Nonlinear filters, such as median filters, can preserve edges while reducing noise. Compressive Sensing (CS) Restoration Approaches: Compressive sensing is a signal processing technique that exploits the sparsity of signals or images to reconstruct them from fewer measurements. CS-based restoration methods aim to recover high-quality images from compressed or incomplete measurements. Neural Networks Approaches: With the advancements in deep learning, neural networks have been widely used for image restoration tasks. Convolutional neural networks (CNNs) and generative adversarial networks (GANs) have shown promising results in restoring degraded images by learning from large datasets. Result: The paper likely provides a detailed analysis and comparison of these approaches, highlighting their strengths, weaknesses, and performance in different scenarios. Conclusion: This paper aims to improve the quality of restored images. Several image restoration approaches have been compared, and they have exhibited enhanced performance compared to several existing image restoration approaches.

Marine remote target signal extraction based on 128 line-array single photon LiDAR

LiDAR technology has garnered significant attention in recent years due to its superior directivity, high resolution, and precise 3D information acquisition capabilities, making it indispensable in navigation systems. Among its variants, single-photon LiDAR stands out for maritime applications, owing to its reduced power consumption and extended detection range. However, the high sensitivity of single-photon detectors often results in substantial noise, necessitating effective denoising before data can be utilized for identification, tracking, and other purposes. In this study, we present a novel 128-line, 1550 nm shipborne long-range single-photon LiDAR system, with data collected and analyzed in maritime environments. This system contends with challenges such as a large dynamic range, abundant noise photons, and the complexity of sea surface conditions. To address these issues, we propose an efficient and adaptive denoising algorithm based on the k-th nearest neighbor (KNN) methodology. By examining the distribution characteristics of signal and noise photons, our approach enables target extraction even under conditions of intense noise and sparse signals. Our method exhibits robust adaptability across various detection scenarios. Experimental evaluations demonstrate its efficacy, accurately identifying targets at distances of 3.2 km in clear weather and 1.6 km in foggy conditions.

Decomposition-Estimation-Reconstruction: An Automatic and Accurate Neuron Extraction Paradigm.

The extraction of spatiotemporal neuron activity from calcium imaging videos plays a crucial role in unraveling the coding properties of neurons. While existing neuron extraction approaches have shown promising results, disturbing and scattering background and unused depth still impede their performance. To address these limitations, we develop an automatic and accurate neuron extraction paradigm, dubbed as decomposition-estimation-reconstruction (DER), consisting of D-procedure, E-procedure, and R-procedure. Specifically, the D-procedure first decomposes the raw data into a low-rank background and a sparse neuron signal, and regularizes L0 -norm priors of intensity and gradient of the neuron signal to suppress blurring and artifact effects. Then, the E-procedure estimates the depth-dependent transmission of the neuron signal based on its bright and dark channel priors. The R-procedure finally integrates the depth estimation of the neuron signal as a content-importance weight into a constrained non-negative matrix decomposition framework, which facilitates accurate neuron locations to boost the quality of extracted neurons. These three procedures are coupled in a cascade manner, where the former copes with calcium imaging data to facilitate the subsequent one. Comprehensive experiments on neuron extraction from calcium imaging videos demonstrate the superiority of our DER paradigm in both qualitative results and quantitative assessments over state-of-the-art methods.

A threshold activation-based simplified Lv's transform algorithm for transient multi-component linear frequency modulation signals analysis.

The high sampling rate in modern digital systems generates a large scale of data. To address the computational burden, this paper proposes a threshold activation-based simplified Lv's transform (SLVT) algorithm to analyze the transient multi-component linear frequency modulation signals. Only the signal arrival can trigger the signal analysis. This mechanism alleviates the computation pressure because of the sparsity of signals. The threshold activation mechanism enables transient signal detection and sampling rate adjustment, thereby enhancing the efficiency and effectiveness of the analytical process. The simplified Lv's transform (LVT) removes redundant computations on stretch weighting and the Discrete Fourier Transform (DFT) in Lv's transform. SLVT uses the efficient Bluestein chirp-z algorithm to implement the stretch keystone transform. The comparison results show that SLVT reduces the computational complexity of the original LVT by at least 30.8%. This algorithm exhibits superior performance compared to other advanced signal processing methods, such as discrete chirp Fourier transform, fractional Fourier transform, and Radon Wigner transform algorithms, in terms of parameter extraction accuracy, computational complexity, and execution time. Moreover, the implementation of a field programmable gate array accelerates SLVT computing by a factor of 116 in comparison to the CPU (Central Processing Unit) platform.

Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

This paper presents a strategy called the alternating iterative minimization method (AIMM), aimed at enhancing the precision of direction of arrival (DOA) estimation when utilizing an acoustic vector sensor array (AVSA) with unknown swing deviation elements (SDEs). The AVSA model with unknown SDEs is formulated by incorporating the swing deviation parameter. Later, to estimate the swing deviation matrix (SDM) and the sparse signal power by using the alternating iteration method, the auxiliary cost functions with respect to SDM and the sparse signal power are formulated based on the regularized weighted least squares (RWLS) and regularized covariance matrix fitting (RCMF) criteria. Furthermore, their analytical expressions have also been quantified. In order to mitigate the effect of unknown SDEs on the accuracy of DOA estimation, any sub-time segment (STS) in the dataset is selected as the reference to convert the received data of different STS into the reference STS using the estimated SDM. The simulation and experimental outcomes conclusively represent the effectiveness of the suggested TSIM approach using AVSA in handling unknown SDEs.

Compressing and Recovering Short-Range MEMS-Based LiDAR Point Clouds Based on Adaptive Clustered Compressive Sensing and Application to 3D Rock Fragment Surface Point Clouds.

Short-range MEMS-based (Micro Electronical Mechanical System) LiDAR provides precise point cloud datasets for rock fragment surfaces. However, there is more vibrational noise in MEMS-based LiDAR signals, which cannot guarantee that the reconstructed point cloud data are not distorted with a high compression ratio. Many studies have illustrated that wavelet-based clustered compressive sensing can improve reconstruction precision. The k-means clustering algorithm can be conveniently employed to obtain clusters; however, estimating a meaningful k value (i.e., the number of clusters) is challenging. An excessive quantity of clusters is not necessary for dense point clouds, as this leads to elevated consumption of memory and CPU resources. For sparser point clouds, fewer clusters lead to more distortions, while excessive clusters lead to more voids in reconstructed point clouds. This study proposes a local clustering method to determine a number of clusters closer to the actual number based on GMM (Gaussian Mixture Model) observation distances and density peaks. Experimental results illustrate that the estimated number of clusters is closer to the actual number in four datasets from the KEEL public repository. In point cloud compression and recovery experiments, our proposed approach compresses and recovers the Bunny and Armadillo datasets in the Stanford 3D repository; the experimental results illustrate that our proposed approach improves reconstructed point clouds' geometry and curvature similarity. Furthermore, the geometric similarity increases to 0.9 above in our complete rock fragment surface datasets after selecting a better wavelet basis for each dimension of MEMS-based LiDAR signals. In both experiments, the sparsity of signals was 0.8 and the sampling ratio was 0.4. Finally, a rock outcrop point cloud data experiment is utilized to verify that the proposed approach is applicable for large-scale research objects. All of our experiments illustrate that the proposed adaptive clustered compressive sensing approach can better reconstruct MEMS-based LiDAR point clouds with a lower sampling ratio.

Signal recognition based on transfer learning for Φ-OTDR fiber optic distributed disturbance sensor

Abstract Traditional classification models for optical fiber vibration signals can achieve good recognition results when there are a large number of samples. However, it is difficult to obtain sufficient training samples in real scenes. A method of Φ-OTDR sensor signal recognition based on VGGish transfer learning is proposed in this paper. Firstly, a selection indicator is designed to filter out vibration signals from sparse signals. Then, the VGGish network pretrained for sound classification is used for transfer learning as a feature extractor for optical fiber vibration signals. This method was applied to classify 6 kinds of optical fiber vibration signals. When the number of training samples is reduced to 480 samples, the method can still achieve 84.17% classification accuracy. Compared to the method of training from scratch, this proposed method reduces training time by 73.9%.

Hybrid Block Chaotic Compressive Sensing and Chaotic Scrambling Algorithms for Color Image Encryption System

This paper suggests a new image encryption algorithm based on block compressive sensing (BCS) and chaotic scrambling techniques. With compressive sensing (CS), signals can be sampled much lower than the Nyquist-Shannon rate while preserving their information content. BCS can be used as a one-step process by using a 3D logistic chaotic map, the measurement matrix is used as a secret key for encryption. BCS algorithm used an individual image reconstruction algorithm that leverages l_1norm minimization to promote signal sparsity, and a smoothing operator to enhance image quality. An encrypted image is first decomposed into three sub-images based on the tricolor theory; then, a discrete wavelet transform is used to sparsely process the three decomposed images. A 2D Henon map is used to scramble the compressed image after compression. This process further enhances the security of the system by increasing the complexity of the encryption process. The results showed that the proposed system provides better security and has a lower computational complexity than other methods. Furthermore, the proposed system is resistant to known attacks such as brute force and statistical attacks.

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.

Multi-angle speed-of-sound imaging with sparse sampling to characterize medical tissue properties

Medical Speed-of-sound (SoS) imaging, which can characterize medical tissue properties better by quantifying their different SoS, is an effective imaging method compared with conventional B-mode ultrasound imaging. As a commonly used diagnostic instrument, a hand-held array probe features convenient and quick inspection. However, artifacts will occur in the single-angle SoS imaging, resulting in indistinguishable tissue boundaries. In order to build a high-quality SoS image, a number of raw data are needed, which will bring difficulties to data storage and processing. Compressed sensing (CS) theory offers theoretical support to the feasibility that a sparse signal can be rebuilt with random but less sampling data. In this study, we proposed an SoS reconstruction method based on CS theory to process signals obtained from a hand-held linear array probe with a passive reflector positioned on the opposite side. The SoS reconstruction method consists of three parts. Firstly, a sparse transform basis is selected appropriately for a sparse representation of the original signal. Then, considering the mathematical principles of SoS imaging, the ray-length matrix is used as a sparse measurement matrix to observe the original signal, which represents the length of the acoustic propagation path. Finally, the orthogonal matching pursuit algorithm is introduced for image reconstruction. The experimental result of the phantom proves that SoS imaging can clearly distinguish tissues that show similar echogenicity in B-mode ultrasound imaging. The simulation and experimental results show that our proposed method holds promising potential for reconstructing precision SoS images with fewer signal samplings, transmission, and storage.

Hybrid Hu-Storey type methods for large-scale nonlinear monotone systems and signal recovery

We propose two hybrid methods for solving large-scale monotone systems, which are based on derivative-free conjugate gradient approach and hyperplane projection technique. The conjugate gradient approach is efficient for large-scale systems due to low memory, while projection strategy is suitable for monotone equations because it enables simply globalization. The derivative-free function-value-based line search is combined with Hu-Storey type search directions and projection procedure, in order to construct globally convergent methods. Furthermore, the proposed methods are applied into solving a number of large-scale monotone nonlinear systems and reconstruction of sparse signals. Numerical experiments indicate the robustness of the proposed methods.

The stable reconstruction of strongly-decaying block sparse signals

The stable reconstruction of strongly-decaying block sparse signals

Stretched non-negative matrix factorization

A novel algorithm, stretchedNMF, is introduced for non-negative matrix factorization (NMF), accounting for signal stretching along the independent variable’s axis. It addresses signal variability caused by stretching, proving beneficial for analyzing data such as powder diffraction at varying temperatures. This approach provides a more meaningful decomposition, particularly when the component signals resemble those from chemical components in the sample. The stretchedNMF model introduces a stretching factor to accommodate signal expansion, solved using discretization and Block Coordinate Descent algorithms. Initial experimental results indicate that the stretchedNMF model outperforms conventional NMF for datasets exhibiting such expansion. An enhanced version, sparse-stretchedNMF, optimized for powder diffraction data from crystalline materials, leverages signal sparsity for accurate extraction, especially with small stretches. Experimental results showcase its effectiveness in analyzing diffraction data, including success in real-time chemical reaction experiments.