Compressive Sensing Research Articles

Sparse recovery by genetic algorithms for acoustic testing applications

Various acoustic testing applications involve solving inverse problems from acoustic measurements, such as acoustic imaging and duct mode identification. In these problems, the physical quantity to be inferred is sparse, which allows applications of certain sparse recovery techniques, such as the compressive sensing. But such methods usually involve very complex theory, which therefore set a high threshold for beginners. By contrast, this work proposes a similar but much simpler method based on the well-known genetic algorithm, which borrows only a few easily understood concepts from nature evolution and can rely on easily accessed software/toolboxes. The performance of the developed method is demonstrated by two acoustic testing experiments in an anechoic chamber, i.e., acoustic imaging and duct mode identification.

Analyses of the tail-[formula omitted] minimization for fast and enhanced sparse selections

We investigate the effectiveness and efficiency of the iterative tail-ℓ2 minimization (tail-ℓ2-min) technique for its sparse selection capabilities. We conduct profile analyses on the tail-ℓ2-min, establishing the equivalence of the tail-ℓ2-min problem to a two-stage profile ℓ2 formulation, both featuring analytical solutions. The tail null space property (NSP) of sensing matrix A is shown to be equivalent to the NSP of the newly defined profile matrix Ã. Besides the error bound analysis for the tail-ℓ2-min under the typical tail-NSP condition, a novel error bound of the tail-ℓ2-min formulation is also established without relying on NSP or restricted isometry property (RIP) assumptions. It merely contains tractable coefficients of A, and offers insights into successful recovery, with the observation of the convergent iterative procedure. Numerical studies and the applications to image reconstruction demonstrate the superiority and fast convergence of the tail-ℓ2 sparse solution over state-of-the-art sparse selection methodologies. The sparsity level of a signal that the tail-ℓ2 profile algorithm guarantees the recovery is around 41% higher than that of the basis pursuit algorithm. The analytical solutions of the tail-ℓ2 method at each iteration also ensure that the tail-ℓ2 sparse recovery process is notably fast, especially for high dimensions and high sparsity levels.

Approximate Observation Weighted ℓ2/3 SAR Imaging under Compressed Sensing.

Compressed Sensing SAR Imaging is based on an accurate observation matrix. As the observed scene enlarges, the resource consumption of the method increases exponentially. In this paper, we propose a weighted ℓ2/3-norm regularization SAR imaging method based on approximate observation. Initially, to address the issues brought by the precise observation model, we employ an approximate observation operator based on the Chirp Scaling Algorithm as a substitute. Existing approximate observation models typically utilize ℓq(q = 1, 1/2)-norm regularization for sparse constraints in imaging. However, these models are not sufficiently effective in terms of sparsity and imaging detail. Finally, to overcome the aforementioned issues, we apply ℓ2/3 regularization, which aligns with the natural image gradient distribution, and further constrain it using a weighted matrix. This method enhances the sparsity of the algorithm and balances the detail insufficiency caused by the penalty term. Experimental results demonstrate the excellent performance of the proposed method.

Blade tip timing signals parameters identification based on Displacement Offset Decreased and Compressed Sensing

High-speed rotating blade vibration monitoring is of great significance for the safe operation of turbomachinery. Blade Tip Timing (BTT) is considered a promising technology in the field of blade vibration monitoring. The BTT signal analysis has the following problem, the displacement offset was caused by speed variation which affected the accuracy of the blade vibration parameter identification. Owing to the under-sampled characteristics of the BTT signals and multiple sensor data are required to identify the parameters. The accurate extraction of blade vibration characteristics is challenging. Thus, a vibration analysis method is proposed based on Displacement Offset Decreased and Compressed Sensing (DOD-CS). Firstly, the BTT signal pairwise is subtracted to reduce the impact of the displacement offset, and based on the subtractive results, a basis function is constructed to rebuild the dictionary matrix of the compressed sensing method. Then, we solved the signal sparse representation equation and obtained the spectrum estimation result, that is, the structure vibration parameters. The analysis of simulation data shows that the parameter identification accuracy of the DOD-CS method is higher than that of the OMP-CS (Orthogonal Matching Pursuit and Compressed Sensing) method, and the identification errors of frequency and amplitude are within 1% and 5%, respectively. The experimental results confirm the feasibility of the proposed method in identifying vibration parameters. Compared with existing methods, the innovation of the proposed method is that it eliminates the influence of displacement offset on the accuracy of parameter identification. For under-sampled signals, only two sensor data information are needed to complete spectrum estimation and parameter identification.

A Lightweight Recurrent Learning Network for Sustainable Compressed Sensing

Recently, deep learning-based compressed sensing (CS) has achieved great success in reducing the sampling and computational cost of sensing systems and improving the reconstruction quality. These approaches, however, largely overlook the issue of the computational cost; they rely on complex structures and task-specific operator designs, resulting in extensive storage and high energy consumption in CS imaging systems. In this article, we propose a lightweight but effective deep neural network based on recurrent learning to achieve a sustainable CS system; it requires a smaller number of parameters but obtains high-quality reconstructions. Specifically, our proposed network consists of an initial reconstruction sub-network and a residual reconstruction sub-network. While the initial reconstruction sub-network has a hierarchical structure to progressively recover the image, reducing the number of parameters, the residual reconstruction sub-network facilitates recurrent residual feature extraction via recurrent learning to perform both feature fusion and deep reconstructions across different scales. In addition, we also demonstrate that, after the initial reconstruction, feature maps with reduced sizes are sufficient to recover the residual information, and thus we achieved a significant reduction in the amount of memory required. Extensive experiments illustrate that our proposed model can achieve a better reconstruction quality than existing state-of-the-art CS algorithms, and it also has a smaller number of network parameters than these algorithms. Our source codes are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/C66YU/CSRN</uri> .

Characterization of 3D printed samples from biomass-fungi composite materials

Biomass-fungi composite materials are derived from sustainable sources and can biodegrade at the end of their service. In these composite materials, the biomass particles (made from agricultural waste such as hemp hurd) act as the substrate, and a network of fungal hyphae grow through and bind the biomass particles together. These composite materials can be used to manufacture products traditionally made from petroleum-based plastics. Potential applications of these products are in the packaging, furniture, and construction industries. Typically, molding-based methods are used to manufacture products using these composite materials. Recently, the authors reported a novel 3D printing-based method using these composite materials. This paper reports a follow-up investigation into the characterization of 3D printed samples from biomass-fungi composite materials. Tensile and compressive testing samples were shaped using molds from a portion of each printed sample. Mechanical properties of these tensile and compressive testing samples and chemical properties of the printed samples were measured. Tensile and compressive testing measurement results showed that, at the significance level of 0.05, effects of 3D printing parameters studied (printing speed and extrusion pressure) were not statistically significant on Young’s modulus and ultimate tensile strength of the tensile testing samples, as well as on compressive strength and compressive modulus of the compressive testing samples. Results obtained from the Fourier transform infrared spectroscopy analysis show that chemical composition of printed samples was consistent with the data in the literature.

VSHARP: Variable Splitting Half-quadratic ADMM algorithm for reconstruction of inverse-problems

Medical Imaging (MI) tasks, such as accelerated parallel Magnetic Resonance Imaging (MRI), often involve reconstructing an image from noisy or incomplete measurements. This amounts to solving ill-posed inverse problems, where a satisfactory closed-form analytical solution is not available. Traditional methods such as Compressed Sensing (CS) in MRI reconstruction can be time-consuming or prone to obtaining low-fidelity images. Recently, a plethora of Deep Learning (DL) approaches have demonstrated superior performance in inverse-problem solving, surpassing conventional methods. In this study, we propose vSHARP (variable Splitting Half-quadratic ADMM algorithm for Reconstruction of inverse Problems), a novel DL-based method for solving ill-posed inverse problems arising in MI. vSHARP utilizes the Half-Quadratic Variable Splitting method and employs the Alternating Direction Method of Multipliers (ADMM) to unroll the optimization process. For data consistency, vSHARP unrolls a differentiable gradient descent process in the image domain, while a DL-based denoiser, such as a U-Net architecture, is applied to enhance image quality. vSHARP also employs a dilated-convolution DL-based model to predict the Lagrange multipliers for the ADMM initialization. We evaluate vSHARP on tasks of accelerated parallel MRI Reconstruction using two distinct datasets and on accelerated parallel dynamic MRI Reconstruction using another dataset. Our comparative analysis with state-of-the-art methods demonstrates the superior performance of vSHARP in these applications.

An accelerated alternating direction method of multiplier for MRI with TV regularisation

Compressed Sensing (CS) is important in the field of image processing and signal processing, and CS-Magnetic Resonance Imaging (MRI) is used to reconstruct image from undersampled k-space data. Total Variation (TV) regularisation is a common technique to improve the sparsity of image, and the Alternating Direction Multiplier Method (ADMM) plays a key role in the variational image processing problem. This paper aims to improve the quality of MRI and shorten the reconstruction time. We consider MRI to solve a linear inverse problem, we convert it into a constrained optimization problem based on TV regularisation, then an accelerated ADMM is established. Through a series of theoretical derivations, we verify that the algorithm satisfies the convergence rate of O1/k2 under the condition that one objective function is quadratically convex and the other is strongly convex. We select five undersampled templates for testing in MRI experiment and compare it with other algorithms, experimental results show that our proposed method not only improves the running speed but also gives better reconstruction results.

Complex-valued image reconstruction for compressed sensing MRI using hierarchical constraint

In Magnetic Resonance Imaging (MRI), the sequential acquisition of raw complex-valued image data in Fourier space, also known as k-space, results in extended examination times. To speed up the MRI scans, k-space data are usually undersampled and processed using numerical techniques such as compressed sensing (CS). While the majority of CS-MRI algorithms primarily focus on magnitude images due to their significant diagnostic value, the phase components of complex-valued MRI images also hold substantial importance for clinical diagnosis, including neurodegenerative diseases. In this work, complex-valued MRI reconstruction is studied with a focus on the simultaneous reconstruction of both magnitude and phase images. The proposed algorithm is based on the nonsubsampled contourlet transform (NSCT) technique, which offers shift invariance in images. Instead of directly transforming the complex-valued image into the NSCT domain, we introduce a wavelet transform within the NSCT domain, reducing the size of the sparsity of coefficients. This two-level hierarchical constraint (HC) enforces sparse representation of complex-valued images for CS-MRI implementation. The proposed HC is seamlessly integrated into a proximal algorithm simultaneously. Additionally, to effectively minimize the artifacts caused by sub-sampling, thresholds related to different sub-bands in the HC are applied through an alternating optimization process. Experimental results show that the novel method outperforms existing CS-MRI techniques in phase-regularized complex-valued image reconstructions.

Reconstructing Human Pose From Inertial Measurements: A Generative Model-Based Compressive Sensing Approach

Reconstructing Human Pose From Inertial Measurements: A Generative Model-Based Compressive Sensing Approach

Distributed Inertial Proximal Neurodynamic Approach for Sparse Recovery on Directed Networks

Distributed Inertial Proximal Neurodynamic Approach for Sparse Recovery on Directed Networks

Crystallographic Preferred Orientation of Phase D at High Pressure and Temperature: Implications for Seismic Anisotropy in the Mid‐Mantle

AbstractSeismic anisotropy has been widely observed in the lower mantle transition zone and the uppermost lower mantle near several subducting slabs, which is typically attributed to the crystallographic preferred orientation (CPO) of constituent minerals. In this study, well‐controlled uniaxial and simple shear deformation experiments were conducted on Mg‐endmember phase D and Al‐bearing phase D aggregates at 20 GPa and 500–1,000°C. Strong (0001) fabrics were observed in the uniaxially compressed samples. The CPO from all experiments, including extension and simple shear, indicated that the most active slip systems in phase D were &lt;110&gt;(0001) and &lt;100&gt;(0001), with a dominance of &lt;110&gt;(0001). The calculated seismic velocity suggests that the deformed phase D generates positive radial seismic anisotropy (VSH &gt; VSV) in both subhorizontal shearing and subvertical compression, causing significant shear‐wave splitting time. Our results suggest that the observed seismic anisotropy in the mid‐mantle in several cold subduction zones can be well explained by the presence of deformed phase D.

Image compression encryption algorithm combining two-dimensional modular hyperchaotic map and compressed sensing

Recently, to offer better ensure for image privacy security, numerous new image encryption algorithms have been proposed. However, these algorithms still suffer from the problems of chaotic performance scarcity, low encryption effect, and high consumption of computational resources. To solve the above issues, we first construct a two-dimensional modular hyperchaotic map (2D-MHM). Then, we further develop an image encryption algorithm based on 2D-MHM and compressed sensing (CS). Several chaotic metrics verify the randomness and validity of 2D-MHM. These metrics include bifurcation diagram, Lyapunov exponent, initial value sensitivity, 0–1 test, and NIST test. Specifically, CS significantly reduces the ciphertext image size thereby reducing its resource consumption during transmission. Reality-preserving fractional DCT (RP-Fdct) diffusion is utilized to transform pixels into the frequency domain to enhance the encryption effect. Subsequently, lightweight index confusion and XOR diffusion further improve the algorithm security. The security of the algorithm is verified through various experiments. It is able to encrypt grayscale and color images of different sizes with good results. Notably, this algorithm also implements the encryption requirements for binary images. Due to our designs, it outperforms recently reported encryption algorithms in several areas, especially in reconstruction performance.

Advanced Compressive Sensing and Dynamic Sampling for 4D-STEM Imaging of Interfaces.

Interfaces in energy materials and devices often involve beam-sensitive materials such as fast ionic, soft, or liquid phases. 4D scanning transmission electron microscopy (4D-STEM) offers insights into local lattice, strain charge, and field distributions, but faces challenges in analyzing beam-sensitive interfaces at high spatial resolutions. Here, a 4D-STEM compressive sensing algorithm is introduced that significantly reduces data acquisition time and electron dose. This method autonomously allocates probe positions on interfaces and reconstructs missing information from datasets acquired via dynamic sampling. This algorithm allows for the integration of various scanning schemes and electron probe conditions to optimize data integrity. Its data reconstruction employs a neural network and an autoencoder to correlate diffraction pattern features with measured properties, significantly reducing training costs. The accuracy of the reconstructed 4D-STEM datasets is verified using a combination of explicitly and implicitly trained parameters from atomic resolution datasets. This method is broadly applicable for 4D-STEM imaging of any local features of interest and will be available on GitHub upon publication.

Combining CBAM and Iterative Shrinkage-Thresholding Algorithm for Compressive Sensing of Bird Images

Combining CBAM and Iterative Shrinkage-Thresholding Algorithm for Compressive Sensing of Bird Images

Compressed sensing reconstruction for high-SNR, rapid dissolved 129Xe gas exchange MRI.

Three-dimensional hyperpolarized 129Xe gas exchange imaging suffers from low SNR and long breath-holds, which could be improved using compressed sensing (CS). The purpose of this work was to assess whether gas exchange ratio maps are quantitatively preserved in CS-accelerated dissolved-phase 129Xe imaging and to investigate the feasibility of CS-dissolved 129Xe imaging with reduced-cost natural abundance (NA) xenon. 129Xe gas exchange imaging was performed at 1.5 T with a multi-echo spectroscopic imaging sequence. A CS reconstruction with an acceleration factor of 2 was compared retrospectively with conventional gridding reconstruction in a cohort of 16 healthy volunteers, 5 chronic obstructive pulmonary disease patients, and 23 patients who were hospitalized following COVID-19 infection. Metrics of comparison included normalized mean absolute error, mean gas exchange ratio, and red blood cell (RBC) image SNR. Dissolved 129Xe CS imaging with NA xenon was assessed in 4 healthy volunteers. CS reconstruction enabled acquisition time to be halved, and it reduced background noise. Median RBC SNR increased from 6 (2-18) to 11 (2-100) with CS, and there was strong agreement between CS and gridding mean ratio map values (R2 = 0.99). Image fidelity was maintained for gridding RBC SNR > 5, but below this, normalized mean absolute error increased nonlinearly with decreasing SNR. CS increased the mean SNR of NA 129Xe images 3-fold. CS reconstruction of dissolved 129Xe imaging improved image quality with decreased scan time, while preserving key gas exchange metrics. This will benefit patients with breathlessness and/or low gas transfer and shows promise for NA-dissolved 129Xe imaging.

A Highly Efficient Compressive Sensing Algorithm Based on Root-Sparse Bayesian Learning for RFPA Radar

Off-grid issues and high computational complexity are two major challenges faced by sparse Bayesian learning (SBL)-based compressive sensing (CS) algorithms used for random frequency pulse interval agile (RFPA) radar. Therefore, this paper proposes an off-grid CS algorithm for RFPA radar based on Root-SBL to address these issues. To effectively cope with off-grid issues, this paper derives a root-solving formula inspired by the Root-SBL algorithm for velocity parameters applicable to RFPA radar, thus enabling the proposed algorithm to directly solve the velocity parameters of targets during the fine search stage. Meanwhile, to ensure computational feasibility, the proposed algorithm utilizes a simple single-level hierarchical prior distribution model and employs the derived root-solving formula to avoid the refinement of velocity grids. Moreover, during the fine search stage, the proposed algorithm combines the fixed-point strategy with the Expectation-Maximization algorithm to update the hyperparameters, further reducing computational complexity. In terms of implementation, the proposed algorithm updates hyperparameters based on the single-level prior distribution to approximate values for the range and velocity parameters during the coarse search stage. Subsequently, in the fine search stage, the proposed algorithm performs a grid search only in the range dimension and uses the derived root-solving formula to directly solve for the target velocity parameters. Simulation results demonstrate that the proposed algorithm maintains low computational complexity while exhibiting stable performance for parameter estimation in various multi-target off-grid scenarios.

A novel wind turbine fault diagnosis method based on compressive sensing and lightweight SqueezeNet model

The fault diagnosis method based on model and signal processing has some problems, such as difficulty in modeling and difficulty in extracting signal features; As the depth of the neural network deepens, there will be the problem of gradient vanishing or mass, and directly converting the fault signal into a one-dimensional or two-dimensional image as the network input cannot retain the time information between the signals, resulting in the loss of information. In order to solve the above problems, this paper proposes a fault diagnosis method based on Compressed Sensing (CS) and lightweight SqueezeNet model. Firstly, the Compressive Sensing (CS) technology was used to sparse the original signal, and the Compressed Sampling Matching Pursuit (CoSaMP) algorithm was used to compress and reconstruct the signal to complete the signal noise reduction and remove the data redundancy. Secondly, the compressed and reconstructed signal was encoded by recursive graph (RP) to generate a two-dimensional image, and the temporal correlation characteristics of the signal were retained. Thirdly, the traditional SqueezeNet model is improved by using the residual idea to enhance the feature extraction ability. The RP dataset was input into the improved SqueezeNet model for fault feature extraction and fault classification. Finally, the experimental results show that compared with other methods, the proposed method can identify faults and have high diagnostic accuracy on the rolling bearing data samples of wind turbines.

Sparse recovery using expanders via hard thresholding algorithm

Expanders play an important role in combinatorial compressed sensing. Via expanders measurements, we propose the expander normalized heavy ball hard thresholding algorithm (ENHB-HT) based on expander iterative hard thresholding (E-IHT) algorithm. We provide convergence analysis of ENHB-HT, and it turns out that ENHB-HT can recover an s-sparse signal if the measurement matrix A∈{0,1}m×n satisfies some mild conditions. Numerical experiments are simulated to support our two main theorems which describe the convergence rate and the accuracy of the proposed algorithm. Simulations are also performed to compare the performance of ENHB-HT and several existing algorithms under different types of noise, the empirical results demonstrate that our algorithm outperform a few existing ones in the presence of outliers.

Nonparametric and Continuous Variable-Based Stratigraphic Modelling from Sparse Boreholes using Signed Distance Function and Bayesian Compressive Sensing

An accurate stochastic interpretation of subsurface stratigraphy with quantified uncertainty can benefit the subsequent risk management of geotechnical infrastructure. Traditional approaches to developing geological cross-sections from sparse boreholes typically require the calibration or definition of empirical model parameters and functions, which may introduce subjectivity and bias. In this study, a non-parametric and continuous variable-based spatial predictor that leverages the signed distance function and Bayesian compressive sensing (BCS) is proposed for subsurface stratigraphic modelling. The proposed method transforms sparse categorical borehole data from a low-dimensional space into continuous variables in a high-dimensional space, enabling a comprehensive representation of more implicit characteristics of intricate geological patterns. This transformation facilitates the use of the continuous-variable-based BCS for non-parametric spatial prediction. The most probable geological cross-section and uncertainty qualification plot are derived after transforming spatially interpreted fields of continuous variables back into soil types. The performance of the proposed method is demonstrated using synthetic and real-world cases. Results indicate that the proposed approach can handle intricate stratigraphic scenarios characterized by complex geological structures, such as crossed-inclined, folded, inclined-folded, and interbedded strata, in a data-driven and non-parametric manner. The advantages of the proposed method over existing spatial predictors for developing geological cross-sections are also demonstrated.