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Abstract In this paper, we consider the frame-based block sparse signal recovery via a $$l_2/l_1$$ l 2 / l 1 -synthesis method. A new kind of null space property based on the given dictionary D(block D-NSP) is proposed. It is proved that sensing matrices satisfying the block D-NSP is not just a sufficient and necessary condition for the $$l_2/l_1$$ l 2 / l 1 -synthesis method to exactly recover signals that are block sparse in frame D, but also a sufficient and necessary condition for the $$l_2/l_1$$ l 2 / l 1 -synthesis to stably recover signals which are block-compressible in frame D. To the best of our knowledge, this new property is the first sufficient and necessary condition for successful signal recovery via the $$l_2/l_1$$ l 2 / l 1 -synthesis. In addition, we also characterize the theoretical performance of recovering signals via the $$l_2/l_1$$ l 2 / l 1 -synthesis in the case of the measurements are disturbed.

Abstract The authors focus on the waveform design for Code Division Multiple Access Multiple Input Multiple Output (CDMA‐MIMO) radar systems, with a specific emphasis on Compressed Sensing (CS) based target estimation. The selection of an appropriate waveform is a critical determinant in the effectiveness of estimation algorithms. Recent studies show the possibilities of optimising waveform parameters to improve the efficiency of CS based estimation. The authors introduce an optimisation framework designed to modify the phase components of code sequences used in CS‐CDMA MIMO radar systems. The objective of this optimisation is to minimise the l∞ norm of off‐diagonal elements within the Gramian matrix of the underlying sensing matrix, focusing on phase modulation of the waveform. Solving this optimisation problem requires dealing with a non‐convex, combinatorial and non‐linear scenario. Simulated Annealing is employed as the solution technique. To assess the effectiveness of the proposed optimisation approach, the resulting optimised sequence is rigorously compared against well‐established Hadamard and Gold sequences across various performance metrics. These metrics encompass correlation properties, ambiguity function behaviour, recovery percentage and recovery error. The study demonstrates that the generated poly‐phase sequences outperform existing sequences, leading to significantly improved target reconstruction results in the context of CDMA‐MIMO radar systems with CS‐based estimation.

Abstract Background Preoperative discrimination between non-muscle-invasive bladder cancer (NMIBC) and the muscle invasive bladder cancer (MIBC) is a determinant of management. The purpose of this research is to employ radiomics to evaluate the diagnostic value in determining muscle invasiveness of compressed sensing (CS) accelerated 3D T2-weighted-SPACE sequence with high resolution and short acquisition time. Methods This prospective study involved 108 participants who underwent preoperative 3D-CS-T2-weighted-SPACE, 3D-T2-weighted-SPACE and T2-weighted sequences. The cohort was divided into training and validation cohorts in a 7:3 ratio. In the training cohort, a Rad-score was constructed based on radiomic features selected by intraclass correlation coefficients, pearson correlation coefficient and least absolute shrinkage and selection operator . Multivariate logistic regression was used to develop a nomogram combined radiomics and clinical indices. In the validation cohort, the performances of the models were evaluated by ROC, calibration, and decision curves. Results In the validation cohort, the area under ROC curve of 3D-CS-T2-weighted-SPACE, 3D-T2-weighted-SPACE and T2-weighted models were 0.87(95% confidence interval (CI):0.73-1.00), 0.79(95%CI:0.63–0.96) and 0.77(95%CI:0.60–0.93), respectively. The differences in signal-to-noise ratio and contrast-to-noise ratio between 3D-CS-T2-weighted-SPACE and 3D-T2-weighted-SPACE sequences were not statistically significant(p > 0.05). While the clinical model composed of three clinical indices was 0.74(95%CI:0.55–0.94) and the radiomics-clinical nomogram model was 0.88(95%CI:0.75-1.00). The calibration curves confirmed high goodness of fit, and the decision curve also showed that the radiomics model and combined nomogram model yielded higher net benefits than the clinical model. Conclusion The radiomics model based on compressed sensing 3D T2WI sequence, which was acquired within a shorter acquisition time, showed superior diagnostic efficacy in muscle invasion of bladder cancer. Additionally, the nomogram model could enhance the diagnostic performance.

Abstract Compressive sensing provides a promising sampling paradigm for video acquisition for resource‐limited sensor applications. However, the reconstruction of original video signals from sub‐sampled measurements is still a great challenge. To exploit the temporal redundancies within videos during the recovery, previous works tend to perform alignment on initial reconstructions, which are too coarse to provide accurate motion estimations. To solve this problem, the authors propose a novel reconstruction network, named TSRN, for compressive video sensing. Specifically, the authors utilise a number of stacked temporal shift reconstruction blocks (TSRBs) to enhance the initial reconstruction progressively. Each TSRB could learn the temporal structures by exchanging information with last and next time step, and no additional computations is imposed on the network compared to regular 2D convolutions due to the high efficiency of temporal shift operations. After the enhancement, a bidirectional alignment module to build accurate temporal dependencies directly with the help of optical flows is employed. Different from previous methods that only extract supplementary information from the key frames, the proposed alignment module can receive temporal information from the whole video sequence via bidirectional propagations, thus yielding better performance. Experimental results verify the superiority of the proposed method over other state‐of‐the‐art approaches quantitatively and qualitatively.

Abstract We introduce three architecture modifications to enhance the performance of the end-to-end (E2E) variational network (VarNet) for undersampled MRI reconstructions. We first implemented the Feature VarNet, which propagates information throughout the cascades of the network in an N-channel feature-space instead of a 2-channel feature-space. Then, we add an attention layer that utilizes the spatial locations of Cartesian undersampling artifacts to further improve performance. Lastly, we combined the Feature and E2E VarNets into the Feature-Image (FI) VarNet, to facilitate cross-domain learning and boost accuracy. Reconstructions were evaluated on the fastMRI dataset using standard metrics and clinical scoring by three neuroradiologists. Feature and FI VarNets outperformed the E2E VarNet for 4 $$\times$$ × , 5 $$\times$$ × and 8 $$\times$$ × Cartesian undersampling in all studied metrics. FI VarNet secured second place in the public fastMRI leaderboard for 4 $$\times$$ × Cartesian undersampling, outperforming all open-source models in the leaderboard. Radiologists rated FI VarNet brain reconstructions with higher quality and sharpness than the E2E VarNet reconstructions. FI VarNet excelled in preserving anatomical details, including blood vessels, whereas E2E VarNet discarded or blurred them in some cases. The proposed FI VarNet enhances the reconstruction quality of undersampled MRI and could enable clinically acceptable reconstructions at higher acceleration factors than currently possible.

Compressed Sensing (CS) has been shown to be an effective technique for improving the resolution of inverse synthetic aperture radar (ISAR) imaging and reducing the hardware requirements of radar systems. In this paper, our focus is on the l_p 0 p 1 model, which is a well-known non-convex and non-Lipschitz regularization model in the field of compressed sensing. In this study, we propose a novel algorithm, namely the Accelerated Iterative Support Shrinking with Full Linearization (AISSFL) algorithm, which aims to solve the l_p regularization model for ISAR imaging. The AISSFL algorithm draws inspiration from the Majorization-Minimization (MM) iteration algorithm and integrates the principles of support shrinkage and Nestrove's acceleration technique. The algorithm employed in this study demonstrates simplicity and efficiency. Numerical experiments demonstrate that AISSFL performs well in the field of ISAR imaging.

Abstract The authors study the problem of compressive target detection in a single‐frequency network (SFN)‐based multistatic passive radar system (MS‐PRS) consisting of multiple illuminators of opportunity (IOs) and one receiver. Firstly, a generalised likelihood ratio test (GLRT)‐based SFN‐based compressive subspace detector (SFN‐CSD) is derived by exploiting the sparsity of the target echoes for the case of known noise variance. When the noise variance is unknown, an SFN‐based unknown‐noise (UN) compressive subspace detector is proposed, referred to as the SFN‐UNCSD. Moreover, closed‐form expressions of the probability of false alarm and detection of the proposed detectors are deriived. It is proved that the SNF‐UNCSD has a constant false alarm rate (CFAR) property. Finally, numerical simulations are conducted to verify the theoretical analysis and illustrate the performance of the proposed detector relative to several benchmark detectors.

IntroductionHigh-resolution whole-heart coronary magnetic resonance angiography (CMRA) often suffers from unreasonably long scan times, rendering imaging acceleration highly desirable. Traditional reconstruction methods used in CMRA rely on either hand-crafted priors or supervised learning models. Although the latter often yield superior reconstruction quality, they require a large amount of training data and memory resources, and may encounter generalization issues when dealing with out-of-distribution datasets.MethodsTo address these challenges, we introduce an unsupervised reconstruction method that combines deep image prior (DIP) with compressed sensing (CS) to accelerate 3D CMRA. This method incorporates a slice-by-slice DIP reconstruction and 3D total variation (TV) regularization, enabling high-quality reconstruction under a significant acceleration while enforcing continuity in the slice direction. We evaluated our method by comparing it to iterative SENSE, CS-TV, CS-wavelet, and other DIP-based variants, using both retrospectively and prospectively undersampled datasets.ResultsThe results demonstrate the superiority of our 3D DIP-CS approach, which improved the reconstruction accuracy relative to the other approaches across both datasets. Ablation studies further reveal the benefits of combining DIP with 3D TV regularization, which leads to significant improvements of image quality over pure DIP-based methods. Evaluation of vessel sharpness and image quality scores shows that DIP-CS improves the quality of reformatted coronary arteries.DiscussionThe proposed method enables scan-specific reconstruction of high-quality 3D CMRA from a five-minute acquisition, without relying on fully-sampled training data or placing a heavy burden on memory resources.

The article aims to address the challenges of information degradation and distortion in graphic design, focusing on optimizing the traditional compressed sensing (CS) model. This optimization involves creating a co-reconstruction group derived from compressed observations of local image blocks. Following an initial reconstruction of compressed observations within similar groups, an initially reconstructed image block co-reconstruction group is obtained, featuring degraded reconstructed images. These images undergo channel stitching and are input into a global residual network. This network is composed of a non-local feature adaptive interaction module stacked with the aim of fusion to enhance local feature reconstruction. Results indicate that the solution space constraint for reconstructed images is achieved at a low sampling rate. Moreover, high-frequency information within the images is effectively reconstructed, improving image reconstruction accuracy.

ObjectiveTo investigate the feasibility and performance of 4D flow MRI accelerated by compressed sensing (CS) for the hemodynamic quantification of intracranial artery and venous sinus.Materials and methodsForty healthy volunteers were prospectively recruited, and 20 volunteers underwent 4D flow MRI of cerebral artery, and the remaining volunteers underwent 4D flow MRI of venous sinus. A series of 4D flow MRI was acquired with different acceleration factors (AFs), including sensitivity encoding (SENSE, AF = 4) and CS (AF = CS4, CS6, CS8, and CS10) at a 3.0 T MRI scanner. The hemodynamic parameters, including flow rate, mean velocity, peak velocity, max axial wall shear stress (WSS), average axial WSS, max circumferential WSS, average circumferential WSS, and 3D WSS, were calculated at the internal carotid artery (ICA), transverse sinus (TS), straight sinus (SS), and superior sagittal sinus (SSS).ResultsCompared to the SENSE4 scan, for the left ICA C2, mean velocity measured by CS8 and CS10 groups, and 3D WSS measured by CS6, CS8, and CS10 groups were underestimated; for the right ICA C2, mean velocity measured by CS10 group, and 3D WSS measured by CS8 and CS10 groups were underestimated; for the right ICA C4, mean velocity measured by CS10 group, and 3D WSS measured by CS8 and CS10 groups were underestimated; and for the right ICA C7, mean velocity and 3D WSS measured by CS8 and CS10 groups, and average axial WSS measured by CS8 group were also underestimated (all p

The performance of most existing tomographic synthetic aperture radar (SAR) (TomoSAR) methods that reconstruct the scene pixel-by-pixel is degraded by speckle noise and low signal-to-noise ratio. To solve these problems, we propose a homogeneous region-based compressed sensing (HomoR-CS) method for SAR tomography. This method enhances the processing approach by transitioning from the traditional pixel-by-pixel processing to the joint processing based on multiple adjacent pixels in homogeneous regions. First, a similarity measure is designed to cluster pixels that have similar electromagnetic scattering intensities and three-dimensional (3-D) positions into homogeneous regions. Then, the homogeneous region-oriented TomoSAR signal model is proposed and the solution is given. Sparse approximation at the homogeneous region level is used to estimate the elevation for every pixel. The multiple adjacent pixels within the homogeneous region are jointly processed to determine the initial elevation centers, which are used as the prior information for the subsequent accurate elevation estimation of each pixel. Finally, the experimental analyses using both simulated and measured data validate the effectiveness of the HomoR-CS method. The results show that the HomoR-CS method reduces the outliers of 3-D reconstruction results and enhances the recovery of weak scattering targets.

Abstract Beamspace processing is widely applied in Direction‐of‐Arrival (DOA) estimation thanks to dimensional reduction and super‐resolution characterisations. However, the conventional atomic norm minimisation (ANM) based methods for beamspace DOA estimation are of high computational complexity for large arrays. To deal with this issue, the proposed method focuses on locating the sources in the mainlobe of the beamspace and encodes such prior information into the ANM problem without frequency‐selective constraints. The proposed method approximates the beamspace array manifold in the mainlobe sector with the truncated sector Fourier series. The theoretical analysis shows that such approximation with the properly designed fitting error relaxation on the boundary yields the low dimensional semidefinite programming (SDP) approximate implementation of the proposed ANM method and guarantees the support recovery inside the mainlobe. Furthermore, the low complexity Burer‐Monteiro factorisation based alternating direction method of multipliers method is proposed to solve the SDP problem. The complexity analysis and simulations show that the proposed method results in significant computational complexity reduction and slightly better performance compared with state‐of‐art benchmarks.

Abstract Recently, biometric recognition has become a significant field of research. The concept of cancelable biometrics (CB) has been introduced to address security concerns related to the handling of sensitive data. In this paper, we address unconstrained face verification by proposing a deep cancelable framework called BiometricNet+ that employs random projections (RP) to conceal face images and compressive sensing (CS) to reconstruct measurements in the original domain. Our lightweight design enforces the properties of unlinkability, revocability, and non-invertibility of the templates while preserving face recognition accuracy. We compare facial features by learning a regularized metric: at training time, we jointly learn facial features and the metric such that matching and non-matching pairs are mapped onto latent target distributions; then, for biometric verification, features are randomly projected via random matrices changed at every enrollment and query and reconstructed before the latent space mapping is computed. We assess the face recognition accuracy of our framework on challenging datasets such as LFW, CALFW, CPLFW, AgeDB, YTF, CFP, and RFW, showing notable improvements over state-of-the-art techniques while meeting the criteria for secure cancelable template design. Since our method requires no fine-tuning of the learned features, it can be applied to pre-trained networks to increase sensitive data protection.

Abstract Background This study aimed to determine the optimal scan time for high temporal resolution magnetic resonance (MR) imaging of the liver with gadoxetate disodium injection in combination with compressed sensing (CS) and parallel imaging (PI) techniques under single breath-holding using a 1.5-T MR system. Methods Sixty-two participants underwent multiple arterial phases of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the liver with gadoxetate disodium using fat-suppressed GRE T1-weighted imaging—liver acquisition with volume acceleration (LAVA)—in combination with CS and PI using a 1.5-T MR system. Forty-six and 22 participants underwent 6-s and 10-s scans, respectively. Pre-contrast, multiple arterial, portal venous, and hepatobiliary phase images were acquired. Two radiologists evaluated the visual scores for the outline of the liver, inferior right hepatic vein (IRHV), right portal vein, right hepatic artery, appropriateness of the arterial phase, and overall image quality using a 4- or 5-point scale. Results The overall image quality and the image quality of the outline of the liver in the pre-contrast and arterial phases and IRHV in the pre-contrast phase were significantly better (P

Abstract When traditional EEG signals are collected based on the Nyquist theorem, long-time recordings of EEG signals will produce a large amount of data. At the same time, limited bandwidth, end-to-end delay, and memory space will bring great pressure on the effective transmission of data. The birth of compressed sensing alleviates this transmission pressure. However, using an iterative compressed sensing reconstruction algorithm for EEG signal reconstruction faces complex calculation problems and slow data processing speed, limiting the application of compressed sensing in EEG signal rapid monitoring systems. As such, this paper presents a non-iterative and fast algorithm for reconstructing EEG signals using compressed sensing and deep learning techniques. This algorithm uses the improved residual network model, extracts the feature information of the EEG signal by one-dimensional dilated convolution, directly learns the nonlinear mapping relationship between the measured value and the original signal, and can quickly and accurately reconstruct the EEG signal. The method proposed in this paper has been verified by simulation on the open BCI contest dataset. Overall, it is proved that the proposed method has higher reconstruction accuracy and faster reconstruction speed than the traditional CS reconstruction algorithm and the existing deep learning reconstruction algorithm. In addition, it can realize the rapid reconstruction of EEG signals.

Abstract Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization problems via minimizing the $$\ell _{p}$$ ℓ p quasi-norm, where $$0

Abstract When using untrusted third parties to compress and transmit images in real‐life scenarios, it is vital to encrypt them before compression. In order to better address the issues of low security in the original image and poor reconstruction quality of the encrypted image during compressed sensing, this paper proposes a 2D compressed sensing scheme for encrypted images based on complex‐valued measurement matrix (2DCS‐CVM). Firstly, the SHA‐256 algorithm generates keys for the hyperchaotic Lorenz system, and then the chaotic sequences are used to create encrypted images with increased security through subtractive diffusion and global permutation. Secondly, the complex‐valued Vandermonde measurement matrix is utilized for 2D compressed sensing on the encrypted image, and the two‐dimensional projected gradient with embedding decryption algorithm is used to generate recovered images with improved reconstruction performance. Finally, the measurement matrix's computational complexity and transmission bandwidth are reduced through structural sparsification with sparse random matrices. Simulation results demonstrate that this scheme offers an optimal balance between storage, computational complexity, hardware implementation, and reconstruction performance while providing excellent security and robustness.

This research paper explores the rising interest in utilising deep learning methods, specifically Convolution Neural Network (CNN), to improve the reconstruction of Compressively Sampled Magnetic Resonance Imaging (CS MRI) images from under-sampled data. By training deep learning architectures on extensive data sets of paired under sampled and fully sampled MR images, these models aim to capture intricate patterns and structures, ultimately enhancing the accuracy of MR image reconstructions. A novel deep learning model is proposed dubbed as “Deep Iterative Shrinkage Thresholding Algorithm-Compressed Sensing Network” (DISTA-CSNet), specifically designed for efficient recovery of CS MRI. Our model showcases impressive results with only 20 epochs and can be effortlessly trained on diverse datasets. To ensure robustness across different datasets, the dropouts are incorporated into the model, evident from testing results. The trained DISTA-CSNet exhibits remarkable performance in recovering CS MRI from various data sets, surpassing several advanced deep learning techniques with changing compression ratios consistently. The proposed model demonstrates significant enhancements in both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) metrics, affirming the efficacy of our proposed model. The capability of our DISTA-CSNet in accurately reconstructing CS MRI images from 5-fold undersampled data shows promise in improving medical imaging applications and advancing the field of compressed sensing MRI.

This study investigates a continuous-time method for sparse signal recovery, which is suitable for analog optical circuit implementation. The proposed method is defined by a nonlinear ordinary differential equation (ODE) derived from the gradient flow dynamics of the Lasso objective function. Numerical experiments show that the proposed method certainly finds original sparse vectors within reasonable accuracy. To gain insight into the local convergence properties of the proposed method, a linear approximation around the equilibrium point is applied, yielding a closed-form error evolution ODE. This analysis shows the behavior of convergence to the equilibrium point. In addition, a variational optimization problem is proposed to optimize a time-dependent regularization parameter in order to improve both convergence speed and solution quality. The deep unfolded variational optimization method is introduced as a means of solving this optimization problem, and its effectiveness is validated through numerical experiments.

The development of measurement matrices remains a pivotal focus within the domain of compressed sensing theory. This paper introduces an innovative methodology for the construction of a deterministic binary measurement matrix, harnessing the properties of chaotic sequences. This approach streamlines the process and only requires a fixed number of initial variables for matrix construction. The construction method of the measurement matrix is divided into two distinct stages. Initially, the matrix elements are extracted through gapless sampling of chaotic sequences. Recognizing the inherent correlation among chaotic sequence elements due to gapless sampling, this paper introduces a novel nonlinear binary transformation. This innovative approach effectively mitigates the correlation and concurrently addresses storage limitations. Thereafter, the entries are integrated into a Toeplitz matrix, leveraging its structured row and columnar properties to augment storage efficiency. In subsequent steps, the approach integrates the Householder transformation to generate an orthogonal basis, thereby enhancing the matrix’s performance. Additionally, an XOR operation is employed to optimize the distribution of entries across each column vector. The research substantiates that the resultant matrix exhibits low correlation, is facile in generation, and amenable to reconstruction. Comprehensive experimental data corroborate the efficacy of the constructed measurement matrix in processing both one-dimensional and two-dimensional signals. The matrix demonstrates a strong potential to meet the Restricted Isometry Property (RIP), thereby underscoring its substantial advantages across a myriad of considerations.

Blade tip-timing (BTT) is a direct blade vibration monitoring technique and how to use under-sampled BTT signals for blade damage detection is still challenging under variable conditions. Compressed sensing (CS) has been introduced for reconstructing BTT vibration signals, but classical CS reconstruction algorithms are limited by the sparsity and slow optimization process. In order to overcome this issue, this paper presents an iteratively learning reconstruction method by introducing the vector approximate message passing (VAMP) algorithm, called VampNet. Firstly, a discrete Multi-coset sampling (MCS)-based CS model is built for BTT vibration signals in order domain and an improved Hanning-Possion window is integrated to reduce the order spectrum leakage in discretization. Then the VampNet model is proposed to reconstruct blade vibration engine orders (EOs) and the sensing matrix is discussed. Based on reconstructed vibration EOs, a cointegration-based method is proposed for blade damage detection, so that the influences of variable conditions can be reduced. Finally, the feasibility of the proposed method is testified by Matlab simulations and experimental dataset. The results show that blade vibration EOs can be accurately reconstructed by the VampNet and then small cracks can be detected by using the cointegrating residual.

The cumulative coherence condition serves as a valuable tool within the realm of Compressed Sensing. However, its application to the $\ell _{1}-\ell _{2}$ -minimization model lacks thorough discussion. This paper aims to address this gap by introducing a sufficient condition for stable recovery of sparse vectors under the $\ell _{1}-\ell _{2}$ -minimization model, building upon the cumulative coherence condition. Moreover, employing graphical analysis, this study contrasts our proposed sufficient condition with existing criteria for stable recovery using both $\ell _{1}-\ell _{2}$ -minimization and $\ell _{1}$ -minimization models. Experimental data illustrate that our proposed sufficiency conditions exhibit less stringent requirements compared to established conclusions.

In compressed sensing (CS), coherence is a simple and practical measure of the quality of a sensing matrix. The smaller the coherence of the sensing matrix, the better the reconstruction result. Most strategies for optimizing the coherence of a sensing matrix are only applicable to gray-value matrices and are not to binary matrices with fast computation speed and smaller storage space. Under a certain condition, the coherence can be improved by weighting the sensing matrix to make its condition number equal to 1, i.e., all non-zero singular values become the same. In this paper, we propose a method for reweighting CS models to reduce the condition number of the sensing matrix so as to improve its coherence, prove that the condition number decreases monotonically to 1 as the weighting times approaches infinity, and then obtain a coherence improvement model equivalent to the original CS model. Finally, we give the RwOMP recovery algorithm based on the proposed reweighted method and verify its superiority by using different binary sensing matrices for CS experiments.

This paper presents a comparison between compressed sensing (CS) and auto-encoder (AE) for compression and restoration of signals. The study used K-sparse vectors and generated an under-determined system, which is a system of linear equations with fewer equations than unknowns. By using CS and AE under various specific conditions, the accuracy of the signal restoration is compared with mean squared error (MSE). The experimental methodology includes comparing and analyzing the signal recovery performance by altering the algorithm and various parameters. The result represents the performance and accuracy of signal compression and restoration obtained using both techniques. It also provides a comprehensive analysis of CS and AE methods. The importance of this research and the possibility of practical application in various fields are discussed. Overall, this study provides insights into the comparison of CS and AE techniques in the field of sparse signal compression and restoration.

Abstract With the booming of cloud-based digital twin systems, monitoring key performance indicators has become crucial for ensuring system security and reliability. Due to the massive amount of monitoring data generated, data compression is necessary to save data transmission bandwidth and storage space. Although the existing research has proposed compression methods for multivariate time series (MTS), it is still a challenge to guarantee the correlation between data when compressing the MTS. This paper proposes an MTS Collaborative Compression (MTSCC) method based on the two-step compression scheme. First, shape-based clustering is implemented to group the MTS. Afterward, the compressed sensing is optimized to achieve collaborative compression of grouped data. Based on a real-world MTS dataset, the experimental results show that the proposed MTSCC can effectively preserve the complex temporal correlation between indicators while achieving efficient data compression, and the root mean squared error of correlation between the reconstructed and original data is only 0.0489 in the case of 30% compression ratio. Besides, it is verified that using the reconstructed data in the production environment has almost the same performance as using the original data.

The fifth generation of wireless communication is anticipated to provide improved quality of service and enhanced data rates to the end users. One such technology that stands out as a potential transmission scheme for 5G systems is Filter Bank Multicarrier using Offset Quadrature Amplitude Modulation (FBMC/OQAM) with an effective channel estimation technique for improved performance. However, due to the inherent imaginary interference, channel estimation methods relying on preamble structures in FBMC/OQAM systems exhibit sub-optimal performance, particularly within Multiple-Input Multiple-Output (MIMO) setups. For channel estimation schemes based on compressed sensing, the inherent sparsity of wireless channels can be exploited for accurate channel reconstruction and overall performance improvement.We propose a novel compressed sensing based algorithm namely, Adaptive Refined Random Orthogonal Matching Pursuit (ARROMP), for MIMO-FBMC system with Coordinated MultiPoint (CoMP) scheduling. This algorithm adaptively selects a support set by utilizing a double threshold for the minimization of mean squared error and for accurate channel reconstruction. The proposed algorithm's performance is compared with existing Orthogonal Matching Pursuit (OMP) schemes such as random OMP, refined random OMP, and least square-based estimation. The numerical simulations suggest that the proposed adaptive algorithm provides performance improvement in terms of reduced Mean Squared Error (MSE) of channel reconstruction and Bit Error Rate (BER). Moreover, the proposed ARROMP algorithm for MIMO-FBMC is rigorously tested with CoMP scheduling for a cellular network using frequency division duplex mode. The proposed system presents significant improvements in throughput and spectral efficiency for all types of cell users, including cell-edge users. The simulation results validate the improved performance of the proposed algorithm with CoMP scheduling over the existing single-cell system with no coordination.

Abstract Two‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

In this paper, an evaluation of the multiwavelet basis’ capability to represent the ECG signal sparsely was performed. The paper includes the mathematical formulation of sparsity, a brief introduction to the multiwavelet transform, as well as details about the simulation setup used for evaluation. Throughout the paper, various multiwavelets were investigated. The reported results show that the BAT and DB multiwavelets performed well, thus they could be used in the ECG signal sparsification. The investigation also focused on the ECG signals displaying deformations associated with illnesses. Preliminary results suggest that multiwavelets may prove beneficial for diverse processing of ECG signals.

Abstract This study aims to reconstruct signals that are sparse with a tight frame from undersampled data by using the ℓ q $\ell _{q}$ -minimization method. This problem can be cast as a ℓ q $\ell _{q}$ -minimization problem with a tight frame subjected to an undersampled measurement with a known noise bound. We proved that if the measurement matrix satisfies the restricted isometry property with δ 2 s ≤ 1 / 2 $\delta _{2s}\leq 1/2$ , there exists a value q 0 $q_{0}$ such that for any q ∈ ( 0 , q 0 ] $q\in (0,q_{0}]$ , any signal that is s-sparse with a tight frame can be robustly recovered to the true signal. We estimated q 0 $q_{0}$ as q 0 = 2 / 3 $q_{0} = 2/3$ in the case of δ 2 s ≤ 1 / 2 $\delta _{2s}\leq 1/2$ and discussed that the value of q 0 $q_{0}$ can be much higher. We also showed that when δ 2 s ≤ 0.3317 $\delta _{2s}\leq 0.3317$ , for any q ∈ ( 0 , 1 ] $q\in (0,1]$ , robust recovery for signals via ℓ q $\ell _{q}$ -minimization holds, which is consistent with the case of ℓ q $\ell _{q}$ -minimization without a tight frame.

Abstract This paper proposes a Boolean network model with high dimensional chaos driving and investigates the synchronization of the chaos‐driven Boolean network with a semi‐tensor product. In order to protect the privacy and ensure the security of image transmission, the synchronization results are utilized in the image cryptosystem to achieve compression and encryption. First, the driving chaos system is coupled with multiple local systems and synchronized with the transmitted encrypted signals. Second, the Boolean network is driven and synchronized with derived chaos signals. Finally, images are encrypted and compressed with chaos‐driven Boolean network signals in the transmitter, and then decrypted and recovered with synchronized chaos and Boolean network signals in the recipient. Because of the complexities of high dimensional chaos and Boolean network, the proposed cryptosystem has good security in the secure communication and image process.

Abstract Here, a novel image‐based quantized compressive sensing (QCS) framework based on complex‐valued Vandermonde (Vander) matrix is proposed. In the proposed QCS framework, a discrete wavelet transform (DWT) serves as a sparse basis and a partial complex‐valued Vander matrix serves as a measurement matrix. The theoretical analysis based on mutual coherence metric of compressive sensing (CS) theory shows that the proposed Vander measurement matrix has the best reconstruction performance among other conventional measurement matrices. The simulation results also show that the recovery quality using the proposed measurement matrix can be greatly improved compared with the other existing real‐valued measurement matrices. In particular, the experiment results also show that under the same measurement matrix, the reconstruction performance of Smoothed l0 norm (SL0) algorithm is better than that of Orthogonal Matching Pursuit (OMP) algorithm, sparsity adaptive matching pursuit (SAMP) algorithm and approximate message passing (AMP) algorithm. In addition, a sparse measurement matrix scheme is further proposed to achieve a trade‐off between recovery performance and computational complexity. The theoretical analysis and simulation results both show the proposed image‐based QCS is efficient.

An improved Synthetic Aperture Radar (SAR) imaging algorithm is proposed to address the issues of low azimuth resolution and noise interference in the sparse sampling condition. Based on the existing L1/2 regularization theory and iterative threshold algorithm, the gradient operator is modified, which can improve the solution accuracy of the reconstructed image and reduce the load of calculation. Then, under full sampling and under-sampling conditions, the original and improved L1/2 iterative threshold algorithm are combined with the approximate observation model to image SAR echo signals and compare their imaging performance. The experimental findings demonstrate that the improved algorithm improves the azimuth resolution of SAR images and has higher convergence performance.

In mineral, environmental, and engineering explorations, we frequently encounter geological bodies with varied sizes, depths, and conductivity contrasts with surround rocks and try to interpret them with single survey data. The conventional three-dimensional (3-D) inversions significantly rely on the size of the grids, which should be smaller than the smallest geological target to achieve a good recovery to anomalous electric conductivity. However, this will create a large amount of unknowns to be solved and cost significant time and memory. In this paper, we present a multi-scale (MS) stochastic inversion scheme based on shearlet transform for airborne electromagnetic (AEM) data. The shearlet possesses the features of multi-direction and multi-scale, allowing it to effectively characterize the underground conductivity distribution in the transformed domain. To address the practical implementation of the method, we use a compressed sensing method in the forward modeling and sensitivity calculation, and employ a preconditioner that accounts for both the sampling rate and gradient noise to achieve a fast stochastic 3-D inversion. By gradually updating the coefficients from the coarse to fine scales, we obtain the multi-scale information on the underground electric conductivity. The synthetic data inversion shows that the proposed MS method can better recover multiple geological bodies with different sizes and depths with less time consumption. Finally, we conduct 3-D inversions of a field dataset acquired from Byneset, Norway. The results show very good agreement with the geological information.

Interrupted-sampling repeater jamming (ISRJ) is widely used in the field of electronic countermeasures, and can severely affect radar detection. Therefore, the problem of ISRJ suppression is a compelling task. In this paper, we propose an ISRJ suppression method based on an intrapulse frequency-coded joint frequency modulation (FM) slope agile waveform. The intrapulse frequency-coded joint FM slope agile waveform is first designed. The delay inserted between subpulses makes the waveform easy to implement in engineering, and the ambiguity function diagram of the waveform approximates the ideal thumbtack type. Next, the echo slices are classified in the fractional domain utilizing the discontinuity of ISRJ and the focusing property of fractional Fourier transform for chirp signals. Then, the target and interference in the interfered echo slices are reconstructed by compressed sensing, and a time-domain filter is constructed based on interference-free echo slices. Finally, the echo signal after interference suppression is further filtered in the time domain to degrade range sidelobes. Simulation results show that the proposed method can effectively suppress three typical types of ISRJ. Moreover, the probability of target detection after interference suppression exceeds 90% when the jamming-to-signal ratio equals 50 dB.

With the increasingly complex electromagnetic environment faced by radar, random stepped frequency (RSF) has garnered widespread attention owing to its remarkable Electronic Counter-Countermeasure (ECCM) characteristic, and it has been universally applied in inverse synthetic aperture radar (ISAR) in recent years. However, if the phase error induced by the translational motion of the target in RSF ISAR is not precisely compensated, the imaging result will be defocused. To address this challenge, a novel 2D method based on sparse Bayesian learning, denoted as 2D-autofocusing complex-value inverse-free SBL (2D-AFCIFSBL), is proposed to accomplish joint ISAR imaging and autofocusing for RSF ISAR. First of all, to integrate autofocusing into the ISAR imaging process, phase error estimation is incorporated into the imaging model. Then, we increase the speed of Bayesian inference by relaxing the evidence lower bound (ELBO) to avoid matrix inversion, and we further convert the iterative process into a matrix form to improve the computational efficiency. Finally, the 2D phase error is estimated through maximum likelihood estimation (MLE) in the image reconstruction iteration. Experimental results on both simulated and measured datasets have substantiated the effectiveness and computational efficiency of the proposed 2D joint imaging and autofocusing method.

In insecure communication environments where the communication bandwidth is limited, important image data must be compressed and encrypted for transmission. However, existing image compression and encryption algorithms suffer from poor image reconstruction quality and insufficient image encryption security. To address these problems, this paper proposes an image-compression and encryption scheme based on a newly designed hyperchaotic system and two-dimensional compressed sensing (2DCS) technique. In this paper, the chaotic performance of this hyperchaotic system is verified by bifurcation diagrams, Lyapunov diagrams, approximate entropy, and permutation entropy, which have certain advantages over the traditional 2D chaotic system. The new 2D chaotic system as a pseudo-random number generator can completely pass all the test items of NIST. Meanwhile, this paper improves on the existing 2D projected gradient (2DPG) algorithm, which improves the quality of image compression and reconstruction, and can effectively reduce the transmission pressure of image data confidential communication. In addition, a new image encryption algorithm is designed for the new 2D chaotic system, and the security of the algorithm is verified by experiments such as key space size analysis and encrypted image information entropy.

Objective: The objective of this study was to evaluate the clinical feasibility of deep learning reconstruction-accelerated thin-slice single-breath-hold half-Fourier single-shot turbo spin echo imaging (HASTEDL) for detecting pancreatic lesions, in comparison with two conventional T2-weighted imaging sequences: compressed-sensing HASTE (HASTECS) and BLADE. Methods: From March 2022 to January 2023, a total of 63 patients with suspected pancreatic-related disease underwent the HASTEDL, HASTECS, and BLADE sequences were enrolled in this retrospectively study. The acquisition time, the pancreatic lesion conspicuity (LCP), respiratory motion artifact (RMA), main pancreatic duct conspicuity (MPDC), overall image quality (OIQ), signal-to-noise ratio (SNR), and contrast-noise-ratio (CNR) of the pancreatic lesions were compared among the three sequences by two readers. Results: The acquisition time of both HASTEDL and HASTECS was 16 s, which was significantly shorter than that of 102 s for BLADE. In terms of qualitative parameters, Reader 1 and Reader 2 assigned significantly higher scores to the LCP, RMA, MPDC, and OIQ for HASTEDL compared to HASTECS and BLADE sequences; As for the quantitative parameters, the SNR values of the pancreatic head, body, tail, and lesions, the CNR of the pancreatic lesion measured by the two readers were also significantly higher for HASTEDL than for HASTECS and BLADE sequences. Conclusions: Compared to conventional T2WI sequences (HASTECS and BLADE), deep-learning reconstructed HASTE enables thin slice and single-breath-hold acquisition with clinical acceptable image quality for detection of pancreatic lesions.

The Internet of Things (IoT)’s rapid development is placing new demands on communication technology for power distribution. This paper proposes the application scheme of RSSI adaptive and dual-mode communication technology in the power distribution area, realizes the dual-mode networking technology adopted to improve communication quality, and verifies the reliability and superiority of the dual-mode communication technology scheme through analysis and application. The RSSI adaptive dual-mode communication module is designed, the RSSI model algorithm is modified, and the logical topology of the communication network and the data processing technology based on compressed sensing are analyzed. We focus on analyzing the performance of dual-mode communication networks for power consumption information collection and the information reception rate and real-time performance of MQTT protocol mapping for power distribution IoT. The average transmission delay was tested to be 198.5ms for QoS=0, 478.0ms for QoS=1, and 786.3ms for QoS=2 without encryption. When using SASL/TLS for transmission encryption, the average transmission delay is 992.7ms for QoS=0, 1203.6ms for QoS=1, and 1461.1ms for QoS=2.

BackgroundDue to its potential to significantly reduce scanning time while delivering accurate results for cardiac volume function, compressed sensing (CS) has gained traction in cardiovascular magnetic resonance (CMR) cine. However, further investigation is necessary to explore its feasibility and impact on myocardial strain results.Materials and methodsA total of 102 participants [75 men, 46.5 ± 17.1 (SD) years] were included in this study. Each patient underwent four consecutive cine sequences with the same slice localization, including the reference multi-breath-hold balanced steady-state free precession (bSSFPref) cine, the CS cine with the same flip angle as bSSFPref before (CS45) and after (eCS45) contrast enhancement, and the CS cine (eCS70) with a 70-degree flip angle after contrast enhancement. Biventricular strain parameters were derived from cine images. Two-tailed paired t-tests were used for data analysis.ResultsGlobal radial strain (GRS), global circumferential strain (GCS), and global longitudinal strain (GLS) were observed to be significantly lower in comparison to those obtained from bSSFPref sequences for both the right and left ventricles (all p

The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the l1 norm as a substitute for the l0 norm. Many efforts have been made to minimize the lp norm (0 < p < 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the lp norm with 0 < p < 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 p→0+. Therefore, the CS method with the limit p→0+ is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing p→0+ is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.

Purposes Deep compressed sensing is the use of deep learning to solve the problems existing in traditional compressed sensing, such as the adaptability of observation matrix to traditional signal compression and the dependency on dictionary by reconstruction algorithm. Methods In this paper, the deep belief network (DBN) is used to adaptively compress the signal without destroying the randomness of observation matrix. At the same time, the stacked auto encoder (SAE) is used to train the reconstruction network end-to-end to get rid of the dependence of the reconstruction algorithm on sparse dictionary. According to the discrimination of the sparse representation of signal, a compressed sensing recognition model based on DBN and SAE is proposed (CS-DBN-SAE). Findings The results of four classification experiments on DEAP emotional EEG database show that the recognition rate of CS-DBN-SAE model is 83.29%, which is oven 4.3% higher than that of traditional compressed sensing recognition model.

Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. These methods, such as the Proper Orthogonal Decomposition (POD) or Reduced Basis (RB) methods, are very effective when the family of solutions has fast-decaying Karhunen–Loève eigenvalues or Kolmogorov widths, reflecting the approximability by finite-dimensional linear spaces. On the other hand, they become ineffective when these quantities have a slow decay, in particular for families of solutions to hyperbolic transport equations with parameter-dependent shock positions. The objective of this work is to explore the ability of nonlinear model reduction to circumvent this particular situation. To this end, we first describe particular notions of nonlinear widths that have a substantially faster decay for the aforementioned families. Then, we discuss a systematic approach for achieving better performance via a nonlinear reconstruction from the first coordinates of a linear reduced model approximation, thus allowing us to stay in the same “classical” framework of projection-based model reduction. We analyze the approach and report on its performance for a simple and yet instructive univariate test case.

Abstract Purpose Highly accelerated compressed sensing cine has allowed for quantification of ventricular function in a single breath hold. However, compared to segmented breath hold techniques, there may be underestimation or overestimation of LV volumes. Furthermore, a heterogeneous sample of techniques have been used in volunteers and patients for pre-clinical and clinical use. This can complicate individual comparisons where small, but statistically significant differences exist in left ventricular morphological and/or functional parameters. This meta-analysis aims to provide a comparison of conventional cine versus compressed sensing based reconstruction techniques in patients and volunteers. Methods Two investigators performed systematic searches for eligible studies using PubMed/MEDLINE and Web of Science to identify studies published 1/1/2010-3/1/2021. Ultimately, 15 studies were included for comparison between compressed sensing cine and conventional imaging. Results Compared to conventional cine, there were small, statistically significant overestimation of LV mass, underestimation of stroke volume and LV end diastolic volume (mean difference 2.65 g [CL 0.57–4.73], 2.52 mL [CL 0.73–4.31], and 2.39 mL [CL 0.07–4.70], respectively). Attenuated differences persisted across studies using prospective gating (underestimated stroke volume) and non-prospective gating (underestimation of stroke volume, overestimation of mass). There were no significant differences in LV volumes or LV mass with high or low acceleration subgroups in reference to conventional cine except slight underestimation of ejection fraction among high acceleration studies. Reduction in breath hold acquisition time ranged from 33 to 64%, while reduction in total scan duration ranged from 43 to 97%. Conclusion LV volume and mass assessment using compressed sensing CMR is accurate compared to conventional parallel imaging cine.

Abstract Non‐sidelooking airborne radar encounters significant non‐stationary and heterogeneous clutter environments, resulting in a severe shortage of samples. Sparse recovery‐based space‐time adaptive processing (SR‐STAP) methods can achieve good clutter suppression performance with limited samples. Nonetheless, grid‐based SR‐STAP algorithms encounter off‐grid effects in non‐sidelooking arrays, which can severely degrade the clutter suppression performance. In this study, the authors propose a novel gridless SR‐STAP method in the continuous spatial‐temporal domain to address the issue of off‐grid effects. Inspired by the fact that sparse Bayesian learning (SBL) framework implicitly performs a structured covariance matrix estimation, the authors reparameterise its cost function to directly estimate the block‐Toeplitz structured matrix from the measurements in a gridless manner. Since the proposed cost function is non‐convex, we utilise a majorisation‐minimisation‐based iterative procedure to estimate the clutter covariance matrix. Finally, using the standard concept of semidefinite programming, the authors derive a convex gridless implementation of the SBL cost function for uniformly sampled radar systems. Extensive simulation experiments demonstrate the exceptional clutter suppression and target detection performance of the proposed algorithm.

In the conventional single-molecule localizations and super-resolution microscopy, the pixel size of a raw image is approximately equal to the standard deviation of the point spread function. Such a raw image is referred to herein as a conventional raw image, based on which better single molecule localization effect and efficiency can be achieved. It is found that both interpolation and de-noising can effectively improve the Signal to Noise Ratio of the conventional raw image. The conventional raw image, the de-noised, the interpolated and the de-noised interpolated are compared and analyzed and compressed sensing is used for super-resolution reconstruction. The simulation results show that both the highest Signal to Noise Ratio and the best super-resolution reconstruction can be obtained by de-noising the interpolated conventional raw image. This method also renders the best super-resolution reconstruction and minimum gradient in the real experiment. De-noising the interpolated conventional raw image is an effective method to improve the super-resolution microscopy.

Abstract Partial discharge (PD) signals have a large amount of data and a low energy proportion of pulse signals, resulting in difficult data transmission and poor reconstruction efficiency. To this end, a PD signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold (TSR‐DRRT) is proposed. TSR‐DRRT is centred on the sparse representation (SR) and accurate reconstruction of noisy signals. The intrinsic pulse of PD signals is extracted by signal decomposition, and jointly trained with different types of signals to establish the transfer SR dictionary. The compressed signal accurately retains the essential characteristics of the pulse information by improving the match between the dictionary atoms and the polymorphic PD pulses. To match the transfer SR dictionary, the inner and outer DRRT iteration termination conditions are set adaptively during the reconstruction process based on the correlation difference between the dictionary and signal frames. Independent control of PD pulse recognition and reconstruction accuracy is achieved, and its performance under noisy signals is improved. The results show that the method can achieve high ratio compression and efficient reconstruction of noisy signals. Different types of PD signals can also have high matching accuracy. This method can meet the demand for PD signals compression and transmission to the terminal for accurate reconstruction.

Abstract The Internet of Things (IoT) has grown rapidly over the past few years. The main challenges for people who design and make these systems are to make them use less energy and use as small hardware as possible. Recording and sending compressed images in IoT systems must be secure. Secure image transmission requires encryption, watermarking, and compression. In choosing these algorithms, one should always consider energy efficiency and low hardware complexity. So, we propose a secure way to send data in IoT systems by combining encryption, watermarking, and compression. Depending on what is needed, we use a lightweight encryption algorithm, discrete wavelet transform (DWT) watermarking, and Discrete cosine transform + Lempel‐Ziv‐Welch (DCT+LZW) compression. In this method, the main contribution is to make a security pack that is small, strong, and easy to implement for secure image transmission on IoT systems. In the experiments, several images are used to judge how well the proposed integrated method works and how well it compares to other methods. When the proposed method was compared to other methods, the peak signal‐to‐noise ratio (PSNR) parameter improved by more than 20% in the Lena image and by more than 11% in the Baboon image.

Abstract Purpose To investigate the feasibility and clinical utility of a compressed-sensing-accelerated subtractionless whole-body MRA (CS-WBMRA) protocol with only contrast injection for suspected arterial diseases, by comparison to conventional dual-pass subtraction-based whole-body MRA (conventional-WBMRA) and available computed tomography angiography (CTA). Materials and methods This prospective study assessed 86 patients (mean age, 56 years ± 16.4 [standard deviation]; 25 women) with suspected arterial diseases from May 2021 to December 2022, who underwent CS-WBMRA (n = 48, mean age, 55.9 years ± 16.4 [standard deviation]; 25 women) and conventional-WBMRA (n = 38, mean age, 48 years ± 17.4 [standard deviation]; 20 women) on a 3.0 T MRI after random group assignment based on the chronological order of enrolment. Of all enrolled patients administered the CS-WBMRA protocol, 35% (17/48) underwent CTA as required by clinical demands. Two experienced radiologists independently scored the qualitative image quality and venous enhancement contamination. Quantitative image assessment was carried out by determining and comparing the apparent signal-to-noise ratios (SNRs) and contrast-to-noise ratios (CNRs) of four representative arterial segments. The total examination time and contrast-dose were also recorded. The independent samples t-test or the Wilcoxon rank sum test was used for statistical analysis. Results The overall scores of CS-WBMRA outperformed those of conventional-WMBRA (3.40 ± 0.60 vs 3.22 ± 0.55, P 0.05) between the two protocols. In the quantitative analysis, overall apparent SNRs were significantly higher in the conventional-WBMRA group than in the CS-WBMRA group (214.98 ± 136.05 vs 164.90 ± 118.05; P 0.05). In the CS-WBMRA group, 7 of 1776 (0.4%) vessel segments were contaminated severely by venous enhancement, while in the convention-WBMRA group, 317 of 1406 (23%) were rated as severe contamination. In the CS-WBMRA group, total examination and reconstruction times were only 7 min and 10 min, respectively, vs 20 min and

Block compressed sensing (BCS) is a promising method for resource-constrained image/video coding applications. However, the quantization of BCS measurements has posed a challenge, leading to significant quantization errors and encoding redundancy. In this paper, we propose a quantization method for BCS measurements using convolutional neural networks (CNN). The quantization process maps measurements to quantized data that follow a uniform distribution based on the measurements’ distribution, which aims to maximize the amount of information carried by the quantized data. The dequantization process restores the quantized data to data that conform to the measurements’ distribution. The restored data are then modified by the correlation information of the measurements drawn from the quantized data, with the goal of minimizing the quantization errors. The proposed method uses CNNs to construct quantization and dequantization processes, and the networks are trained jointly. The distribution parameters of each block are used as side information, which is quantized with 1 bit by the same method. Extensive experiments on four public datasets showed that, compared with uniform quantization and entropy coding, the proposed method can improve the PSNR by an average of 0.48 dB without using entropy coding when the compression bit rate is 0.1 bpp.

The large amount of sampled data in coherent phase-sensitive optical time-domain reflectometry (Φ-OTDR) brings heavy data transmission, processing, and storage burdens. By using the comparator combined with undersampling, we achieve simultaneous reduction of sampling rate and sampling resolution in hardware, thus greatly decreasing the sampled data volume. But this way will inevitably cause the deterioration of detection signal-to-noise ratio (SNR) due to the quantization noise’s dramatic increase. To address this problem, denoising the demodulated phase signals using compressed sensing, which exploits the sparsity of spectrally sparse vibration, is proposed, thereby effectively enhancing the detection SNR. In experiments, the comparator with a sampling parameter of 62.5 MS/s and 1 bit successfully captures the 80 MHz beat signal, where the sampled data volume per second is only 7.45 MB. Then, when the piezoelectric transducer’s driving voltage is 1 Vpp, 300 mVpp, and 100 mVpp respectively, the SNRs of the reconstructed 200 Hz sinusoidal signals are respectively enhanced by 23.7 dB, 26.1 dB, and 28.7 dB by using compressed sensing. Moreover, multi-frequency vibrations can also be accurately reconstructed with a high SNR. Therefore, the proposed technique can effectively enhance the system’s performance while greatly reducing its hardware burden.