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Cardiovascular magnetic resonance (CMR) protocols can be lengthy and complex, which has driven the research community to develop new technologies to make these protocols more efficient and patient-friendly. Two different approaches to improving CMR have been proposed, specifically "all-in-one" CMR, where several contrasts and/or motion states are acquired simultaneously, and "real-time" CMR, in which the examination is accelerated to avoid the need for breathholding and/or cardiac gating. The goal of this two-part manuscript is to describe these two different types of emerging rapid CMR. To this end, the vision of each is described, along with techniques which have been devised and tested along the pathway of clinical implementation. The pros and cons of the different methods are presented, and the remaining open needs of each are detailed. Part 1 will tackle the "all-in-one" approaches, and Part 2 the "real-time" approaches along with an overall summary of these emerging methods.

Binding energies of radicals and molecules at dust grain surfaces are important parameters for understanding and modeling the chemical inventory of interstellar gas clouds. While first-principles methods can reliably be used to compute such binding energies, the complex structure and varying sizes and stoichiometries of realistic dust grains make a complete characterization of all adsorption sites exposed by their surfaces challenging. Here, we focus on nanoclusters composed of Mg-rich silicates as models of interstellar dust grains and two adsorbates of particular astrochemical relevance; H and CO. We employ a compressed sensing method to identify descriptors for the binding energies, which are expressed as analytical functions of intrinsic properties of the clusters, obtainable through a single first-principles calculation of the cluster. The descriptors are identified based on a diverse training dataset of binding energies at low-energy structures of nanosilicate clusters, where the latter structures were obtained using a first-principles-based global optimization method. The composition of the descriptors reveals how electronic, electrostatic, and geometric properties of the nanosilicates control the binding energies and demonstrates distinct physical origins of the bond formation for H and CO. The predictive performance of the descriptors is found to be limited by cluster reconstruction, e.g., breaking of internal metal–oxygen bonds, upon the adsorption event, and strategies to account for this phenomenon are discussed. The identified descriptors and the computed datasets of stable nanosilicate clusters along with their binding energies are expected to find use in astrochemical models of reaction networks occurring at silicate grain surfaces. [ABSTRACT FROM AUTHOR]

It is well-known that the problem of sampling recovery in the L_2-norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as Hölder classes suffers from the curse of dimensionality. We show that the problem is tractable for those classes if they are intersected with the Wiener algebra of functions with summable Fourier coefficients. In fact, this is a relatively simple implication of powerful results from the theory of compressed sensing. Tractability is achieved by the use of non-linear algorithms, while linear algorithms cannot do the job. [ABSTRACT FROM AUTHOR]

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 × , 5 × and 8 × Cartesian undersampling in all studied metrics. FI VarNet secured second place in the public fastMRI leaderboard for 4 × 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. [ABSTRACT FROM AUTHOR]

Photoacoustic imaging (PAI) is a rapidly developing emerging non-invasive biomedical imaging technique that combines the strong contrast from optical absorption imaging and the high resolution from acoustic imaging. Abnormal biological tissues (such as tumors and inflammation) generate different levels of thermal expansion after absorbing optical energy, producing distinct acoustic signals from normal tissues. This technique can detect small tissue lesions in biological tissues and has demonstrated significant potential for applications in tumor research, melanoma detection, and cardiovascular disease diagnosis. During the process of collecting photoacoustic signals in a PAI system, various factors can influence the signals, such as absorption, scattering, and attenuation in biological tissues. A single ultrasound transducer cannot provide sufficient information to reconstruct high-precision photoacoustic images. To obtain more accurate and clear image reconstruction results, PAI systems typically use a large number of ultrasound transducers to collect multi-channel signals from different angles and positions, thereby acquiring more information about the photoacoustic signals. Therefore, to reconstruct high-quality photoacoustic images, PAI systems require a significant number of measurement signals, which can result in substantial hardware and time costs. Compressed sensing is an algorithm that breaks through the Nyquist sampling theorem and can reconstruct the original signal with a small number of measurement signals. PAI based on compressed sensing has made breakthroughs over the past decade, enabling the reconstruction of low artifacts and high-quality images with a small number of photoacoustic measurement signals, improving time efficiency, and reducing hardware costs. This article provides a detailed introduction to PAI based on compressed sensing, such as the physical transmission model-based compressed sensing method, two-stage reconstruction-based compressed sensing method, and single-pixel camera-based compressed sensing method. Challenges and future perspectives of compressed sensing-based PAI are also discussed. [ABSTRACT FROM AUTHOR]

In inverse synthetic aperture radar (ISAR) imaging, the conventional range-Doppler (RD) algorithm cannot obtain satisfactory imaging results for sparse aperture. Compressed sensing (CS) imaging methods, such as the typical iterative shrinkage and thresholding algorithm (ISTA), are often used in sparse aperture radar imaging. However, CS-based methods have high computational complexity and difficulty in setting parameters. To overcome the shortcomings, a new deep unfolding network named complex-valued weighted learning ISTA (CV-WLISTA) is proposed in this paper. The new network is very efficient and can learn the parameters adaptively. Based on ISTA and a new weighting strategy, it takes advantage of both the sparsity and the structural property of ISAR images to improve imaging performance. The experimental results show that CV-WLISTA has better reconstruction performance and higher efficiency compared with the traditional algorithms. Therefore, CV-WLISTA is an efficient ISAR imaging method with excellent performance. [ABSTRACT FROM AUTHOR]

Due to the limitations of the actual acquisition environment in the field, especially in ocean bottom seismometer (OBS) acquisition, the acquired seismic data are often irregular and incomplete, which affects the subsequent data imaging, interpretation and hydrocarbon‐bearing reservoir prediction. The interpolation reconstruction algorithm based on the compressive sensing theory can reconstruct the data without the limitation of Nyquist sampling interval. However, the reconstruction accuracy and effect are different for different sparse representations of the data. On the basis of compressed sensing theory, we propose a Bregman iterative seismic data reconstruction method based on the sparse decomposition of discrete orthonormal Coiflets and Symlets wavelet transforms. First, the discrete orthonormal matrix is constructed by using the above two wavelet functions to make the original seismic data sparse, then the Bregman iterative algorithm is used to reconstruct the sparse coefficients in the discrete wavelet domain, and finally the recovery matrix is used to reconstruct the seismic data. The discrete orthonormal Coiflets and Symlets wavelet transforms have good sparse representation ability and can compensate for the problem that discrete Fourier transform cannot well sparse representation of the data. After numerical experiments on horizontal‐layered model, Marmousi2 model and actual data, it is verified that the proposed method can reconstruct the missing seismic data under the regular observation system and under the irregular observation system with non‐uniform OBS distribution. Furthermore, this method can hardly bring the interference of random noise, and the reconstruction result is of high accuracy. [ABSTRACT FROM AUTHOR]

Sparse arrays are widely used to achieve full array performance with fewer elements to reduce the cost of array and beamforming computation. Sparse array synthesis methods such as Bayesian compressed sensing (BCS) yield small element numbers; however, they are limited by the tradeoff between complexity and accuracy. Herein, a novel sparse array synthesis method with two-stage progressive BCS and an undirected graph-based element spacing constraint is proposed. The two-stage progressive BCS includes fast on-grid sparsification and accurate off-grid global re-estimation. First, the multitask BCS is solved using a relevance vector machine to efficiently select elements from candidate positions. Subsequently, a convex surrogate cost function is applied to the global re-estimation of the element weights to increase the beam pattern matching accuracy of the sparse array. Global optimization can improve the array performance. In addition, to satisfy the spacing constraint, a weighted merging method based on an undirected graph is proposed and inserted between the two stages to merge elements that are too close, which ensures the processability of the array. Simulations and experiments involving a variety of arrays were conducted to confirm the advantages of the method with regard to array sparsity, sidelobe suppression, beam pattern matching accuracy, and array processability. The proposed method achieved accurate and effective sparse array synthesis and outperformed existing methods. [ABSTRACT FROM AUTHOR]

To assess the utility of deep learning (DL)-based image reconstruction with the combination of compressed sensing (CS) denoising cycle by comparing images reconstructed by conventional CS-based method without DL in fat-suppressed (Fs)-contrast enhanced (CE) three-dimensional (3D) T1-weighted images (T1WIs) of the head and neck. We retrospectively analyzed the cases of 39 patients who had undergone head and neck Fs-CE 3D T1WI applying reconstructions based on conventional CS and CS augmented by DL, respectively. In the qualitative assessment, we evaluated overall image quality, visualization of anatomical structures, degree of artifacts, lesion conspicuity, and lesion edge sharpness based on a five-point system. In the quantitative assessment, we calculated the signal-to-noise ratios (SNRs) of the lesion and the posterior neck muscle and the contrast-to-noise ratio (CNR) between the lesion and the adjacent muscle. For all items of the qualitative analysis, significantly higher scores were awarded to images with DL-based reconstruction (p < 0.001). In the quantitative analysis, DL-based reconstruction resulted in significantly higher values for both the SNR of lesions (p < 0.001) and posterior neck muscles (p < 0.001). Significantly higher CNRs were also observed in images with DL-based reconstruction (p < 0.001). DL-based image reconstruction integrating into the CS-based denoising cycle offered superior image quality compared to the conventional CS method. This technique will be useful for the assessment of patients with head and neck disease. • The acquisition of good image quality poses challenges in MRI of the head and neck. • Superior image quality in CE 3D-T1WI was achieved using CS-based DL reconstruction. • CS-based DL reconstruction may serve as a beneficial tool for head and neck MRI. [ABSTRACT FROM AUTHOR]

The purpose of this study was to determine the utility of compressed sensing (CS) with deep learning reconstruction (DLR) for improving spatial resolution, image quality and focal liver lesion detection on high-resolution contrast-enhanced T1-weighted imaging (HR-CE-T1WI) obtained by CS with DLR as compared with conventional CE-T1WI with parallel imaging (PI). Seventy-seven participants with focal liver lesions underwent conventional CE-T1WI with PI and HR-CE-T1WI, surgical resection, transarterial chemoembolization, and radiofrequency ablation, followed by histopathological or >2-year follow-up examinations in our hospital. Signal-to-noise ratios (SNRs) of liver, spleen and kidney were calculated for each patient, after which each SNR was compared by means of paired t -test. To compare focal lesion detection capabilities of the two methods, a 5-point visual scoring system was adopted for a per lesion basis analysis. Jackknife free-response receiver operating characteristic (JAFROC) analysis was then performed, while sensitivity and false positive rates (/data set) for consensus assessment of the two methods were also compared by using McNemar's test or the signed rank test. Each SNR of HR-CE-T1WI was significantly higher than that of conventional CE-T1WI with PI (p < 0.05). Sensitivities for consensus assessment showed that HR-CE-MRI had significantly higher sensitivity than conventional CE-T1WI with PI (p = 0.004). Moreover, there were significantly fewer FP/cases for HR-CE-T1WI than for conventional CE-T1WI with PI (p = 0.04). CS with DLR are useful for improving spatial resolution, image quality and focal liver lesion detection capability of Gd-EOB-DTPA enhanced 3D T1WI without any need for longer breath-holding time. • SNR of HR-CE-T1WI for each organ were significantly higher than that of conventional CE-T1WI with PI (p<0.05). • Qualitative indexes of HR-CE-T1WI were significantly improved, when compared with conventional CE-T1WI with PI (p<0.05). • HR-CE-T1WI demonstrated significantly better diagnostic performance with conventional CE-T1WI with PI (p<0.05). [ABSTRACT FROM AUTHOR]

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the generalized orthogonal matching pursuit (gOMP) algorithm. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is presented based on restricted isometry property (RIP) and restricted orthogonality constant (ROC). [ABSTRACT FROM AUTHOR]

Background: Cardiac MRI feature‐tracking (FT) with breath‐holding (BH) cine balanced steady state free precession (bSSFP) imaging is well established. It is unclear whether FT‐strain measurements can be reliably derived from free‐breathing (FB) compressed sensing (CS) bSSFP imaging. Purpose: To compare left ventricular (LV) strain analysis and image quality of an FB CS bSSFP cine sequence with that of a conventional BH bSSFP sequence in children. Study Type: Prospective. Subjects: 40 children able to perform BHs (cohort 1 [12.1 ± 2.2 years]) and 17 children unable to perform BHs (cohort 2 [5.2 ± 1.8 years]). Field Strength/Sequence: 3T, bSSFP sequence with and without CS. Assessment: Acquisition times and image quality were assessed. LV myocardial deformation parameters were compared between BH cine and FB CS cine studies in cohort 1. Strain indices and image quality of FB CS cine studies were also assessed in cohort 2. Intraobserver and interobserver variability of strain parameters was determined. Statistical Tests: Paired t‐test, Wilcoxon signed‐rank test, intraclass correlation coefficient (ICC), and Bland–Altman analysis. A P‐value <0.05 was considered statistically significant. Results: In cohort 1, the mean acquisition time of the FB CS cine study was significantly lower than for conventional BH cine study (15.6 s vs. 209.4 s). No significant difference were found in global circumferential strain rate (P = 0.089), global longitudinal strain rate (P = 0.366) and EuroCMR image quality scores (P = 0.128) between BH and FB sequences in cohort 1. The overall image quality score of FB CS cine in cohort 2 was 3.5 ± 0.5 with acquisition time of 14.7 ± 2.1 s. Interobserver and intraobserver variabilities were good to excellent (ICC = 0.810 to 0.943). Data Conclusion: FB CS cine imaging may be a promising alternative technique for strain assessment in pediatric patients with poor BH ability. Level of Evidence: 1 Technical Efficacy: Stage 1 [ABSTRACT FROM AUTHOR]

Purpose: To develop a highly‐accelerated, real‐time phase contrast (rtPC) MRI pulse sequence with 40 fps frame rate (25 ms effective temporal resolution). Methods: Highly‐accelerated golden‐angle radial sparse parallel (GRASP) with over regularization may result in temporal blurring, which in turn causes underestimation of peak velocity. Thus, we amplified GRASP performance by synergistically combining view‐sharing (VS) and k‐space weighted image contrast (KWIC) filtering. In 17 pediatric patients with congenital heart disease (CHD), the conventional GRASP and the proposed GRASP amplified by VS and KWIC (or GRASP + VS + KWIC) reconstruction for rtPC MRI were compared with respect to clinical standard PC MRI in measuring hemodynamic parameters (peak velocity, forward volume, backward volume, regurgitant fraction) at four locations (aortic valve, pulmonary valve, left and right pulmonary arteries). Results: The proposed reconstruction method (GRASP + VS + KWIC) achieved better effective spatial resolution (i.e., image sharpness) compared with conventional GRASP, ultimately reducing the underestimation of peak velocity from 17.4% to 6.4%. The hemodynamic metrics (peak velocity, volumes) were not significantly (p > 0.99) different between GRASP + VS + KWIC and clinical PC, whereas peak velocity was significantly (p < 0.007) lower for conventional GRASP. RtPC with GRASP + VS + KWIC also showed the ability to assess beat‐to‐beat variation and detect the highest peak among peaks. Conclusion: The synergistic combination of GRASP, VS, and KWIC achieves 25 ms effective temporal resolution (40 fps frame rate), while minimizing the underestimation of peak velocity compared with conventional GRASP. [ABSTRACT FROM AUTHOR]

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This paper concentrates on the recovery of block-sparse signals, which are not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP, which could ensure the exact recovery of every block s-sparse signal in the noiseless case via mixed l 2 / l p {l_{2}/l_{p}} minimization method, and the stable and robust recovery in the case that signals are not accurately block-sparse in the presence of noise. Additionally, a lower bound on necessary number of random Gaussian measurements is gained for the condition to be true with overwhelming probability. Furthermore, a series of numerical experiments are conducted to demonstrate the performance of the mixed l 2 / l p {l_{2}/l_{p}} minimization. To the best of the authors’ knowledge, the recovery guarantees established in this paper are superior to those currently available. [ABSTRACT FROM AUTHOR]

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l 1 − l 1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Large-aperture, lightweight, and high-resolution imaging are hallmarks of major optical systems. To eliminate aberrations, traditional systems are often bulky and complex, whereas the small volume and light weight of diffractive lenses position them as potential substitutes. However, their inherent diffraction mechanism leads to severe dispersion, which limits their application in wide spectral bands. Addressing the dispersion issue in diffractive lenses, we propose a chromatic aberration correction algorithm based on compressed sensing. Utilizing the diffractive lens's focusing ability at the reference wavelength and its degradation performance at other wavelengths, we employ compressed sensing to reconstruct images from incomplete image information. In this work, we design a harmonic diffractive lens with a diffractive order of M = 150 , an aperture of 40 mm, a focal length f 0 = 320 mm, a reference wavelength λ 0 = 550 nm, a wavelength range of 500–800 nm, and 7 annular zones. Through algorithmic recovery, we achieve clear imaging in the visible spectrum, with a peak signal-to-noise ratio (PSNR) of 22.85 dB, a correlation coefficient of 0.9596, and a root mean square error (RMSE) of 0.02, verifying the algorithm's effectiveness. [ABSTRACT FROM AUTHOR]

In the paper, we investigate a massive machine-type communication (mMTC), where numerous single-antenna users communicate with a single-antenna base station while being active. However, the status of user can undergoes multiple transitions between active and inactive states across whole consecutive intervals. Then, we formulate the problem of joint user activity detection and channel estimation within the dynamic compressed sensing (DCS) framework, considering the temporally-correlated user activity across the entire consecutive intervals. To be specific, we introduce a new hybrid vector approximate message passing algorithm for DCS (HyVAMP-DCS). The proposed algorithm comprises a VAMP block for estimating channel and a loopy belief propagation (LBP) block for detecting user activity. Moreover, these two blocks can exchange messages, enhancing the performance of both channel estimation and user activity detection. Importantly, compared to the fragile GAMP algorithm, VAMP is robust and applicable to a much broader class of large random matrices. Furthermore, the fixed points of VAMP's state evolution align with the replica prediction of the minimum mean-squared error. The simulation results illustrate the superiority of HyVAMP-DCS, demonstrating its significant outperformance over HyGAMP-DCS. [ABSTRACT FROM AUTHOR]

Background: To investigate the potential of combining compressed sensing (CS) and artificial intelligence (AI), in particular deep learning (DL), for accelerating three-dimensional (3D) magnetic resonance imaging (MRI) sequences of the knee. Methods: Twenty healthy volunteers were examined using a 3-T scanner with a fat-saturated 3D proton density sequence with four different acceleration levels (10, 13, 15, and 17). All sequences were accelerated with CS and reconstructed using the conventional and a new DL-based algorithm (CS-AI). Subjective image quality was evaluated by two blinded readers using seven criteria on a 5-point-Likert-scale (overall impression, artifacts, delineation of the anterior cruciate ligament, posterior cruciate ligament, menisci, cartilage, and bone). Using mixed models, all CS-AI sequences were compared to the clinical standard (sense sequence with an acceleration factor of 2) and CS sequences with the same acceleration factor. Results: 3D sequences reconstructed with CS-AI achieved significantly better values for subjective image quality compared to sequences reconstructed with CS with the same acceleration factor (p ≤ 0.001). The images reconstructed with CS-AI showed that tenfold acceleration may be feasible without significant loss of quality when compared to the reference sequence (p ≥ 0.999). Conclusions: For 3-T 3D-MRI of the knee, a DL-based algorithm allowed for additional acceleration of acquisition times compared to the conventional approach. This study, however, is limited by its small sample size and inclusion of only healthy volunteers, indicating the need for further research with a more diverse and larger sample. Trial registration: DRKS00024156. Relevance statement: Using a DL-based algorithm, 54% faster image acquisition (178 s versus 384 s) for 3D-sequences may be possible for 3-T MRI of the knee. Key points: • Combination of compressed sensing and DL improved image quality and allows for significant acceleration of 3D knee MRI. • DL-based algorithm achieved better subjective image quality than conventional compressed sensing. • For 3D knee MRI at 3 T, 54% faster image acquisition may be possible. [ABSTRACT FROM AUTHOR]

Traditional bridge health monitoring methods that necessitate sensor installation are not only costly but also time-consuming. In contrast, utilizing smartphone data collected from vehicles as they traverse bridges offers an efficient and cost-effective alternative. This paper introduces a cutting-edge damage detection framework for indirect monitoring of bridge structures, leveraging a substantial volume of acceleration data collected from smartphones in vehicles passing over the bridge. Our innovative approach addresses the challenge of collecting and transmitting high-frequency data while preserving smartphone battery life and data plans through the integration of compressed sensing (CS) into the crowdsensing-based monitoring framework. CS employs random sampling and signal recovery from a significantly reduced number of samples compared to the requirements of the Nyquist–Shannon sampling theorem. In the proposed framework, acceleration signals from vehicles are initially acquired using smartphone sensors, undergo compression, and are then transmitted for signal reconstruction. Subsequently, feature extraction and dimensionality reduction are performed using Mel-frequency cepstral coefficients and principal component analysis. Damage indexes are computed based on the dissimilarity between probability distribution functions utilizing the Wasserstein distance metric. The efficacy of the proposed methodology in bridge monitoring has been substantiated through the utilization of numerical models and a lab-scale bridge. Furthermore, the feasibility of implementing the framework in a real-world application has been investigated, leveraging the smartphone data from 102 vehicle trips on the Golden Gate Bridge. The results demonstrate that damage detection using the reconstructed signals obtained through compressed sensing achieves comparable performance to that obtained with the original data sampled at the Nyquist measurement sampling rate. However, it is observed that to retain severity information within the signals for accurate damage severity identification, the compression level should be limited to 20%. These findings affirm that compressed sensing significantly reduces the data collection requirements for crowdsensing-based monitoring applications, without compromising the accuracy of damage detection while preserving essential damage-sensitive information within the dataset. [ABSTRACT FROM AUTHOR]

Scalable numerical solutions to the time dependent Schrodinger equation remain an outstanding goal in theoretical chemistry. Here we present a method which utilises recent breakthroughs in signal processing to consistently adapt a dictionary of basis functions to the dynamics of the system. We show that for two low-dimensional model problems the size of the basis set does not grow quickly with time and appears only weakly dependent on dimensionality. The generality of this finding remains to be seen. The method primarily uses energies and gradients of the potential, opening the possibility for its use in on-the-fly ab initio quantum wavepacket dynamics. [ABSTRACT FROM AUTHOR]

EEG signals combined with deep learning play an important role in the study of human–computer interaction. However, the limited dataset makes it challenging to study EEG signals using deep learning methods. Inspired by the GAN network in image generation, this paper presents an improved generative adversarial network model L-C-WGAN-GP to generate artificial EEG data to augment training sets and improve the application of BCI in various fields. The generator consists of a long short-term memory (LSTM) network and the discriminator consists of a convolutional neural network (CNN) which uses the gradient penalty-based Wasserstein distance as the loss function in model training. The model can learn the statistical features of EEG signals and generate EEG data that approximate real samples. In addition, the performance of the compressed sensing reconstruction model can be improved by using augmented datasets. Experiments show that, compared with the existing advanced data amplification techniques, the proposed model produces EEG signals closer to the real EEG signals as measured by RMSE, FD and WTD indicators. In addition, in the compressed reconstruction of EEG signals, adding the new data reduces the loss by about 15% compared with the original data, which greatly improves the reconstruction accuracy of the EEG signals' compressed sensing. [ABSTRACT FROM AUTHOR]

Microphone array-based beamforming algorithms are widely used in sound source identification, fault diagnosis, and radar communication because of their excellent performance. However, their limited spatial resolution and high dynamic side flap level seriously affect the recognition accuracy. To explore a high-performance beamforming sound source identification algorithm, the microphone array compressed beamforming underdetermined equation is solved by extending the iterative threshold. A sound source identification model is established, and a new compressed beamforming (CSB-II) algorithm is proposed. Numerical simulations show that the CSB-II algorithm can effectively reduce the starting frequency of sound source identification and has high sound source identification accuracy. The effects of signal-to-noise ratio, sound source distance, and array number on sound source identification accuracy are analyzed separately. The laws affecting sound source identification accuracy are derived from guiding actual sound source measurements. [ABSTRACT FROM AUTHOR]

This paper studies the ℓ 1 - α ℓ 2 local minimization model for α ∈ (0 , 2 ] , which is the first time to consider the case of α > 1 . We obtain the necessary and sufficient conditions for a fixed sparse signal to be recovered from this model. Based on this condition, we also obtain the necessary and sufficient conditions for any k-sparse signal to be recovered from ℓ 1 - α ℓ 2 local minimization model with 0 < α < 1 , α = 1 and 1 < α ≤ 2 . The experimental data show that the size of α is positively correlated with the success rate of signal recovery. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Connectome spectrum electromagnetic tomography (CSET) combines diffusion MRI‐derived structural connectivity data with well‐established graph signal processing tools to solve the M/EEG inverse problem. Using simulated EEG signals from fMRI responses, and two EEG datasets on visual‐evoked potentials, we provide evidence supporting that (i) CSET captures realistic neurophysiological patterns with better accuracy than state‐of‐the‐art methods, (ii) CSET can reconstruct brain responses more accurately and with more robustness to intrinsic noise in the EEG signal. These results demonstrate that CSET offers high spatio‐temporal accuracy, enabling neuroscientists to extend their research beyond the current limitations of low sampling frequency in functional MRI and the poor spatial resolution of M/EEG. [ABSTRACT FROM AUTHOR]

Diffusion Spectrum Imaging (DSI) using dense Cartesian sampling of q‐space has been shown to provide important advantages for modeling complex white matter architecture. However, its adoption has been limited by the lengthy acquisition time required. Sparser sampling of q‐space combined with compressed sensing (CS) reconstruction techniques has been proposed as a way to reduce the scan time of DSI acquisitions. However prior studies have mainly evaluated CS‐DSI in post‐mortem or non‐human data. At present, the capacity for CS‐DSI to provide accurate and reliable measures of white matter anatomy and microstructure in the living human brain remains unclear. We evaluated the accuracy and inter‐scan reliability of 6 different CS‐DSI schemes that provided up to 80% reductions in scan time compared to a full DSI scheme. We capitalized on a dataset of 26 participants who were scanned over eight independent sessions using a full DSI scheme. From this full DSI scheme, we subsampled images to create a range of CS‐DSI images. This allowed us to compare the accuracy and inter‐scan reliability of derived measures of white matter structure (bundle segmentation, voxel‐wise scalar maps) produced by the CS‐DSI and the full DSI schemes. We found that CS‐DSI estimates of both bundle segmentations and voxel‐wise scalars were nearly as accurate and reliable as those generated by the full DSI scheme. Moreover, we found that the accuracy and reliability of CS‐DSI was higher in white matter bundles that were more reliably segmented by the full DSI scheme. As a final step, we replicated the accuracy of CS‐DSI in a prospectively acquired dataset (n = 20, scanned once). Together, these results illustrate the utility of CS‐DSI for reliably delineating in vivo white matter architecture in a fraction of the scan time, underscoring its promise for both clinical and research applications. [ABSTRACT FROM AUTHOR]

Objective: We aimed to compare the image quality and focal lesion detection ability of hepatobiliary phase (HBP) images obtained using compressed sensing (CS) and controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) in patients with liver cirrhosis. Materials and methods: We retrospectively included 244 gadoxetic acid–enhanced liver MRI from 244 patients with cirrhosis obtained by two HBP images using CS and CAIPIRINHA from July 2020 to December 2020. The optimized resolution and scan time for CS–HBP and CAIPIRINHA–HBP were 0.9 × 0.9 × 1.5 mm3 and 15 s and 1.3 × 1.3 × 3 mm3 and 16 s, respectively. We compared the image quality between the two sets of images in 244 patients and focal lesion (n = 294) analyses for 112 patients. Results: CS–HBP showed comparable overall image quality (3.7 ± 0.9 vs. 3.6 ± 0.8, p = 0.680), superior liver edge sharpness (3.9 ± 0.6 vs. 3.6 ± 0.5, p < 0.001), and fewer respiratory motion artifacts (4.0 ± 0.7 vs. 3.8 ± 0.5, p < 0.001), but higher non-respiratory artifacts (3.4 ± 0.7 vs. 3.6 ± 0.6, p < 0.001) and subjective image noise (3.5 ± 0.8 vs. 3.6 ± 0.7, p = 0.014) than CAIPIRINHA–HBP. CS–HBP showed a higher signal-to-noise ratio in the liver than CAIPIRINHA–HBP (20.9 ± 9.0 vs. 18.9 ± 7.1, p = 0.008). The pooled sensitivity, specificity, and AUC were 90.0%, 77.5%, and 0.84 for CS–HBP and 73.5%, 82.4%, and 0.78 for CAIPIRINHA–HBP, respectively. Conclusions: CS–HBP showed better focal lesion detection ability, comparable overall image quality, and fewer respiratory motion artifacts, but higher non-respiratory artifacts and noise compared to CAIPIRINHA–HBP. Thus, CS-HBP could be recommended for liver MRI in patients with cirrhosis to improve diagnostic performance. Clinical relevance statement: Thin-slice CS–HBP may be useful for detecting sub-centimeter hepatocellular carcinoma in cirrhotic patients with Child-Pugh classification A while maintaining comparable subjective image quality. Key Points: • Compared with controlled aliasing in parallel imaging results in higher acceleration, compressed sensing hepatobiliary phase yielded thinner slices and shorter scan time at a higher accelerating factor. • Compressed sensing hepatobiliary phase showed comparable overall image quality, superior liver edge sharpness, and fewer respiratory motion artifacts, but higher non-respiratory artifacts and subjective image noise than controlled aliasing in parallel imaging results in higher acceleration-hepatobiliary phase. • Compressed sensing hepatobiliary phase can detect sub-centimeter hepatocellular carcinoma in cirrhotic patients with Child-Pugh classification A. [ABSTRACT FROM AUTHOR]

The relaxed CQ algorithm is one of the most important algorithms for solving the split feasibility problem. We study the issue of strong convergence of the relaxed CQ algorithm in Hilbert spaces together with estimates on the convergence rate. Under a kind of Hölderian type bounded error bound property, strong convergence of the relaxed CQ algorithm is established. Furthermore, qualitative estimates on the convergence rate is presented. In particular, for the case when the involved exponent is equal to 1, the linear convergence of the relaxed CQ algorithm is established. Finally, numerical experiments are performed to show the convergence property of the relaxed CQ algorithm for the compressed sensing problem. [ABSTRACT FROM AUTHOR]

This paper proposes a dual-channel speech separation method based on spatial estimation via sparse Bayesian inference (SBI) and nonnegative matrix factorization (NMF). The spatial information estimated by traditional compressed sensing (CS) models is insufficient when two microphones receive limited columns of mixed signals. Considering the sparsity of peak values in the cross-correlation spectrum between two received signals, the proposed method builds a new CS model based on cross-correlation spectrum and applies SBI algorithm to solve this model to improve the estimation accuracy of spatial information. Combined the spatial information with the spectral features decomposed by NMF, NMF coefficient matrix masks belonging to individual source are generated for pre-separation. To mitigate retained potential interference components, a post-separation processing stage is designed using an expectation maximization (EM) algorithm based on a Gaussian mixture model (GMM). The estimated spatial information and binary time–frequency masks are used for parameter initialization of the EM algorithm. The experimental results using real-world speech data show that the proposed method can achieve better separation performance compared to various existing methods. [ABSTRACT FROM AUTHOR]

Multiple-quantum-filtered (MQF) sodium magnetic resonance imaging (MRI), such as enhanced single-quantum and triple-quantum-filtered imaging of 23Na (eSISTINA), enables images to be weighted towards restricted sodium, a promising biomarker in clinical practice, but often suffers from clinically infeasible acquisition times and low image quality. This study aims to mitigate the above limitation by implementing a novel eSISTINA sequence at 7 T with the application of compressed sensing (CS) to accelerate eSISTINA acquisitions without a noticeable loss of information. A novel eSISTINA sequence with a 3D spiral-based sampling scheme was implemented at 7 T for the application of CS. Fully sampled datasets were obtained from one phantom and ten healthy subjects, and were then retrospectively undersampled by various undersampling factors. CS undersampled reconstructions were compared to fully sampled and undersampled nonuniform fast Fourier transform (NUFFT) reconstructions. Reconstruction performance was evaluated based on structural similarity (SSIM), signal-to-noise ratio (SNR), weightings towards total and compartmental sodium, and in vivo quantitative estimates. CS-based phantom and in vivo images have less noise and better structural delineation while maintaining the weightings towards total, non-restricted (predominantly extracellular), and restricted (primarily intracellular) sodium. CS generally outperforms NUFFT with a higher SNR and a better SSIM, except for the SSIM in TQ brain images, which is likely due to substantial noise contamination. CS enables in vivo quantitative estimates with <15% errors at an undersampling factor of up to two. Successful implementation of an eSISTINA sequence with an incoherent sampling scheme at 7 T was demonstrated. CS can accelerate eSISTINA by up to twofold at 7 T with reduced noise levels compared to NUFFT, while maintaining major structural information, reasonable weightings towards total and compartmental sodium, and relatively reliable in vivo quantification. The associated reduction in acquisition time has the potential to facilitate the clinical applicability of MQF sodium MRI. [ABSTRACT FROM AUTHOR]

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients, cf. Candés (C. R. Acad. Sci. Paris, Ser. I 346, 589–592 (2008)), Candés et al. (IEEE Trans. Inf. Theo (2006)), Donoho (IEEE Trans. Inf. Theo. 52(4), (2006)), Donoho et al. (IEEE Trans. Inf. Theo. 52(1), (2006)). Its applications span various fields, including mathematics, physics, engineering, and several medical sciences, cf. Adcock and Hansen (Compressive Imaging: Structure, Sampling, Learning, p. 2021), Berk et al. (2019 13th International conference on Sampling Theory and Applications (SampTA) pp. 1-5. IEEE (2019)), Brady et al. (Opt. Express 17(15), 13040–13049 (2009)), Chan (Terahertz imaging with compressive sensing. Rice University, USA (2010)), Correa et al. (2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 7789–7793 (2014, May) IEEE), Gao et al. (Nature 516(7529), 74–77 (2014)), Liu and Kang (Opt. Express 18(21), 22010–22019 (2010)), McEwen and Wiaux (Mon. Notices Royal Astron. Soc. 413(2), 1318–1332 (2011)), Marim et al. (Opt. Lett. 35(6), 871–873 (2010)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)). Motivated by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and CS, we employ convex analysis techniques to analytically determine equivalents of Lagrange multipliers for optimization problems with inequality constraints, specifically a weighted LASSO with voxel-wise weighting. We investigate this problem under assumptions on the fidelity term A x - b 2 2 , either concerning the sign of its gradient or orthogonality-like conditions of its matrix. To be more precise, we either require the sign of each coordinate of 2 (A x - b) T A to be fixed within a rectangular neighborhood of the origin, with the side lengths of the rectangle dependent on the constraints, or we assume A T A to be diagonal. The objective of this work is to explore the relationship between Lagrange multipliers and the constraints of a weighted variant of LASSO, specifically in the mentioned cases where this relationship can be computed explicitly. As they scale the regularization terms of the weighted LASSO, Lagrange multipliers serve as tuning parameters for the weighted LASSO, prompting the question of their potential effective use as tuning parameters in applications like MR image reconstruction and denoising. This work represents an initial step in this direction. [ABSTRACT FROM AUTHOR]

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When investigating the vortex-induced vibration (VIV) of marine risers, extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers. The problem is conventionally solved using the modal decomposition method, based on the principle that the response can be approximated by a weighted sum of limited vibration modes. However, the method is not valid when the problem is underdetermined, i.e., the number of unknown mode weights is more than the number of known measurements. This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit (CoSaMP) algorithm, exploiting the sparsity of VIV in the modal space. In the validation study based on high-order VIV experiment data, the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed. A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem, which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring. [ABSTRACT FROM AUTHOR]

Image reconstruction is a crucial aspect of computational imaging. The compressed sensing reconstruction (CS) method has been developed to obtain high-quality images. However, the CS method is commonly time-consuming in image reconstruction. To overcome this drawback, we propose a compressed sensing reconstruction method with fast convolution filtering (F-CS method), which significantly increases reconstruction speed by reducing the number of convolution operations without image fill. The experimental results show that by using the F-CS method, the reconstruction speed can be increased by a factor of 7 compared to the conventional CS method. Moreover, the F-CS method proposed in this paper is compared with the back-propagation reconstruction (BP) method and super-resolution reconstruction (SR) method, and it is validated that the proposed method has a lower computational resource cost for high-quality image reconstruction and exhibits a much more balanced capability. [ABSTRACT FROM AUTHOR]

Because biological signal transmission in real time might be very demanding, cloud and internet of things (IoT) infrastructure are required. To do this, the main component of the signal serves as the focal point of a reconstruction strategy that has been developed. The input is transferred to the intended destination once it has been encoded. Security is an important consideration that must not be disregarded. For long-term healthcare monitoring via lightweight wireless networks, electrocardiogram (ECG) compression is a major difficulty. Reducing energy consumption in wireless data transmission and precisely calculating error rates for data reconstruction are two essential components of compressed sensing. The application of effective encoding methods is crucial for these considerations. We present multi-task compressed sensing (MT-CS), a unique method for compressing ECG data. When used to wireless network systems with several embedded sensors, this technique is quite effective. From the ECG data, the model learns the fundamental adaptive properties needed for correlation. We use the multiparameter intelligent monitoring in intensive care (MIMIC-II) dataset to investigate the performance of the suggested MT-CS reconstruction technique in order to assess its strength and application. In comparison to current compressed sensing methods, the simulation results demonstrate that the suggested reconstruction methodology utilizing MT-CS generates high-quality reconstruction signals with fewer observations. [ABSTRACT FROM AUTHOR]

Challenge is to find the support vectors of the unknown block sparse vector with compressed measurements in an underdetermined system where the number of unknowns is more than that of measurements. To recover unknown block sparse vector, restricted isometry property (RIP) is a sufficient condition need to be satisfied. Finding the restricted isometric constant is a non-polynomial hard problem for large values of n. In this paper coherence-based recovery guarantee has been proposed to recover the support vectors using block generalized orthogonal matching pursuit (BGOMP). It is proved that BGOMP can able to recover the support vectors with lesser number of iteration than block orthogonal matching pursuit (BOMP) by selecting multiple block support elements per iteration. Simulation results show detection performance of BGOMP is better than BOMP, block subspace pursuit (BSP) and block compressive sampling matching pursuit (BCoSaMP) for different block sparsity and block length. In most of the cases for different block sparsity and block length computation time for BGOMP is lesser than BCoSaMP, BSP and BOMP due to the multiple selection of elements in each iteration. [ABSTRACT FROM AUTHOR]

Fluorine MRI is finding wider acceptance in theranostics applications where imaging of 19F hotspots of fluorinated contrast material is central. The essence of such applications is to capture ghosting‐artifact‐free images of the inherently low MR response under clinically viable conditions. To serve this purpose, this work introduces the balanced spiral spectroscopic imaging (BaSSI) sequence, which is implemented on a 3.0 T clinical scanner and is capable of generating 19F hotspot images in an efficient manner. The sequence utilizes an all‐phase‐encoded pseudo‐spiral k‐space trajectory, enabling the acquisition of broadband (80 ppm) fluorine spectra free from chemical shift ghosting. BaSSI can acquire a 64 × 64 image with 1 mm × 1 mm voxels in just 14 s, significantly outperforming typical MRSI sequences used in 1H or 31P imaging. The study employed in silico characterization to verify essential design choices such as the excitation pulse, as well as to identify the boundaries of the parameter space explored for optimization. BaSSI's performance was further benchmarked against the 3D ultrashort‐echo‐time balanced steady‐state free precession (3D UTE BSSFP) sequence, a well established method used in 19F MRI, in vitro. Both sequences underwent extensive optimization through exploration of a wide parameter space on a small phantom containing 10 μL of non‐diluted bulk perfluorooctylbromide (PFOB) prior to comparative experiments. Subsequent to optimization, BaSSI and 3D UTE BSSFP were employed to capture images of small non‐diluted bulk PFOB samples (0.10 and 0.05 μL), with variations in the number of signal averages, and thus the total scan time, in order to assess the detection sensitivities of the sequences. In these experiments, the detection sensitivity was evaluated using the Rose criterion (Rc), which provides a quantitative metric for assessing object visibility. The study further demonstrated BaSSI's utility as a (pre)clinical tool through postmortem imaging of polymer microspheres filled with PFOB in a BALB/c mouse. Anatomic localization of 19F hotspots was achieved by denoising raw data obtained with BaSSI using a filter based on the Rose criterion. These data were then successfully registered to 1H anatomical images. BaSSI demonstrated superior detection sensitivity in the benchmarking analysis, achieving Rc values approximately twice as high as those obtained with the 3D UTE BSSFP method. The technique successfully facilitated imaging and precise localization of 19F hotspots in postmortem experiments. However, it is important to highlight that imaging 10 mM PFOB in small mice postmortem, utilizing a 48 × 48 × 48 3D scan, demanded a substantial scan time of 1 h and 45 min. Further studies will explore accelerated imaging techniques, such as compressed sensing, to enhance BaSSI's clinical utility. [ABSTRACT FROM AUTHOR]