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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]

Aiming at the problem that existing channel estimation methods are unable to track the channel parameter variations within a single frame under continuous Doppler spread channel (CoDSC) which leads to serious estimation errors, this paper proposes a basis expansion model (BEM) orthogonal time frequency space (OTFS) channel estimation method based on Cluster-Pruning Stagewise Weak Orthogonal Matching Pursuit (CP-SWOMP). This method first uses a discrete prolate spheroidal sequences (DPSS) as a basis function to model the channel response, converting the underdetermined channel estimation into a sparse reconstruction problem with basis coefficients. Then the basis coefficients are solved for using compressed sensing methods, the nearest neighbor clustering criterion is introduced into the Stagewise Weak Orthogonal Matching Pursuit (SWOMP) algorithm, and the atoms of the iterative intermediate process are subjected to a quadratic pruning operation, which solves the redundancy problem of the support set and improves the reconstruction accuracy. In this paper, multiple methods are simulated and validated at different normalized Doppler frequency, and the results demonstrate that the proposed method can achieve better normalized mean square error (NMSE) and bit error rate (BER) performance with less pilot overhead. [ABSTRACT FROM AUTHOR]

Background: We aimed to determine the capabilities of compressed sensing (CS) and deep learning reconstruction (DLR) with those of conventional parallel imaging (PI) for improving image quality while reducing examination time on female pelvic 1.5-T magnetic resonance imaging (MRI). Methods: Fifty-two consecutive female patients with various pelvic diseases underwent MRI with T1- and T2-weighted sequences using CS and PI. All CS data was reconstructed with and without DLR. Signal-to-noise ratio (SNR) of muscle and contrast-to-noise ratio (CNR) between fat tissue and iliac muscle on T1-weighted images (T1WI) and between myometrium and straight muscle on T2-weighted images (T2WI) were determined through region-of-interest measurements. Overall image quality (OIQ) and diagnostic confidence level (DCL) were evaluated on 5-point scales. SNRs and CNRs were compared using Tukey's test, and qualitative indexes using the Wilcoxon signed-rank test. Results: SNRs of T1WI and T2WI obtained using CS with DLR were higher than those using CS without DLR or conventional PI (p < 0.010). CNRs of T1WI and T2WI obtained using CS with DLR were higher than those using CS without DLR or conventional PI (p < 0.003). OIQ of T1WI and T2WI obtained using CS with DLR were higher than that using CS without DLR or conventional PI (p < 0.001). DCL of T2WI obtained using CS with DLR was higher than that using conventional PI or CS without DLR (p < 0.001). Conclusion: CS with DLR provided better image quality and shorter examination time than those obtainable with PI for female pelvic 1.5-T MRI. Relevance statement: CS with DLR can be considered effective for attaining better image quality and shorter examination time for female pelvic MRI at 1.5 T compared with those obtainable with PI. Key Points: Patients underwent MRI with T1- and T2-weighted sequences using CS and PI. All CS data was reconstructed with and without DLR. CS with DLR allowed for examination times significantly shorter than those of PI and provided significantly higher signal- and CNRs, as well as OIQ. [ABSTRACT FROM AUTHOR]

The one parameter conjugate gradient method by Hager and Zhang (Pac J Optim, 2(1):35–58, 2006) represents a family of descent iterative methods for solving large‐scale minimization problems. The nonnegative parameter of the scheme determines the weight of conjugacy and descent, and by extension, the numerical performance of the method. The scheme, however, does not converge globally for general nonlinear functions, and when the parameter approaches 0, the scheme reduces to the conjugate gradient method by Hestenes and Stiefel (J Res Nat Bur Stand, 49:409–436, 1952), which in practical sense does not perform well due to the jamming phenomenon. By carrying out eigenvalue analysis of an adaptive two parameter Hager–Zhang type method, a new scheme is presented for system of monotone nonlinear equations with its application in compressed sensing. The proposed scheme was inspired by nice attributes of the Hager–Zhang method and the various schemes designed with double parameters. The scheme is also applicable to nonsmooth nonlinear problems. Using fundamental assumptions, analysis of the global convergence of the scheme is conducted and preliminary report of numerical experiments carried out with the scheme and some recent methods indicate that the scheme is promising. [ABSTRACT FROM AUTHOR]

Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line of work has shown that (stochastic) gradient descent tends to have an implicit bias towards low rank and/or sparse solutions when used to train deep linear networks, explaining to some extent why overparameterized neural network models trained by gradient descent tend to have good generalization performance in practice. However, existing theory for square-loss objectives often requires very small initialization of the trainable weights, which is at odds with the larger scale at which weights are initialized in practice for faster convergence and better generalization performance. In this paper, we aim to close this gap by incorporating and analysing gradient flow (continuous-time version of gradient descent) with weight normalization , where the weight vector is reparameterized in terms of polar coordinates, and gradient flow is applied to the polar coordinates. By analysing key invariants of the gradient flow and using Lojasiewicz's Theorem, we show that weight normalization also has an implicit bias towards sparse solutions in the diagonal linear model, but that in contrast to plain gradient flow, weight normalization enables a robust bias that persists even if the weights are initialized at practically large scale. Experiments suggest that the gains in both convergence speed and robustness of the implicit bias are improved dramatically using weight normalization in overparameterized diagonal linear network models. [ABSTRACT FROM AUTHOR]

Wireless sensor networks (WSNs) are structured for monitoring an area with distributed sensors and built-in batteries. However, most of their battery energy is consumed during the data transmission process. In recent years, several methodologies, like routing optimization, topology control, and sleep scheduling algorithms, have been introduced to improve the energy efficiency of WSNs. This study introduces a novel method based on a deep learning approach that utilizes variational autoencoders (VAEs) to improve the energy efficiency of WSNs by compressing transmission data. The VAE approach is customized in this work for compressing WSN data by retaining its important features. This is achieved by analyzing the statistical structure of the sensor data rather than providing a fixed-size latent representation. The performance of the proposed model is verified using a MATLAB simulation platform, integrating a pre-trained variational autoencoder model with openly available wireless sensor data. The performance of the proposed model is found to be satisfactory in comparison to traditional methods, like the compressed sensing technique, lightweight temporal compression, and the autoencoder, in terms of having an average compression rate of 1.5572. The WSN simulation also indicates that the VAE-incorporated architecture attains a maximum network lifetime of 1491 s and suggests that VAE could be used for compression-based transmission using WSNs, as its reconstruction rate is 0.9902, which is better than results from all the other techniques. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging (MRI) is crucial for accurately diagnosing a wide spectrum of musculoskeletal conditions due to its superior soft tissue contrast resolution. However, the long acquisition times of traditional two-dimensional (2D) and three-dimensional (3D) fast and turbo spin-echo (TSE) pulse sequences can limit patient access and comfort. Recent technical advancements have introduced acceleration techniques that significantly reduce MRI times for musculoskeletal examinations. Key acceleration methods include parallel imaging (PI), simultaneous multi-slice acquisition (SMS), and compressed sensing (CS), enabling up to eightfold faster scans while maintaining image quality, resolution, and safety standards. These innovations now allow for 3- to 6-fold accelerated clinical musculoskeletal MRI exams, reducing scan times to 4 to 6 min for joints and spine imaging. Evolving deep learning-based image reconstruction promises even faster scans without compromising quality. Current research indicates that combining acceleration techniques, deep learning image reconstruction, and superresolution algorithms will eventually facilitate tenfold accelerated musculoskeletal MRI in routine clinical practice. Such rapid MRI protocols can drastically reduce scan times by 80–90% compared to conventional methods. Implementing these rapid imaging protocols does impact workflow, indirect costs, and workload for MRI technologists and radiologists, which requires careful management. However, the shift from conventional to accelerated, deep learning-based MRI enhances the value of musculoskeletal MRI by improving patient access and comfort and promoting sustainable imaging practices. This article offers a comprehensive overview of the technical aspects, benefits, and challenges of modern accelerated musculoskeletal MRI, guiding radiologists and researchers in this evolving field. [ABSTRACT FROM AUTHOR]

This paper introduces a nonconvex ℓ 1 − 2 -analysis model: min x (∥ D ∗ x ∥ 1 − ∥ D ∗ x ∥ 2) s.t.  A x = y , where A is a measurement matrix and D is a tight frame. Our main motivation is to generalize the sparse recovery via ℓ 1 − ℓ 2 minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix A such that a vector x can be recovered from A x with a tight frame D via ℓ 1 − 2 -analysis local minimization, or any vector x can be uniformly recovered from A x with a tight frame D via ℓ 1 − 2 -analysis minimization locally and globally. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging produces detailed anatomical and physiological images of the human body that can be used in the clinical diagnosis and treatment of diseases. However, MRI suffers its comparatively longer acquisition time than other imaging methods and is thus vulnerable to motion artifacts, which ultimately lead to likely failed or even wrong diagnosis. In order to perform faster reconstruction, deep learning-based methods along with traditional strategies such as parallel imaging and compressed sensing come into play in recent years in this field. Meanwhile, in order to better analyze the diseases, it is also often necessary to acquire images in the same region of interest under different modalities, which yield images with different contrast levels. However, most of these aforementioned methods tend to use single-modal images for reconstruction, neglecting the correlation and redundancy information embedded in MR images acquired with different modalities. While there are works on multi-modal reconstruction, the information is yet to be efficiently explored. In this paper, we propose an end-to-end neural network called MLMFNet, which helps the reconstruction of the target modality by using information from the auxiliary modality across feature channels and layers. Specifically, this is highlighted by three components: (I) An encoder based on UNet with a single-stream strategy that fuses auxiliary and target modalities; (II) a decoder that tends to multi-level features from all layers of the encoder, and (III) a channel attention module. Quantitative and qualitative analyses are performed on a public brain dataset and knee brain dataset, which show that the proposed method achieves satisfying results in MRI reconstruction within the multi-modal context, and also demonstrate its effectiveness and potential to be used in clinical practice. [ABSTRACT FROM AUTHOR]

To assess whether diffusion-weighted imaging (DWI) with Compressed SENSE (CS) and deep learning (DL-CS-DWI) can improve image quality and lesion detection in patients at risk for hepatocellular carcinoma (HCC). This single-center prospective study enrolled consecutive at-risk participants who underwent 3.0 T gadoxetate disodium-enhanced MRI. Conventional DWI was acquired using parallel imaging (PI) with SENSE (PI-DWI). In CS-DWI and DL-CS-DWI, CS but not PI with SENSE was used to accelerate the scan with 2.5 as the acceleration factor. Qualitative and quantitative image quality were independently assessed by two masked reviewers, and were compared using the Wilcoxon signed-rank test. The detection rates of clinically-relevant (LR-4/5/M based on the Liver Imaging Reporting and Data System v2018) liver lesions for each DWI sequence were independently evaluated by another two masked reviewers against their consensus assessments based on all available non-DWI sequences, and were compared by the McNemar test. 67 participants (median age, 58.0 years; 56 males) with 197 clinically-relevant liver lesions were enrolled. Among the three DWI sequences, DL-CS-DWI showed the best qualitative and quantitative image qualities (p range, <0.001–0.039). For clinically-relevant liver lesions, the detection rates (91.4%–93.4%) of DL-CS-DWI showed no difference with CS-DWI (87.3%–89.8%, p = 0.230–0.231) but were superior to PI-DWI (82.7%–85.8%, p = 0.015–0.025). For lesions located in the hepatic dome, DL-CS-DWI demonstrated the highest detection rates (94.8%–97.4% vs 76.9%–79.5% vs 64.1%–69.2%, p = 0.002–0.045) among the three DWI sequences. In patients at high-risk for HCC, DL-CS-DWI improved image quality and detection for clinically-relevant liver lesions, especially for the hepatic dome. • DWI with CS and DL demonstrated superior image quality compared to CS-DWI and conventional DWI. • DL-CS-DWI improved detection rate for clinically-relevant liver lesions, especially in hepatic dome, compared to CS-DWI and conventional DWI. • Deep learning combined with compressive SENSE could improve the overall performance of liver DWI. [ABSTRACT FROM AUTHOR]

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In recent years, deep unfolding networks (DUNs) have received widespread attention in the field of compressed sensing (CS) reconstruction due to their good interpretability and strong mapping capabilities. However, existing DUNs often improve the reconstruction effect at the expense of a large number of parameters, and there is the problem of information loss in long-distance feature transmission. Based on the above problems, we propose an unfolded network architecture that mixes Transformer and large kernel convolution to achieve sparse sampling and reconstruction of natural images, namely, a reconstruction network based on Transformer and convolution (TCR-Net). The Transformer framework has the inherent ability to capture global context through a self-attention mechanism, which can effectively solve the challenge of long-range dependence on features. TCR-Net is an end-to-end two-stage architecture. First, a data-driven pre-trained encoder is used to complete the sparse representation and basic feature extraction of image information. Second, a new attention mechanism is introduced to replace the self-attention mechanism in Transformer, and a hybrid Transformer and convolution module based on optimization-inspired is designed. Its iterative process leads to the unfolding framework, which approximates the original image stage by stage. Experimental results show that TCR-Net outperforms existing state-of-the-art CS methods while maintaining fast computational speed. Specifically, when the CS ratio is 0.10, the average PSNR on the test set used in this paper is improved by at least 0.8%, the average SSIM is improved by at least 1.5%, and the processing speed is higher than 70FPS. These quantitative results show that our method has high computational efficiency while ensuring high-quality image restoration. [ABSTRACT FROM AUTHOR]

A T/R-R (transmitting receiving-receiving) radar sparse aperture multi-view fusion imaging method based on the complex Bayesian compressed sensing (BCS) algorithm is proposed for the practical imaging of T/R-R configuration radar, taking into account the orbital priors of space targets and the advantages of the dual-rotation inverse synthetic aperture radar (ISAR) imaging system. On the basis of establishing a dual rotation radar fusion imaging modal, the proposed method utilizes Laplace priors to establish a sparse model of the target in the complex domain, improving the sparsity promotion effort of the algorithm and obtaining high-resolution target images. The stimulation experiment resets show that the proposed method can not only achieve multi-view fusion imaging of dual station radar, but also achieve multi-view fusion imaging of dual-station radar with sparse aperture respectively, further expanding the application scenarios and effectively improving azimuth resolution and imaging quality. [ABSTRACT FROM AUTHOR]

For secure image communications, the Internet must be shielded against unauthorized acquisition or malevolent access. The need for image encryption methods with enough capacity and good efficiency is growing due to the current situation. The purpose of this research work is to solve the problems in today's communication security using a proposed image encryption algorithm. The proposed image encryption system includes the combination of a chaotic system, compressive sensing and Hyper optimization algorithm. The initial values of chaos are extracted using the SHA512. Discrete Wavelet Transform (DWT) is applied to sparse image pixels. The image is shuffled using a FAN transform with a circular map. Next, the image is divided into blocks to facilitate the application of block compressive sensing that utilized the Hadamard measurement matrix. These blocks are masked as one part to quantify the pixels. The logistic map is improved by a hybrid transform which is the combination of Discrete Cosine Transform, Arnold Transform and Discrete Wavelet Transform (CAW). The image is finally scrambled using a Circular Map with a Hyper Optimization that combines two meta-heuristics algorithms namely GWO and COOT. According to simulation experiment findings and security assessments, the algorithm was extremely resilient to differential, statistical, and interference assaults. Based on the experimental results, it was found that the average rate of PSNR was 33.8189, the rate of entropy was 7.99454, the average rate of SSIM was 0.96144, the rate of UACI was 99.62892 and the average rate of NPCI was 33.50304. The results showed that it is an effective method of encryption and strong enough against various types of attacks. [ABSTRACT FROM AUTHOR]

Purpose: To present and assess an outlier mitigation method that makes free‐running volumetric cardiovascular MRI (CMR) more robust to motion. Methods: The proposed method, called compressive recovery with outlier rejection (CORe), models outliers in the measured data as an additive auxiliary variable. We enforce MR physics‐guided group sparsity on the auxiliary variable, and jointly estimate it along with the image using an iterative algorithm. For evaluation, CORe is first compared to traditional compressed sensing (CS), robust regression (RR), and an existing outlier rejection method using two simulation studies. Then, CORe is compared to CS using seven three‐dimensional (3D) cine, 12 rest four‐dimensional (4D) flow, and eight stress 4D flow imaging datasets. Results: Our simulation studies show that CORe outperforms CS, RR, and the existing outlier rejection method in terms of normalized mean square error and structural similarity index across 55 different realizations. The expert reader evaluation of 3D cine images demonstrates that CORe is more effective in suppressing artifacts while maintaining or improving image sharpness. Finally, 4D flow images show that CORe yields more reliable and consistent flow measurements, especially in the presence of involuntary subject motion or exercise stress. Conclusion: An outlier rejection method is presented and tested using simulated and measured data. This method can help suppress motion artifacts in a wide range of free‐running CMR applications. [ABSTRACT FROM AUTHOR]

Purpose: To improve image quality, mitigate quantification biases and variations for free‐breathing liver proton density fat fraction (PDFF) and R2*$$ {\mathrm{R}}_2^{\ast } $$ quantification accelerated by radial k‐space undersampling. Methods: A free‐breathing multi‐echo stack‐of‐radial MRI method was developed with compressed sensing with multidimensional regularization. It was validated in motion phantoms with reference acquisitions without motion and in 11 subjects (6 patients with nonalcoholic fatty liver disease) with reference breath‐hold Cartesian acquisitions. Images, PDFF, and R2*$$ {\mathrm{R}}_2^{\ast } $$ maps were reconstructed using different radial view k‐space sampling factors and reconstruction settings. Results were compared with reference‐standard results using Bland–Altman analysis. Using linear mixed‐effects model fitting (p < 0.05 considered significant), mean and SD were evaluated for biases and variations of PDFF and R2*$$ {\mathrm{R}}_2^{\ast } $$, respectively, and coefficient of variation on the first echo image was evaluated as a surrogate for image quality. Results: Using the empirically determined optimal sampling factor of 0.25 in the accelerated in vivo protocols, mean differences and limits of agreement for the proposed method were [−0.5; −33.6, 32.7] s−1 for R2*$$ {\mathrm{R}}_2^{\ast } $$ and [−1.0%; −5.8%, 3.8%] for PDFF, close to those of a previous self‐gating method using fully sampled radial views: [−0.1; −27.1, 27.0] s−1 for R2*$$ {\mathrm{R}}_2^{\ast } $$ and [−0.4%; −4.5%, 3.7%] for PDFF. The proposed method had significantly lower coefficient of variation than other methods (p < 0.001). Effective acquisition time of 64 s or 59 s was achieved, compared with 171 s or 153 s for two baseline protocols with different radial views corresponding to sampling factor of 1.0. Conclusion: This proposed method may allow accelerated free‐breathing liver PDFF and R2*$$ {\mathrm{R}}_2^{\ast } $$ mapping with reduced biases and variations. [ABSTRACT FROM AUTHOR]

Purpose: To develop a highly accelerated multi‐echo spin‐echo method, TEMPURA, for reducing the acquisition time and/or increasing spatial resolution for kidney T2 mapping. Methods: TEMPURA merges several adjacent echoes into one k‐space by either combining independent echoes or sharing one echo between k‐spaces. The combined k‐space is reconstructed based on compressed sensing theory. Reduced flip angles are used for the refocusing pulses, and the extended phase graph algorithm is used to correct the effects of indirect echoes. Two sequences were developed: a fast breath‐hold sequence; and a high‐resolution sequence. The performance was evaluated prospectively on a phantom, 16 healthy subjects, and two patients with different types of renal tumors. Results: The fast TEMPURA method reduced the acquisition time from 3–5 min to one breath‐hold (18 s). Phantom measurements showed that fast TEMPURA had a mean absolute percentage error (MAPE) of 8.2%, which was comparable to a standardized respiratory‐triggered sequence (7.4%), but much lower than a sequence accelerated by purely k‐t undersampling (21.8%). High‐resolution TEMPURA reduced the in‐plane voxel size from 3 × 3 to 1 × 1 mm2, resulting in improved visualization of the detailed anatomical structure. In vivo T2 measurements demonstrated good agreement (fast: MAPE = 1.3%–2.5%; high‐resolution: MAPE = 2.8%–3.3%) and high correlation coefficients (fast: R = 0.85–0.98; high‐resolution: 0.82–0.96) with the standardized method, outperforming k‐t undersampling alone (MAPE = 3.3–4.5%, R = 0.57–0.59). Conclusion: TEMPURA provides fast and high‐resolution renal T2 measurements. It has the potential to improve clinical throughput and delineate intratumoral heterogeneity and tissue habitats at unprecedented spatial resolution. [ABSTRACT FROM AUTHOR]

Purpose: We present SCAMPI (Sparsity Constrained Application of deep Magnetic resonance Priors for Image reconstruction), an untrained deep Neural Network for MRI reconstruction without previous training on datasets. It expands the Deep Image Prior approach with a multidomain, sparsity‐enforcing loss function to achieve higher image quality at a faster convergence speed than previously reported methods. Methods: Two‐dimensional MRI data from the FastMRI dataset with Cartesian undersampling in phase‐encoding direction were reconstructed for different acceleration rates for single coil and multicoil data. Results: The performance of our architecture was compared to state‐of‐the‐art Compressed Sensing methods and ConvDecoder, another untrained Neural Network for two‐dimensional MRI reconstruction. SCAMPI outperforms these by better reducing undersampling artifacts and yielding lower error metrics in multicoil imaging. In comparison to ConvDecoder, the U‐Net architecture combined with an elaborated loss‐function allows for much faster convergence at higher image quality. SCAMPI can reconstruct multicoil data without explicit knowledge of coil sensitivity profiles. Moreover, it is a novel tool for reconstructing undersampled single coil k‐space data. Conclusion: Our approach avoids overfitting to dataset features, that can occur in Neural Networks trained on databases, because the network parameters are tuned only on the reconstruction data. It allows better results and faster reconstruction than the baseline untrained Neural Network approach. [ABSTRACT FROM AUTHOR]

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression, image reconstruction, and multi-label learning. We introduce an ℓ 2 regularized formulation of CS which we reformulate as a mixed integer second order cone program. We derive a second order cone relaxation of this problem and show that under mild conditions on the regularization parameter, the resulting relaxation is equivalent to the well studied basis pursuit denoising problem. We present a semidefinite relaxation that strengthens the second order cone relaxation and develop a custom branch-and-bound algorithm that leverages our second order cone relaxation to solve small-scale instances of CS to certifiable optimality. When compared against solutions produced by three state of the art benchmark methods on synthetic data, our numerical results show that our approach produces solutions that are on average 6.22 % more sparse. When compared only against the experiment-wise best performing benchmark method on synthetic data, our approach produces solutions that are on average 3.10 % more sparse. On real world ECG data, for a given ℓ 2 reconstruction error our approach produces solutions that are on average 9.95 % more sparse than benchmark methods ( 3.88 % more sparse if only compared against the best performing benchmark), while for a given sparsity level our approach produces solutions that have on average 10.77 % lower reconstruction error than benchmark methods ( 1.42 % lower error if only compared against the best performing benchmark). When used as a component of a multi-label classification algorithm, our approach achieves greater classification accuracy than benchmark compressed sensing methods. This improved accuracy comes at the cost of an increase in computation time by several orders of magnitude. Thus, for applications where runtime is not of critical importance, leveraging integer optimization can yield sparser and lower error solutions to CS than existing benchmarks. [ABSTRACT FROM AUTHOR]

Objective To assess the value of intracranial time-of-flight magnetic resonance angiography (MRA) based on spiral imaging technology (MRAspiral) compared to compressed sensing (CS) reconstruction (MRACS). Methods From 29 May 2021 to 11 June 2022, brain MRA of 49 patients with suspected cerebrovascular disease was prospectively analyzed. MRA sequences with CS factor of 4 (MRACS4) and MRAspiral (the acquisition window τ is 4, 6, 8, 12) were acquired. The regions of interest were placed in the proximal and distal segments of the anterior cerebral artery, middle cerebral artery, and posterior cerebral artery (PCA) to calculate the contrast ratio (CR) with the corpus callosum as the background on both sequences. Qualitative analysis of image quality and diagnostic feasibility were performed independently by two experienced radiologists. One-way repeated measures ANOVA analysis was used to compare the differences in CR values and Friedman test was used to evaluate the differences in qualitative analysis. Results The CR value in the distal PCA (2.61±1.09) of MRAτ6 was significantly lower (P=0.014) than that of MRACS4 (3.16±1.62). The CR values of the other MRAspiral images (MRτ4: 2.73 ±1.45, MRAτ8: 2.78±1.28, MRAτ12: 2.64 ±1.43) were not significantly different from those of MRACS4 (P>0.05). The CR values in the MRAτ4 (4.78±0.41), MRAτ6 (4.77±0.42) and MRAτ8 (4.55±0.52) were significantly better than MRACS4 in distal vascular visualization (P<0.005). MRACS4 showed better performance than MRAspiral in proximal vessels (P>0.005). Conclusion MRAspiral is superior to MRACS in displaying distal intracranial vessels, allowing for a better assessment of the degree of intracranial vascular stenosis. MRAτ8 can reduce acquisition time while ensuring image quality. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To protect visual content in color images, this paper presents an encryption method by employing discrete trinion Fourier transform and compressive sensing. Firstly, each color image is precoded into a trinion matrix for holistically processing. The discrete trinion Fourier transform is performed to construct an enducing matrix. With measurement matrices generated by 3D Lorenz chaotic map, complex-type compressed sensing is then utilized to obtain sparse coefficients. Followed by Josephus scrambling and inverse discrete trinion Fourier transform, the ciphertext can be obtained. The plain-text images can be restored perfectly and the maximum PSNR value is more than 280dB. Additionally, the proposed cryptosystem shows high-level sensitivity, which is evidenced by NPCR and UACI values beyond 99.9998% and 33.3337%, respectively. Compared with several existing methods, the proposed algorithm exhibits stronger resistance against Gaussian noise. [ABSTRACT FROM AUTHOR]

Objective: To 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 methods: Forty 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). Results: Compared 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 < 0.05). For the left TS, max axial WSS and 3D WSS measured by CS10 group were significantly underestimated (p = 0.032 and 0.003). Similarly, for SS, mean velocity, peak velocity, average axial WSS measured by the CS8 and CS10 groups, max axial WSS measured by CS6, CS8, and CS10 groups, and 3D WSS measured by CS10 group were significantly underestimated compared to the SENSE4 scan (p = 0.000-0.021). The hemodynamic parameters measured by CS4 group had only minimal bias and great limits of agreement compared to conventional 4D flow (SENSE4) in the ICA and every venous sinus (the max/min upper limit to low limit of the 95% limits of agreement = 11.4/0.03 to 0.004/-5.7, 14.4/0.05 to -0.03/-9.0, 12.6/0.04 to -0.03/-9.4, 16.8/0.04 to 0.6/-14.1; the max/min bias = 5.0/-1.2, 3.5/-1.4, 4.5/-1.1, 6.6/-4.0 for CS4, CS6, CS8, and CS10, respectively). Conclusion: CS4 strikes a good balance in 4D flow between flow quantifications and scan time, which could be recommended for routine clinical use. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative smartphone‐based strain sensing method (named MaxCpture) for measuring maximum peak tensile and compressive strains. The MaxCpture method is able to record the maximum peak strain of a structure without continuous power supply and real‐time monitoring. This method combines the maximum peak strain sensor, a smartphone, and the microimage sensing algorithm. Crucially, the novel clamping sensitive mechanism in the sensor preserves information about the maximum deformation of the structure. To validate the feasibility of the MaxCpture method, this study conducted a series of experiments, including static tests, the beam of constant strength tests, and dynamic tests. The results show that the MaxCpture method is able to measure the maximum peak tensile and compressive strain effectively. With its convenient acquisition, low cost, and multi‐user collaboration, the MaxCpture method provides a promising approach for seismic response detection of various engineering structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work proposes a novel Noor iterative scheme, called CT‐iteration, to approximate the fixed points in the new context of generalized nonexpansive mappings with property (E)$$ (E) $$. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical examples of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Furthermore, we show the use of the proposed method to generate polynomiographs. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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 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 minimization. To the best of the authors' knowledge, the recovery guarantees established in this paper are superior to those currently available. [ABSTRACT FROM AUTHOR]

The measurement matrices play a crucial role in compressed sensing, directly impacting the performance of signal sampling and reconstruction. As one of the primary construction methods for measurement matrices, designing structured measurement matrices is a challenging problem. In practical sampling, the measurement matrices often have strong coherence. Therefore, it is significant to design structured measurement matrices with superior reconstruction performance at low sampling, although the coherence is strong. In this paper, by introducing a special Gram matrix and merging it with the deterministic Fourier matrix, we construct a kind of measurement matrices with superior signal recovery performance under strong coherence. Furthermore, utilizing Katz' character sum estimation allows us to establish an upper bound on the coherence of the constructed matrices. All experimental results demonstrate that the performance of the proposed matrices outperform that of Fourier matrices and Gaussian random matrices. Consequently, the proposed matrices hold significant application in sparse signal processing. [ABSTRACT FROM AUTHOR]

This paper considers the deep-learning-aided compressed video sensing problem. To this end, a deep generative adversarial network has been proposed to provide an approximation of the non-reference frame using its corresponding reference frame. The tests confirm the superiority of this scheme over the conventional methods used earlier. Furthermore, two scenarios have been suggested for deep compressed video sensing and recovery. In the first scenario, the difference between the non-reference frame and its approximation obtained from the pre-trained network is compressively sampled and transmitted to the receiver where the proposed residual reconstruction network is adopted to reconstruct the signal. The second scenario utilizes a pre-trained network followed by an augmented layer to approximate the non-reference frames. In the transmitter, the parameters of the augmented layer are trained for the current non-reference block. Instead of transmitting the samples of the block, the parameters of its trained augmented layer are sent to the receiver where the reconstruction is done using the same pre-trained network. The performances of the proposed scenarios demonstrate their objective and subjective superiority over the state-of-the-art algorithms in both the reconstruction quality and run time. [ABSTRACT FROM AUTHOR]

Polarized light scattering spectroscopy (PLSS) is a promising nondestructive method for early cancer detection through capturing single scattered light from the epithelium. A novel fiber‐based snapshot PLSS endoscopy capable of collecting single scattered light through a single optical path is introduced. In the endoscope, a simple combination of a fixed multiorder retarder followed by a fixed linear polarizer is proposed at the distal location of multimode fiber for encoding the scattered spectra for the first time. The encoded spectrum is recorded by a fiber spectrometer and subsequently decoded using a compressed sensing (CS) algorithm. The resulting Stokes spectrum S1 is used to iteratively invert the size of the epithelial nucleus for early cancer detection. As an alternative, the normalized spectrum S1 is directly weighted for early cancer identification, offering an innovative non‐iterative method for rapid diagnosis. A proof‐of‐concept prototype of the fiber‐based snapshot PLSS endoscope is built and its effectiveness is validated through experiments on both tissue physical models and ex vivo gastrointestinal samples. [ABSTRACT FROM AUTHOR]

At present, most image encryption schemes directly change plaintext images into ciphertext images without visual significance, and such ciphertext images can be detected by hackers during transmission, and therefore subject to various attacks. To protect the content security and visual safety of images, a learning visual image encryption scheme based on compressed sensing (CS) and cycle generative adversarial network is proposed. First, the secret image is sparse by discrete wavelet transform and compressed by CS. Secondly, the compressed image is permuted and diffused by an improved Henon map to obtain the ciphertext image. Finally, the images are migrated from the ciphertext domain to the plaintext domain by generating an adversarial network to obtain visually meaningful images. We constrain and guide the image generation process by introducing a feature loss function to guarantee the quality of the reconstructed images. Experimental results and security analysis show that the image encryption scheme has sufficient key space, strong key sensitivity, and high reconstruction quality. [ABSTRACT FROM AUTHOR]

Due to its outstanding performance in image processing, deep learning (DL) is successfully utilized in compressed sensing (CS) reconstruction. However, most existing DL-based reconstruction methods capture local features mainly through stacked convolutional layers while ignoring global structural information. In this paper, we propose a novel deep matrix factorization network (dubbed DMFNet), which takes advantage of detailed textures and global structural information of images to achieve better CS reconstruction. Specifically, the proposed DMFNet contains the sampling-initialization module and the DMF reconstruction module. In the sampling-initialization module, a saliency detector is employed to evaluate the salience of different regions and generate the corresponding feature map. Then, a block ratio allocation strategy (BRA) is developed to allocate CS ratios based on the feature map adaptively. Subsequently, we perform a block-by-block initialization reconstruction by a derived mathematical formula. In the DMF reconstruction module, we explore the global structural information by the low-rank matrix factorization. For the variable updating, we design the variables updating networks based on the deep unfolding networks (DUNs) and the U-net but not in a conventional way based on mathematical formulas. Extensive experimental results demonstrate that the proposed DMFNet obtains better reconstruction quality and noise robustness on several benchmark datasets compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The aim of this study is to assess the feasibility of compressed sensing (CS) acceleration methods compared to conventional segmented cine (Seg) cardiac magnetic resonance (CMR) for evaluating left ventricular (LV) function and strain by feature tracking (FT). In this prospective study, 45 healthy volunteers underwent CMR imaging used Seg, threefold (CS3), fourfold (CS4), and eightfold (CS8) CS acceleration. Cine images were scored for quality (1–5 scale). LV volumetric and functional parameters and global longitudinal (GLS), circumferential (GCS), and radial strains (GRS) were quantified. LV volumetric and functional parameters exhibited no differences between Seg and all CS cines (all P > 0.05). The strains were similar for Seg, CS3, and CS4 (all P > 0.05). Similarly, no significant differences were observed in GRS and GCS between Seg and CS8 (all P > 0.05), but the global longitudinal strain was significantly lower for CS8 versus Seg (P < 0.001). Image quality declined with CS acceleration, especially in long-axis views with CS8. CS cine MRI at acceleration factor 4 maintained good image quality and accurate measurements of LV function and strain, although there was a slight reduction in the quality of long-axis images and GLS with CS8. CS acceleration up to a factor of 4 enabled fast CMR evaluations, making it suitable for clinical use. [ABSTRACT FROM AUTHOR]

The development of ultrafast dynamic contrast‐enhanced (UF‐DCE) MRI has occurred in tandem with fast MRI scan techniques, particularly view‐sharing and compressed sensing. Understanding the strengths of each technique and optimizing the relevant parameters are essential to their implementation. UF‐DCE MRI has now shifted from research protocols to becoming a part of clinical scan protocols for breast cancer. UF‐DCE MRI is expected to compensate for the low specificity of abbreviated MRI by adding kinetic information from the upslope of the time‐intensity curve. Because kinetic information from UF‐DCE MRI is obtained from the shape and timing of the initial upslope, various new kinetic parameters have been proposed. These parameters may be associated with receptor status or prognostic markers for breast cancer. In addition to the diagnosis of malignant lesions, more emphasis has been placed on predicting and evaluating treatment response because hyper‐vascularity is linked to the aggressiveness of breast cancers. In clinical practice, it is important to note that breast lesion images obtained from UF‐DCE MRI are slightly different from those obtained by conventional DCE MRI in terms of morphology. A major benefit of using UF‐DCE MRI is avoidance of the marked or moderate background parenchymal enhancement (BPE) that can obscure the target enhancing lesions. BPE is less prominent in the earlier phases of UF‐DCE MRI, which offers better lesion‐to‐noise contrast. The excellent contrast of early‐enhancing vessels provides a key to understanding the detailed pathological structure of tumor‐associated vessels. UF‐DCE MRI is normally accompanied by a large volume of image data for which automated/artificial intelligence‐based processing is expected to be useful. In this review, both the theoretical and practical aspects of UF‐DCE MRI are summarized. Evidence Level: 5 Technical Efficacy: Stage 2 [ABSTRACT FROM AUTHOR]

In this paper, the authors consider a sparse parameter estimation problem in continuous-time linear stochastic regression models using sampling data. Based on the compressed sensing (CS) method, the authors propose a compressed least squares (LS) algorithm to deal with the challenges of parameter sparsity. At each sampling time instant, the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter. Then, the original high-dimensional sparse unknown parameter is recovered by a reconstruction method. By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods, the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals. At last, a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter. [ABSTRACT FROM AUTHOR]

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This paper addresses the problem of complex and challenging disturbance localization in the current power system operation environment by proposing a disturbance localization method for power systems based on group sparse representation and entropy weight method. Three different electrical quantities are selected as observations in the compressed sensing algorithm. The entropy weighting method is employed to calculate the weights of different observations based on their relative disturbance levels. Subsequently, by leveraging the topological information of the power system and pre-designing an overcomplete dictionary of disturbances based on the corresponding system parameter variations caused by disturbances, an improved Joint Generalized Orthogonal Matching Pursuit (J-GOMP) algorithm is utilized for reconstruction. The reconstructed sparse vectors are divided into three parts. If at least two parts have consistent node identifiers, the node is identified as the disturbance node. If the node identifiers in all three parts are inconsistent, further analysis is conducted considering the weights to determine the disturbance node. Simulation results based on the IEEE 39-bus system model demonstrate that the proposed method, utilizing electrical quantity information from only 8 measurement points, effectively locates disturbance positions and is applicable to various disturbance types with strong noise resistance. [ABSTRACT FROM AUTHOR]

Nowadays, magnetic resonance imaging (MRI) is the go-to method for safe and effective diagnosis in hospitals. However, it can be slow and costly due to repeated scans. To speed things up and reduce costs, we use a mathematical approach called compressed sensing. This method generates fewer measurements, but we need an iterative numerical method for accurate reconstruction. This research introduces an effective algorithm aimed at enhancing MRI reconstruction. The proposed algorithm employs a graph-based search approach to locate target atoms within the dictionary. Evaluated using a specifically designed cost function, the paths identified during the search are subjected to pruning techniques that strike a balance between computational complexity and reconstruction accuracy. This approach has demonstrated remarkable efficacy in MRI reconstruction. Through comparative analyses with established methods, we showcase the reconstruction capabilities of the graph search matching pursuit (GSMP) method. The results affirm that GSMP significantly enhances the accuracy of compressed MRI reconstruction. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Objectives: Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k‐space data. Methods: In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction. Results: Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal‐to‐noise ratio of the reconstructed images and preserves more image details. Conclusions: Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The ℓp$$ {\ell}_p $$‐norm with 0

In this paper, we consider the frame-based block sparse signal recovery via a 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 -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 -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 -synthesis. In addition, we also characterize the theoretical performance of recovering signals via the l 2 / l 1 -synthesis in the case of the measurements are disturbed. [ABSTRACT FROM AUTHOR]

In this article, a visual security image encryption algorithm based on compressed sensing is proposed. The algorithm consists of two stages: the compression and encryption stage and the embedding stage. The key streams in the compression and encryption stage are generated by a newly constructed four-dimensional discrete chaotic map, while the Gaussian measurement matrix is generated by a Chebyshev map, and both of their generations are related to the feature code of the carrier image, which enhances the security of the ciphertext. In the compression and encryption stage, a scrambling-cyclic shift-diffusion encryption structure is adopted for the compressed image in which the shift number in the cyclic shift stage and the diffusion key streams are dynamically changed according to each pixel value, so the algorithm can resist chosen plaintext attack. In the embedding stage, the carrier image is first subjected to integer wavelet transform to obtain the high-frequency and low-frequency components of the image, and then the intermediate ciphertext information is embedded into its high-frequency components. Finally, the carrier image is subjected to inverse integer wavelet transform to obtain a visually secure ciphertext image. The experimental results and security analysis indicate that the encryption scheme has a large key space, high decryption key sensitivity, similar histogram distribution between the carrier image and the visual security ciphertext image, and good robustness to noise attacks. [ABSTRACT FROM AUTHOR]

With the rapid development of the Internet of Things (IoT), the sophistication and intelligence of sensors are continually evolving, playing increasingly important roles in smart homes, industrial automation, and remote healthcare. However, these intelligent sensors face many security threats, particularly from malware attacks. Identifying and classifying malware is crucial for preventing such attacks. As the number of sensors and their applications grow, malware targeting sensors proliferates. Processing massive malware samples is challenging due to limited bandwidth and resources in IoT environments. Therefore, compressing malware samples before transmission and classification can improve efficiency. Additionally, sharing malware samples between classification participants poses security risks, necessitating methods that prevent sample exploitation. Moreover, the complex network environments also necessitate robust classification methods. To address these challenges, this paper proposes CSMC (Compressed Sensing Malware Classification), an efficient malware classification method based on compressed sensing. This method compresses malware samples before sharing and classification, thus facilitating more effective sharing and processing. By introducing deep learning, the method can extract malware family features during compression, which classical methods cannot achieve. Furthermore, the irreversibility of the method enhances security by preventing classification participants from exploiting malware samples. Experimental results demonstrate that for malware targeting Windows and Android operating systems, CSMC outperforms many existing methods based on compressed sensing and machine or deep learning. Additionally, experiments on sample reconstruction and noise demonstrate CSMC's capabilities in terms of security and robustness. [ABSTRACT FROM AUTHOR]

With the widespread application of digital images, image processing technology plays an important role in fields such as computer vision and image analysis. Based on the orthogonal matching pursuit algorithm, an image processing method is proposed. In the process, sparse representation and reconstruction algorithm are used for image compressed sensing to complete image sampling operation. Afterwards, the theory of overcomplete sparse representation is introduced to optimize sparse representation, and an overcomplete dictionary is used to remove Gaussian noise, achieving the goal of image processing. The experimental results indicate that the research method do not show significant deficiencies in signal reconstruction when testing reconstructed signals under sparsity of 8; When testing the calculation time, the calculation time of the research method is about 0.212 s when the sparsity is 5 in the Lenna; In the error test, the mean square difference of the research method in the Lenna is stable at about 14.6; When conducting application analysis, the variance eigenvalues of the research method remained below 9.4. This indicates that the research method has good performance and can effectively process images, providing new technical support for image processing. [ABSTRACT FROM AUTHOR]

Further acceleration of DWI in diagnostic radiology is desired but challenging mainly due to low SNR in high b-value images and associated bias in quantitative ADC values. Deep learning-based reconstruction and denoising may provide a solution to address this challenge. The effects of SNR reduction on ADC bias and variability were investigated using a commercial diffusion phantom and numerical simulations. In the phantom, performance of different reconstruction methods, including conventional parallel (SENSE) imaging, compressed sensing (C-SENSE), and compressed SENSE acceleration with an artificial intelligence deep learning-based technique (C-SENSE AI), was compared at different acceleration factors and flip angles using ROI-based analysis. ADC bias was assessed by Lin's Concordance correlation coefficient (CCC) followed by bootstrapping to calculate confidence intervals (CI). ADC random measurement error (RME) was assessed by the mean coefficient of variation (CV ¯) and non-parametric statistical tests. The simulations predicted increasingly negative bias and loss of precision towards lower SNR. These effects were confirmed in phantom measurements of increasing acceleration, for which CCC decreased from 0.947 to 0.279 and CV ¯ increased from 0.043 to 0.439, and of decreasing flip angle, for which CCC decreased from 0.990 to 0.063 and CV ¯ increased from 0.037 to 0.508. At high acceleration and low flip angle, C-SENSE AI reconstruction yielded best denoised ADC maps. For the lowest investigated flip angle, CCC = {0.630, 0.771 and 0.987} and CV ¯ ={0.508, 0.426 and 0.254} were obtained for {SENSE, C-SENSE, C-SENSE AI}, the improvement by C-SENSE AI being significant as compared to the other methods (CV: p = 0.033 for C-SENSE AI vs. C-SENSE and p < 0.001 for C-SENSE AI vs. SENSE; CCC: non-overlapping CI between reconstruction methods). For the highest investigated acceleration factor, CCC = {0.479,0.926,0.960} and CV ¯ ={0.519,0.119,0.118} were found, confirming the reduction of bias and RME by C-SENSE AI as compared to C-SENSE (by trend) and to SENSE (CV: p < 0.001; CCC: non-overlapping CI). ADC bias and random measurement error in DWI at low SNR, typically associated with scan acceleration, can be effectively reduced by deep-learning based C-SENSE AI reconstruction. [ABSTRACT FROM AUTHOR]

We investigated the feasibility of using compressed sensitivity encoding (CS-SENSE) to accelerate high-resolution black-blood T1-weighted imaging with variable flip angles (T1WI-VFA) for efficient visualization and characterization of lenticulostriate arteries (LSAs) on a 3.0 T MR scanner. Twenty-five healthy volunteers and 18 patients with the cerebrovascular disease were prospectively enrolled. Healthy volunteers underwent T1WI-VFA sequences with different acceleration factors (AFs), including conventional sensitivity encoding (SENSE) AF = 3 and CS-SENSE AF = 3, 4, 5, and 6 (SENSE3, CS3, CS4, CS5, CS6, respectively) at 3 Tesla MRI scanner. Objective evaluation (contrast ratio and number, length, and branches of LSAs) and subjective evaluation (overall image quality and LSA visualization scores) were used to assess image quality and LSA visualization. Comparisons were performed among the 5 sequences to select the best AF. All patients underwent both T1WI-VFA with the optimal AF and digital subtraction angiography (DSA) examination, and the number of LSAs observed by T1WI-VFA was compared with that by DSA. Pair-wise comparisons among CS3, CS4, and SENSE3 revealed no significant differences in both objective measurements and subjective evaluation (all P > 0.05). In patients, there was no significant difference in LSA counts on the same side between T1WI-VFA with CS4 and DSA (3, 3–4 and 3, 3–3, P = 0.243). CS3 provided better LSA visualization but a longer scan duration compared to CS4. And, CS4 strikes a good balance between LSA visualization and acquisition time, which is recommended for routine clinical use. [ABSTRACT FROM AUTHOR]