Compressed Sensing Method Research Articles

Hierarchical distillation for image compressive sensing reconstruction

Compressive sensing (CS) is an effective algorithm for reconstructing images from a small sample of data. CS models combining traditional optimisation-based CS methods and deep learning have been used to improve image reconstruction performance. However, if the sample ratio is very low, the performance of the CS method combined with deep learning will be unsatisfactory. In this letter, a deep learning-based CS model incorporating hierarchical knowledge distillation to improve image reconstruction even at varied sample ratios. Compared to the state-of-art methods with all compressive sensing ratios, the proposed method improved performance by an average of 0.26 dB without additional trainable parameters.

Accelerated multi-target chemical exchange saturation transfer magnetic resonance imaging of the mouse heart

Cardiac chemical exchange saturation transfer-magnetic resonance imaging (CEST-MRI) has been used to probe levels of various metabolites that provide insight into myocardial structure and function. However, imaging of the heart using CEST-MRI is prolonged by the need to repeatedly acquire multiple images for a full Z-spectrum and to perform saturation and acquisition around cardiac and respiratory cycles. Compressed sensing (CS) reconstruction of sparse data enables accelerated acquisition, but reconstruction artifacts may bias subsequently derived measures of CEST contrast. In this study, we examine the impact of CS reconstruction of increasingly under-sampled cardiac CEST-MRI data on subsequent CEST contrasts of amine-containing metabolites and amide-containing proteins. Cardiac CEST-MRI data sets were acquired in six mice using low and high RF saturation for single and dual contrast generation, respectively. CEST-weighted images were reconstructed using CS methods at 2–5× levels of under-sampling. CEST contrasts were derived from corresponding Z-spectra and the impact of accelerated imaging on accuracy was assessed via analysis of variance. CS reconstruction preserved myocardial signal to noise ratio as compared to conventional reconstruction. However, greater absolute error and distribution of derived contrasts was observed with increasing acceleration factors. The results from this study indicate that acquisition of radial cardiac CEST-MRI data can be modestly, but meaningfully, accelerated via CS reconstructions with little error in CEST contrast quantification.

Simulation of the Operation of a Single Pixel Camera with Compressive Sensing in the Long-Wave Infrared

Imaging with the use of a single pixel camera and based on compressed sensing (CS) is a new and promising technology. The use of CS allows reconstruction of images in various spectrum ranges depending on the spectrum sensibility of the used detector. During the study image reconstruction was performed in the LWIR range based on a thermogram from a simulated single pixel camera. For needs of reconstruction CS was used. A case analysis showed that the CS method may be used for construction of infrared-based observation single pixel cameras. This solution may also be applied in measuring cameras. Yet the execution of a measurement of radiation temperature requires calibration of results obtained by CS reconstruction. In the study a calibration method of the infrared observation camera was proposed and studies were carried out of the impact exerted by the number of measurements made on the quality of reconstruction. Reconstructed thermograms were compared with reference images of infrared radiation. It has been ascertained that the reduction of the reconstruction error is not directly in proportion to the number of collected samples being collected. Based on a review of individual cases it has been ascertained that apart from the number of collected samples, an important factor that affects the reconstruction fidelity is the structure of the image as such. It has been proven that estimation of the error for reconstructed thermograms may not be based solely on the quantity of executed measurements.

Weak fault signature identification of rolling bearings based on improved adaptive compressed sensing method

In order to extract the weak fault feature mixed in the background noise and escape the constraints of traditional sampling theorems on large-capacity data collection, transmission and storage, an improved compressed sensing (CS) algorithm, in which an adaptive sparse representation based on learning dictionary and an improved reconstruction scheme are integrated, is presented in this paper. The adaptive sparse representation method includes the K-singular value decomposition based dictionary learning algorithm, and the stagewise weak orthogonal matching pursuit reconstruction is improved by the regularization principle, backtracking mechanism, adaptive mechanism and relevant stop criteria. The compressive measurement was completed through Gaussian random matrix. One simulation signal and two different experimental data sets of rolling bearing are utilized to validate the effectiveness of the proposed method, and the results have shown that the reconstruction accuracy and calculation efficiency can be improved simultaneously. Most importantly, the weak fault feature shaded by strong background noise can be effectively identified, which cannot be obtained by traditional CS method.

Low-Frequency Expansion Approach for Seismic Data Based on Compressed Sensing in Low SNR

Low-frequency information can reflect the basic trend of a formation, enhance the accuracy of velocity analysis and improve the imaging accuracy of deep structures in seismic exploration. However, the low-frequency information obtained by the conventional seismic acquisition method is seriously polluted by noise, which will be further lost in processing. Compressed sensing (CS) theory is used to exploit the sparsity of the reflection coefficient in the frequency domain to expand the low-frequency components reasonably, thus improving the data quality. However, the conventional CS method is greatly affected by noise, and the effective expansion of low-frequency information can only be realized in the case of a high signal-to-noise ratio (SNR). In this paper, well information is introduced into the objective function to constrain the inversion process of the estimated reflection coefficient, and then, the low-frequency component of the original data is expanded by extracting the low-frequency information of the reflection coefficient. It has been proved by model tests and actual data processing results that the objective function of estimating the reflection coefficient constrained by well logging data based on CS theory can improve the anti-noise interference ability of the inversion process and expand the low-frequency information well in the case of a low SNR.

Holographic optical field recovery using a regularized untrained deep decoder network

Image reconstruction using minimal measured information has been a long-standing open problem in many computational imaging approaches, in particular in-line holography. Many solutions are devised based on compressive sensing (CS) techniques with handcrafted image priors or supervised deep neural networks (DNN). However, the limited performance of CS methods due to lack of information about the image priors and the requirement of an enormous amount of per-sample-type training resources for DNNs has posed new challenges over the primary problem. In this study, we propose a single-shot lensless in-line holographic reconstruction method using an untrained deep neural network which is incorporated with a physical image formation algorithm. We demonstrate that by modifying a deep decoder network with simple regularizers, a Gabor hologram can be inversely reconstructed via a minimization process that is constrained by a deep image prior. The outcoming model allows to accurately recover the phase and amplitude images without any training dataset, excess measurements, or specific assumptions about the object’s or the measurement’s characteristics.

Phase2Phase: Respiratory Motion-Resolved Reconstruction of Free-Breathing Magnetic Resonance Imaging Using Deep Learning Without a Ground Truth for Improved Liver Imaging.

Respiratory binning of free-breathing magnetic resonance imaging data reduces motion blurring; however, it exacerbates noise and introduces severe artifacts due to undersampling. Deep neural networks can remove artifacts and noise but usually require high-quality ground truth images for training. This study aimed to develop a network that can be trained without this requirement. This retrospective study was conducted on 33 participants enrolled between November 2016 and June 2019. Free-breathing magnetic resonance imaging was performed using a radial acquisition. Self-navigation was used to bin the k-space data into 10 respiratory phases. To simulate short acquisitions, subsets of radial spokes were used in reconstructing images with multicoil nonuniform fast Fourier transform (MCNUFFT), compressed sensing (CS), and 2 deep learning methods: UNet3DPhase and Phase2Phase (P2P). UNet3DPhase was trained using a high-quality ground truth, whereas P2P was trained using noisy images with streaking artifacts. Two radiologists blinded to the reconstruction methods independently reviewed the sharpness, contrast, and artifact-freeness of the end-expiration images reconstructed from data collected at 16% of the Nyquist sampling rate. The generalized estimating equation method was used for statistical comparison. Motion vector fields were derived to examine the respiratory motion range of 4-dimensional images reconstructed using different methods. A total of 15 healthy participants and 18 patients with hepatic malignancy (50 ± 15 years, 6 women) were enrolled. Both reviewers found that the UNet3DPhase and P2P images had higher contrast (P < 0.01) and fewer artifacts (P < 0.01) than the CS images. The UNet3DPhase and P2P images were reported to be sharper than the CS images by 1 reviewer (P < 0.01) but not by the other reviewer (P = 0.22, P = 0.18). UNet3DPhase and P2P were similar in sharpness and contrast, whereas UNet3DPhase had fewer artifacts (P < 0.01). The motion vector lengths for the MCNUFFT800 and P2P800 images were comparable (10.5 ± 4.2 mm and 9.9 ± 4.0 mm, respectively), whereas both were significantly larger than CS2000 (7.0 ± 3.9 mm; P < 0.0001) and UNnet3DPhase800 (6.9 ± 3.2; P < 0.0001) images. Without a ground truth, P2P can reconstruct sharp, artifact-free, and high-contrast respiratory motion-resolved images from highly undersampled data. Unlike the CS and UNet3DPhase methods, P2P did not artificially reduce the respiratory motion range.

An Improved Background Subtraction Method for Adaptive Rate Compressive Sensing

In Compressive Video Sensing application, the using of Adaptive Rate Compressive Sensing (ARCS) method can predict and adjust the sampling rate for each video frame, reduce the total sampling rate and improve the quality of reconstructed image. In order to use the inter-frame correlation of the video signal efficiently and reduce the sampling rate of the whole signal, an Improved Background Subtraction (IBS) method is proposed in this paper. By alternately using the frame without any foreground objects and the previous frame as the background of the signal, the sparsity of the foreground signal is improved and the total sampling rate is reduced. Experimental results show that, compare with the traditional background subtraction method, the IBS method can significantly reduce the total video sampling rate without apparent degradation of reconstructed image quality under the same ARCS method.

Tracking of an underwater source using sparse method

The sparse method or better known as compressed sensing (CS), is a method often used for the signal reconstruction process. This method had considered better than conventional methods because it can reconstruct a signal with a smaller amount of data. Many algorithms had used for signal reconstruction using the CS method, including l1-minimization and orthogonal matching pursuit (OMP). In this study, the two algorithms were used for signal reconstruction of underwater objects and then compared to find out which algorithm is better for the signal reconstruction of underwater objects. Comparing the two algorithms had based on parameters in the form of PSNR and RMSE against sparsity. Based on the simulations that had been doing, known that the l1-minimization algorithm can reconstruct signal up to 40% sparsity. Whereas the OMP algorithm can only reconstruct signals up to 30% sparsity. PSNR and RMSE generated from the l1-minimization algorithm show that this algorithm provides better reconstruction results than OMP for underwater object signals. The results obtained show that the best tracking process is at an angle of incidence of 90°.

Robust and Fast Super-Resolution SAR Tomography of Forests Based on Covariance Vector Sparse Bayesian Learning

A novel method based on covariance vector sparse Bayesian learning (CV-SBL) is proposed in this letter to reconstruct the vertical structure of forests using a small number of synthetic aperture radar (SAR) images. This method regards the inversion of forests reflectivity profiles in the wavelet domain as a sparse signal reconstruction (SSR). Based on the covariance matrix matching criterion, the backscatter power of forests signal and noise will be jointly solved adaptively. Through a few iterations, the exact positions of the closely spaced phase centers can be obtained to simplify the characterization of the vertical structure of the forests. Unlike the traditional compressive sensing (CS) method based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> norm convex optimization, the novel method can obtain a real sparse solution without setting hyper-parameters and has a more reliable and accurate reconstruction performance. Besides, the computational efficiency of the new method is much higher than that of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> minimization CS method, and it is more suitable for large-scale forests mapping applications. The proposed method is validated using P-band TropiSAR 2009 data set over a test site in Paracou, French Guiana. Furthermore, the reconstruction performance of the proposed method is compared with the spectral analysis methods (Beamforming and Capon) and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> minimization super-resolution CS.

Compressed sensing of large-scale local field potentials using adaptive sparsity analysis and non-convex optimization

Objective. Energy consumption is a critical issue in resource-constrained wireless neural recording applications with limited data bandwidth. Compressed sensing (CS) has emerged as a powerful framework in addressing this issue owing to its highly efficient data compression procedure. In this paper, a CS-based approach termed simultaneous analysis non-convex optimization (SANCO) is proposed for large-scale, multi-channel local field potentials (LFPs) recording. Approach. The SANCO method consists of three parts: (1) the analysis model is adopted to reinforce sparsity of the multi-channel LFPs, therefore overcoming the drawbacks of conventional synthesis models. (2) An optimal continuous order difference matrix is constructed as the analysis operator, enhancing the recovery performance while saving both computational resources and data storage space. (3) A non-convex optimizer that can by efficiently solved with alternating direction method of multipliers is developed for multi-channel LFPs reconstruction. Main results. Experimental results on real datasets reveal that the proposed approach outperforms state-of-the-art CS methods in terms of both recovery quality and computational efficiency. Significance. Energy efficiency of the SANCO make it an ideal candidate for resource-constrained, large scale wireless neural recording. Particularly, the proposed method ensures that the key features of LFPs had little degradation even when data are compressed by 16x, making it very suitable for long term wireless neural recording applications.

WITHDRAWN: Image Art Design Based on Image Compression Sensing System and Embedded Device

ABSTRACT The image Compressed Sensing (CS), two main challenges is to develop the design and reconstruction of the sample matrix. In one aspect, a random sample matrix is generally used and signal characteristics of the signal independent negligible. On the other hand, the most advanced art design image CS method made a very good performance. High computational complexity to meet two challenges recommend using convolution neuroimaging CS architecture. Network includes sampling network (called Convolutional Neural Network (CNN)) Joint Optimization of network reconstruction. Adaptation sampling learning image samples from a training matrix, which can accommodate a plurality of images of the configuration information, better reconstruction CS measurements. Reconstruction network, the network including linear and nonlinear initial reconstructed depth reconstruction networks, learning measuring terminal between CS and the reconstructed image to the end of the map. While achieving high speed of operation, the experimental results show that the most advanced reconstruction quality provided by the state. In addition, the results also show that the trained sample matrix can significantly improve the traditional CS image reconstruction method.

PSO-based sink placement and load-balanced anycast routing in multi-sink WSNs considering compressive sensing theory

This paper deals with the sink placement and anycast routing to increase the lifetime of multi-sink wireless sensor networks. Two algorithms are proposed, namely “Multi-sink Placement and Anycast Routing (MPAR)” and “Extended Multi-sink Placement and Anycast Routing (EMPAR)”, to jointly address the problems of clustering, multi-sink placement, and load-balanced anycast routing. MPAR and EMPAR rely on a two-level architecture in which sensors are clustered at the lower level. Each sensor transmits its data to the corresponding Cluster Head (CH) via a load-balanced data aggregation routing tree. At the upper level, both schemes use a modified particle swarm optimization algorithm to determine the best location of sinks. For each sink, a high-level anycast routing tree is developed using the ant colony optimization algorithm. Each anycast tree uses the hybrid Compressive Sensing (CS) method to forward the aggregated data from CHs to sinks. Extensive simulations are conducted to illustrate the efficiency of the proposed algorithms in terms of energy consumption, energy consumption variance, and network lifetime. The results show that EMPAR has a better performance than MPAR due to its CH selection strategy. As an advantage, EMPAR considers both remaining energy and distance criteria along with a rest factor to select the best CH for each cluster. For an average number of clusters, EMPAR reduces the energy consumption by 5.98% and 12.20%, respectively, compared to the MPAR algorithm and the energy-aware CS-based data aggregation algorithm. It also increases the network lifetime in comparison with the aforementioned algorithms by 12.26% and 30.38%, respectively.

A Recovery Performance Study of Compressive Sensing Methods on Antenna Array Diagnosis from Near-Field Measurements

Antenna testing consists locating the potential defaults from radiated field measurements. It has been established in literature, that compressive sensing methods provide faster results in failure detection from smaller number of measurement data compared to the traditional back-propagation mechanisms. Compressive sensing (CS) methods require a priori measurement of failure-free reference array and require small number of measurements for diagnosis. However, there are conflicting reports in literature regarding the choice of appropriate CS method, and there is no sufficient comparison study to justify which one is a better choice under a very harsh condition. In this study, recovery performance test of CS methods for the diagnosis of antenna array from few near-field measured data under various signal-to-noise ratios (SNRs) is presented. Specifically, we tested three prominent regularization procedures: total variation (TV), mixed l1/ l2 norm, and minimization of the l1 in solving diagnosis problems in antenna array. Linear system that relates the difference between near-field measured data from reference antenna (RA) array and array under test (AUT), and the difference that exist between coefficients of RA and the AUT, is solved by the three compressive sensing regularization methods. Numerical experiment of a 10 × 10 rectangular waveguide array under realistic noise scenario, operating at 10 GHz is used to conduct the test. Minimization l1 technique is more robust to additive data noise. It exhibits better diagnosis at 20 dB and 10 dB SNR, making it a better candidate for noisy measured data as compared to other techniques.

An enhanced diagnosis method for weak fault features of bearing acoustic emission signal based on compressed sensing.

Aiming at the problems of data transmission, storage, and processing difficulties in the fault diagnosis of bearing acoustic emission (AE) signals, this paper proposes a weak fault feature enhancement diagnosis method for processing bearing AE signals in the compressed domain based on the theory of compressed sensing (CS). This method is based on the frequency band selection scheme of CS and particle swarm optimization (PSO) method. Firstly, the method uses CS technology to compress and sample the bearing AE signal to obtain the compressed signal; then, the compressed AE signals are decomposed by the compression domain wavelet packet decomposition matrix to extract the characteristic parameters of different frequency bands, and then the weighted sum of the characteristic parameters is carried out. At the same time, the PSO method is used to optimize the weight coefficient to obtain the enhanced fault characteristics; finally, a feature-enhanced-support vector machine (SVM) fault diagnosis model is established. Different feature parameters are feature-enhanced to form a feature set, which is used as input, and the SVM method is used for pattern recognition of different types and degrees of bearing faults. The experimental results show that the proposed method can effectively extract the fault features in the bearing AE signal while improving the efficiency of signal processing and analysis and realize the accurate classification of bearing faults.

Possibilities of applying Compressive Sensing methods in detection tools

Possibilities of applying Compressive Sensing methods in detection tools

Compressed Sensing via Measurement-Conditional Generative Models

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator to utilize additional information from a given measurement for prior learning, thereby yielding more accurate prediction for signals. As our framework has a simple form, it is easily applied to existing CS methods using pre-trained generators. We demonstrate through extensive experiments that our framework exhibits uniformly superior performances by large margin and can reduce the reconstruction error up to an order of magnitude for some applications. We also explain the experimental success in theory by showing that our framework can slightly relax the stringent signal presence condition, which is required to guarantee the success of signal recovery.

Compressed Sensing-Based Simultaneous Recovery of Magnitude and Phase MR Images via Dual Trigonometric Sparsity

Complex-valued Magnetic Resonance Imaging (MRI) is widely used in clinical diagnosis. The magnitude images are mainly used for structure visualization, and the phase images reveal tissue properties, such as magnetic susceptibility and fluid flow information. While MRI is slow, compressed sensing (CS) can be used to reconstruct the accelerated acquisitions. Current CS-based MRI reconstruction algorithms mostly focus on magnitude image recovery, with less attention to the recovery of phase images. In this paper, we propose a novel CS algorithm to simultaneously recover the magnitude and phase MR images based on the sparsity of the trigonometric function. The CS method requires a sparse representation of the original images, and it is observed the trigonometric functions of phase images in the Wavelet domain promote sparsity. Therefore, rather than transforming the phase images directly into the Wavelet domain, we calculate the sine and cosine of the phase images whose Wavelet transforms are set as the L1-norm regularization term. The combination of the dual trigonometric functions captures a unique, faithful four-quadrant phase information, which also improves the reconstructed magnitude images through an alternating optimization procedure. Reconstructions of simulated images and in vivo images are studied, and both show the superiority of the proposed method over compared phase recovery algorithms.

Parallel magnetic resonance imaging acceleration with a hybrid sensing approach.

In magnetic resonance imaging (MRI), the scan time for acquiring an image is relatively long, resulting in patient uncomfortable and error artifacts. Fortunately, the compressed sensing (CS) and parallel magnetic resonance imaging (pMRI) can reduce the scan time of the MRI without significantly compromising the quality of the images. It has been found that the combination of pMRI and CS can better improve the image reconstruction, which will accelerate the speed of MRI acquisition because the number of measurements is much smaller than that by pMRI. In this paper, we propose combining a combined CS method and pMRI for better accelerating the MRI acquisition. In the combined CS method, the under-sampled data of the K-space is performed by taking both regular sampling and traditional random under-sampling approaches. MRI image reconstruction is then performed by using nonlinear conjugate gradient optimization. The performance of the proposed method is simulated and evaluated using the reconstruction error measure, the universal image quality Q-index, and the peak signal-to-noise ratio (PSNR). The numerical simulations confirmed that, the average error, the Q index, and the PSNR ratio of the appointed scheme are remarkably improved up to 59, 63, and 39% respectively as compared to the traditional scheme. For the first time, instead of using highly computational approaches, a simple and efficient combination of CS and pMRI is proposed for the better MRI reconstruction. These findings are very meaningful for reducing the imaging time of MRI systems.

Structure-Aware Compressive Sensing for Magnetic Flux Leakage Detectors: Theory and Experimental Validation

Compressive sensing (CS) has emerged as a promising technique for collecting and reconstructing digital signals. In this article, we design a CS method for magnetic flux leakage (MFL) detectors based on the problem’s physics. A method is presented to reconstruct $x$ and $y$ components of magnetic $\overrightarrow {B}$ field using a few samples. First, the problem is formulated into an optimization framework where the goal is to minimize Euclidean distance between real and reconstructed signals while preserving the CS acquisition criteria. The resulting optimizations are then simplified and solved through the established majorization minimization (MM) method. Meanwhile, a Gaussian sampling strategy is adopted where samples with more information have a higher chance of being selected. Validation of the proposed method is accomplished through the performance comparison among the proposed method and several established high-performance CS techniques on gathered experimental data. The extensive validation of the signals gathered from 17 artificial defects on the 12-m pipe reveals that the signals can be compressed and recovered with exceptional fidelity when the problem’s physical structure is known.