Compressive Sensing Research Articles

A sparse low-rank matrix recovery strategy to deal with robust identification for multi-model systems with time-varying delays

A robust identification problem for multi-model systems with time-vary delays is considered in this article, where the linear parameter varying model is employed to present the structure of the multi-model systems. To handle outliers in the collected data, we establish an observation model based on a robust principal component analysis (RPCA) algorithm for low-rank matrix recovery. Construct a high-dimensional information matrix using multi-batch measured data. Although this matrix is typically high-dimensional and low-rank, outliers cause it to become high-dimensional and high-rank. By applying the RPCA algorithm, we restore the information matrix to its low-rank form, thus isolating the pure collected data. This process allows us to select a batch of collected data as information vectors for parameter identification. A Markov chain model is established to describe the correlation between time delays. Given the complexity of optimizing log-likelihood functions directly, we derive the estimation problem of model parameters and time delays under the framework of the expectation maximization (EM) algorithm. Therefore, an EM identification algorithm based on RPCA (RPCA-EM) is derived. A numerical simulation and an example involving a continuous stirred tank reactor verify the effectiveness of the proposed RPCA-EM algorithm.

Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring

Structural health monitoring (SHM) data have a large volume, increasing the cost of data storage and transmission and the difficulties of structural parameter identification. The compressed sensing (CS) theory provides a signal acquisition and analysis strategy. Signal reconstruction using limited measurements and CS has attracted significant interest. However, the dynamic responses obtained from civil engineering structures contain noise, resulting in sparse samples and reducing the signal reconstruction accuracy. Therefore, we propose an optimization algorithm for the measurement matrix integrating the Karhunen-Loeve transform (KLT) and approximate QR decomposition (KLT-QR) to improve the accuracy of dynamic response reconstruction of SHM data. The KLT reduces the correlation between the measurement matrix and the sparse basis. The approximate QR decomposition is used to improve the independence between the column vectors of the measurement matrix, optimizing the measurement matrix. The experimental results for a laboratory steel beam indicate that the proposed KLT-QR algorithm outperforms three other algorithms regarding the accuracy of dynamic response reconstruction (acceleration, displacement, and strain), especially at high compression ratios. The acceleration responses from the Ji’an Bridge are utilized to verify the advantages of the proposed algorithm. The results demonstrate that the KLT-QR algorithm has the highest accuracy of reconstructing the vibration signals and yields better Fourier spectra than the conventional Gaussian measurement matrix.

Mode Analysis for the Rotating Aerodynamic Disturbance of a Transonic Fan

Abstract The non-synchronous blade vibration induced by a rotating aerodynamic disturbance is encountered for the fan of a turbofan engine working at 65% speedline. To analyze the unsteady characteristics, two methods based on the phase analysis and the compressive sensing (CS) for spatially-undersampled data are proposed and applied to obtain the circumferential mode order of the aerodynamic disturbance, and their performance has been carefully examined at various parameters. It was shown that when there are sufficient probes, i.e., 7–8 in the present study, both the two methods can give a correct prediction to the dominant mode order (the highest is 26 in this work) for all non-engine-order (EO) frequencies. However, if less probes are used, the deterioration of accuracy can be observed for both the two methods and a better performance can be observed for the CS method. In order to suppress the blade vibration, the fan blade is trimmed to alter its solid eigenfrequencies and avoid the resonance, which is proved to be an effective anti-vibration design. The existence of the aerodynamic disturbance after the blade is trimmed also suggests that the vibration is not self-excited but induced by the resonance of the flow excitation and the structure. For the cases with and without vibration, the origin of these non-EO frequencies can be well explained by the spinning mode theory and the interaction between the blade vibration and a high-order blade passing frequency has been observed in this study.

High-precision MRI of liver and hepatic lesions on gadoxetic acid-enhanced hepatobiliary phase using a deep learning technique.

The purpose of this study was to investigate whether the high-precision magnetic resonance (MR) sequence using modified Fast 3D mode wheel and Precise IQ Engine (PIQE), that was collected in a wheel shape with sequential data filling in the k-space in the phase encode-slice encode plane, is feasible for breath-hold (BH) three-dimensional (3D) T1-weighted imaging of the hepatobiliary phase (HBP) of gadoxetic acid-enhanced MRI in comparison to the compressed sensing (CS) sequence using Advanced Intelligent Clear-IQ Engine (AiCE). This retrospective study included 54 patients with focal hepatic lesions who underwent dynamic contrast-enhanced MRI. Both standard HBP images using CS with AiCE and high-precision HBP images using modified Fast 3D mode wheel and PIQE were obtained. Image quality, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) were evaluated using the Wilcoxon signed-rank test. p values of < 0.05 were considered to be statistically significant. Scores for image noise, conspicuity of liver contours and intrahepatic structures, and overall image quality in high-precision HBP imaging using modified Fast 3D mode wheel and PIQE were significantly higher than those in HBP imaging using CS and AiCE (all p < 0.001). There was no significant difference in the presence of artifact and motion-related blurring. There were no significant differences between the sequences in SNR (p = 0.341) or CNR (p = 0.077). The detection rate of focal hepatic lesions was 71.4-85.3% in CS with AiCE, and 82.2-95.8% in modified Fast 3D mode wheel and PIQE. A high-precision MR sequence using a modified Fast 3D mode wheel and PIQE is applicable for the HBP of BH 3D T1-weighted imaging.

A Sub-Channel Spatial Homogeneity-Based Channel Estimation Method for Underwater Optical Densely Arrayed MIMO Systems

The limited surface area and structural constraints of small underwater communication devices necessitate a dense placement of transmitting and receiving array elements in optical multiple-input multiple-output (MIMO) systems. The compact layout leads to the formation of sub-channels that exhibit notable spatial correlation and a tendency toward homogeneity. Although sub-channel spatial homogeneity (SSH) may diminish the communication capacity of MIMO systems, it provides a significant advantage by reducing the pilot overhead. In this study, we exploit the inherent SSH and the natural time-domain sparsity of channel impulse response (CIR) in the underwater optical densely arrayed MIMO (UODA-MIMO) system to propose an innovative SSH-based channel estimation (SSH-CE) method. We model the underwater optical CIR at Gbaud rates and integrate it with SSH characteristics. This approach transforms the reconstruction targets of compressive sensing (CS) from conventional CIR samples to prior CIR model parameters and the fitting residuals of the homogeneous sub-channels, reducing the pilot overhead. The simulation results of photon tracing for UODA-MIMO sub-channels in turbid harbor water indicate a monotonic, exponential decay in CIR at Gbaud rates, with transmission delays exceeding 5 nanoseconds for distances over 8 m. Moreover, the correlation coefficients among sub-channels reach a minimum of 0.975, confirming the presence of SSH in UODA-MIMO systems. In comparison to existing CS methods that rely on known sparsity, sparsity adaptation, and the structural sparsity of MIMO channels, the SSH-CE method achieves a lower degree of sparsity in reconstruction targets and a reduced lower bound for pilot requirements under the SPARK criterion. Specifically, the SSH-CE method achieves a reduction in the pilot overhead for reconstructing Nt sub-channels of K-sparse to 2Nt irrespective of CIR residual compensation.

Image quality in three-dimensional (3D) contrast-enhanced dynamic magnetic resonance imaging of the abdomen using deep learning denoising technique: intraindividual comparison between T1-weighted sequences with compressed sensing and with a modified Fast 3D mode wheel.

To assess the image quality of a modified Fast three-dimensional (Fast 3D) mode wheel with sequential data filling (mFast 3D wheel) combined with a deep learning denoising technique (Advanced Intelligent Clear-IQ Engine [AiCE]) in contrast-enhanced (CE) 3D dynamic magnetic resonance (MR) imaging of the abdomen during a single breath hold (BH) by intra-individual comparison with compressed sensing (CS) with AiCE. Forty-two patients who underwent multiphasic CE dynamic MRI obtained with both mFast 3D wheel using AiCE and CS using AiCE in the same patient were retrospectively included. The conspicuity, artifacts, image quality, signal intensity ratio (SIR), signal-to-noise ratio (SNR), contrast ratio (CR), and contrast enhancement ratio (CER) of the organs were compared between these 2 sequences. Conspicuity, artifacts, and overall image quality were significantly better in the mFast 3D wheel using AiCE than in the CS with AiCE (all p < 0.001). The SNR of the liver in CS with AiCE was significantly better than that in the mFast 3D wheel using AiCE (p < 0.01). There were no significant differences in the SIR, CR, and CER between the two sequences. A mFast 3D wheel using AiCE as a deep learning denoising technique improved the conspicuity of abdominal organs and intrahepatic structures and the overall image quality with sufficient contrast enhancement effects, making it feasible for BH 3D CE dynamic MR imaging of the abdomen.

Lightweight distributed deep learning on compressive measurements for internet of things

In this work, we investigate the problem of distributed deep learning in Internet of Things (IoT). The proposed learning framework is constructed in a fog–cloud computing architecture, so as to overcome the limitation of resource constrained IoT end device. Compressive Sensing (CS) is used as a lightweight encryption in the framework to preserve the privacy of training data. Specifically, a chaotic-based CS measurement matrix construction mechanism is applied in the system to save the storage and transmission costs. With this design, the computation overhead of the learning framework in IoT can be successfully offloaded from IoT end device to the fog nodes. Theoretical analysis demonstrates that our system can guarantee security of the raw data against chosen plaintext attack (CPA). Experimental and analysis results show that our privacy-preserving proposal can significantly reduce the communication costs and computation costs with only a negligible accuracy penalty (with classification accuracy 91% testing on MNIST dataset under compression rate 0.5) compared to traditional non-private federated learning schemes. Notably, due to the chaotic-based CS measurement matrix construction mechanism, the memory requirement of end device side can be significantly reduced. This makes our framework be very suitable for the IoT applications in which end devices are equipped with low-spec chips.

Considerations for a Micromirror Array Optimized for Compressive Sensing (VIS to MIR) in Space Applications.

Earth observation (EO) is crucial for addressing environmental and societal challenges, but it struggles with revisit times and spatial resolution. The EU-funded SURPRISE project aims to improve EO capabilities by studying space instrumentation using compressive sensing (CS) implemented through spatial light modulators (SLMs) based on micromirror arrays (MMAs) to improve the ground sampling distance. In the SURPRISE project, we studied the development of an MMA that meets the requirements of a CS-based geostationary instrument working in the visible (VIS) and mid-infrared (MIR) spectral ranges. This paper describes the optical simulation procedure and the results obtained for analyzing the performance of such an MMA with the goal of identifying a mirror design that would allow the device to meet the optical requirements of this specific application.

A data assimilation pressure field measurement method for linear turbine cascades based on compressed sensing

One of the most dominant measuring techniques for linear turbine cascades is to obtain the high spatial resolution pressure field by a discrete point array. In this work, a compressed sensing (CS) based data assimilation methodology is proposed, by which a set of optimal sparse measuring points can be derived through an optimization procedure. Combined with numerical simulations and the data-driven modal decomposition, the high spatial resolution pressure distribution can be reconstructed accurately with sparse random sampling. To this end, detailed comparative research is conducted. First, the impacts of different sparse bases, including the discrete Fourier transform (DFT), the discrete cosine transform (DCT), and the proper orthogonal decomposition (POD) matrices, and the compression ratio on the reconstruction performance are compared and analyzed systematically under different incidence angles and cascade exit isentropic Mach numbers. Results reveal that a CS approach on POD subspace (CS-POD) performs remarkably better than the CS-DFT and CS-DCT in capturing the spatially continuous pressure distribution, even with a small number of measuring points. Furthermore, effects of the order of truncated POD modes and the number of training dataset required to conduct POD on the error are also investigated that exhibits a downward trend with the rise in these two elements. To overcome the deficiency of randomly selected sparse observation sites with this methodology and the resulting high measuring cost under different conditions, a vectorized CS-POD (Vec-CS-POD) model is constructed to obtain one set of measuring distribution that could satisfy the multi-conditional measurements simultaneously, and its reliability and robustness are validated through cascade experiments. With the aid of the Vec-CS-POD based data fusion framework, spatially resolved end wall pressure fields can be acquired by only a few measuring ports, the number of which can be reduced by 77% compared to the conventional uniform arrangement. The generalization ability of the proposed framework is also validated and evaluated; thus, it exhibits broad potential in other flow field measurements.

Microstructure and texture evolution of 2A12 aluminum alloy semi-solid billet prepared by SIMA process

In order to make up for the lack of research on the preparation process of semi-solid billet of 2A12 aluminum alloy, this paper adopts strain-induced melting activation (SIMA) process to prepare semi-solid billet of 2A12 aluminum alloy, and studies the effect of different SIMA process parameters on the microstructure and texture evolution. The results indicated a notable increase in both the average grain size (AGS) and shape factor (SF) with prolonged isothermal time under the condition of constant isothermal temperature. When the isothermal time is the same, the AGS is larger at low isothermal temperature, the SF is higher at high isothermal temperature, and the grain spheroidization is more obvious; The influence of the uneven strain distribution of the compression sample on the microstructure evolution during the subsequent semi-solid isothermal treatment (SSIT) process was studied by finite element method; At an isothermal temperature of 590°C and an isothermal time of 15 minutes, the recrystallization is basically completed, and the elongated grains are completely transformed into spherical isaemic crystals. The main texture types of the original extruded sample and the compression sample are <110> ‖CD and <010> ‖CD texture, respectively. The SSIT process will make the grain orientation approach to random orientation; The strong segregation of Cu and mild segregation of Mg and Zn were observed at the grain boundary during SSIT process; A suitable coarsening kinetic equation was determined, and the influence of isothermal temperature on the coarsening rate constant was studied.

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

Image reconstruction from compressed measurements for ultrasound NDT

In ultrasound NDT, Delay-and-Sum schemes are commonly used to reconstruct images from the measurement data. For single channel pulse-echo measurements, this is called Synthetic Aperture Focusing Technique (SAFT). In a multi-channel setup, SAFT is extended to the Total Focusing Method (TFM), where the focused image is reconstructed from measurements of all transmit-receive combinations, called Full Matrix Capture (FMC). In previous work, we showed that both SAFT and TFM can be cast as a sparse recovery problem that enables enhancing the Delay-and-Sum scheme to a physically motivated forward model that leads to improved image quality. The reconstruction is performed using l1 minimization. Further, this also allows to perform the reconstruction from compressed/subsampled measurements following compressed sensing theory. This subsampling was achieved by only measuring a subset of the frequency coefficients of the signal. In both the single channel and the multi-channel setup the amount of measurement data is thereby significantly reduced. Additionally, for the TFM, we added a spatial subsampling by only considering a subset of transmit and receive pairs, further reducing the measurement data and at the same time also reducing the measurement time. In our previous work, the frequency and spatial dimensions were considered separately for simplicity, using the same compression strategy for all spatial measurements. In this work we consider joint frequency/spatial compression schemes. We show that a joint multidimensional compression strategy where different Fourier subsets are considered for each channel pair leads to a superior reconstruction performance when the compression rate is fixed. Analysis based on an analytical model for a single defect and a real-world example with multiple defects shows that the approach works in practice.

Coefficient-Shuffled Variable Block Compressed Sensing for Medical Image Compression in Telemedicine Systems.

Medical professionals primarily utilize medical images to detect anomalies within the interior structures and essential organs concealed by the skeletal and dermal layers. The primary purpose of medical imaging is to extract image features for the diagnosis of medical conditions. The processing of these images is indispensable for evaluating a patient's health. However, when monitoring patients over extended periods using specific medical imaging technologies, a substantial volume of data accumulates daily. Consequently, there arises a necessity to compress these data in order to remove duplicates and speed up the process of acquiring data, making it appropriate for effective analysis and transmission. Compressed Sensing (CS) has recently gained widespread acceptance for rapidly compressing images with a reduced number of samples. Ensuring high-quality image reconstruction using conventional CS and block-based CS (BCS) poses a significant challenge since they rely on randomly selected samples. This challenge can be surmounted by adopting a variable BCS approach that selectively samples from diverse regions within an image. In this context, this paper introduces a novel CS method that uses an energy matrix, namely coefficient shuffling variable BCS (CSEM-VBCS), tailored for compressing a variety of medical images with balanced sparsity, thereby achieving a substantial compression ratio and good reconstruction quality. The results of experimental evaluations underscore a remarkable enhancement in the performance metrics of the proposed method when compared to contemporary state-of-the-art techniques. Unlike other approaches, CSEM-VBCS uses coefficient shuffling to prioritize regions of interest, allowing for more effective compression without compromising image quality. This strategy is especially useful in telemedicine, where bandwidth constraints often limit the transmission of high-resolution medical images. By ensuring faster data acquisition and reduced redundancy, CSEM-VBCS significantly enhances the efficiency of remote patient monitoring and diagnosis.

A novel recursive sub-tensor hyperspectral compressive sensing of plant leaves based on multiple arbitrary-shape regions of interest

Plant hyperspectral images (HSIs) contain valuable information for agricultural disaster prediction, biomass estimation, and other applications. However, they also include a lot of irrelevant background information, which wastes storage resources. In this paper, we propose a novel recursive sub-tensor hyperspectral compressive sensing method for plant leaves. This method uses recursive sub-tensor compressive sensing to compress and reconstruct each arbitrary-shape leaf region, discarding a large amount of background information to achieve the best possible reconstruction performance of the leaf region and significantly reduce storage space. The proposed method involves several key steps. Firstly, the optimal band is determined using the spatial spectral decorrelation criterion, and its corresponding mask image is used to extract the leaf regions from the background. Secondly, the recursive maximum inscribed rectangle algorithm is applied to obtain rectangular sub-tensors of leaves recursively. Each sub-tensor is then individually compressed and reconstructed. Finally, all sub-tensors can be reconstructed to form complete leaf HSIs without background information. Experimental results demonstrate that the proposed method achieves superior image reconstruction quality at extremely low sampling rates compared to other methods. The proposed method can improve average Peak Signal-to-Noise Ratio (PSNR) values by about 3.04% and 0.74% compared to Tensor Compressive Sensing (TCS) at the sampling rate of 2%. In the spectral domain, the proposed method can achieve significantly smaller Spectral Angle Mapper (SAM) values and relatively lower spectral indices errors for Double Difference, Triangular Vegetation Index, Leaf Chlorophyll Index, and Modified Normalized Difference 680 than those of TCS. Therefore, the proposed method achieves better compression performance for reconstructed plant leaf HSIs than the other methods.

Interpretable ADMM-CSNet for interrupted sampling repeater jamming suppression

Interrupted sampling repeater jamming (ISRJ) is a category of coherent jamming that greatly influences radars' detection performance. Since the ISRJ has greater power than true targets, ISRJ signals can be removed in the time domain. Due to frequency band loss, grating lobes will be produced if pulse compression (PC) is performed directly, which may generate false targets. Compressive sensing (CS) is an effective method to restore the original PC signal. However, it is challenging for classic CS approaches to manually select the optimization parameters (e.g., penalty parameters, step sizes, etc.) in different ISRJ backgrounds. In this article, a network method based on the Alternating Direction Method of Multipliers (ADMM), named ADMM-CSNet, is introduced to solve the problem. Based on the strong learning capacity of the deep network, all parameters in the ADMM are learned from radar data utilizing back-propagation rather than manually selecting in traditional CS techniques. Compared with classic CS approaches, a higher ISRJ removal signal restoration accuracy is reached faster. Simulation experiments indicate the proposal performs effectively and accurately for ISRJ removal signal reconstruction.

Image Encrypted Using Circular Map, Block Compressed Sensing and Hyper GWO-COOT Optimization

Image Encrypted Using Circular Map, Block Compressed Sensing and Hyper GWO-COOT Optimization

Predictive coding compressive sensing optical coherence tomography hardware implementation.

Compressed sensing (CS) is an approach that enables comprehensive imaging by reducing both imaging time and data density, and is a theory that enables undersampling far below the Nyquist sampling rate and guarantees high-accuracy image recovery. Prior efforts in the literature have focused on demonstrations of synthetic undersampling and reconstructions enabled by compressed sensing. In this paper, we demonstrate the first physical, hardware-based sub-Nyquist sampling with a galvanometer-based OCT system with subsequent reconstruction enabled by compressed sensing. Acquired images of a variety of samples, with volume scanning time reduced by 89% (12.5% compression rate), were successfully reconstructed with relative error (RE) of less than 20% and mean square error (MSE) of around 1%.

New scheme of cooperative compressed spectrum sensing

Abstract This study addresses key challenges in sparse signal recovery and compressed spectrum sensing (CSS), focusing on low signal-to-noise ratios (SNR), and the computational complexity of cooperative systems. Motivated by the need for faster and more accurate recovery techniques, we first investigate and generalize the Reduced-Set Matching Pursuit (RMP) algorithm, which overcomes the speed and accuracy limitations of conventional greedy algorithms. Secondly, we propose a novel spatial averaging technique that enhances detection performance by exploiting data from multiple users to counteract low SNR. Lastly, we integrate cooperation into CSS, further improving the detection capabilities during the recovery process. Compared to existing techniques like Joint Sparse Recovery (JSR) and CoSaMP, which face computational and accuracy constraints in real-time applications, the RMP algorithm, combined with the Virtual method (data transformation) and AND fusion rule, delivers superior performance than JSR methods. Moreover, spatial averaging significantly increases the probability of cooperative detection Q d , with SNR increasing linearly by a factor of L − 1 per channel. The results are validated through the implementation of SDR. These findings demonstrate the potential of RMP and cooperation to overcome current limitations in CSS, advancing the state-of-the-art in spectrum sensing for collaborative networks.

WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing

Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face the following issues: 1) they learn directly from single-channel images, leading to a simple feature representation that does not fully capture complex features; and 2) they treat various image components uniformly, ignoring the characteristics of different components. To address these issues, we propose a novel wavelet-domain deep unfolding framework named WTDUN, which operates directly on the multi-scale wavelet subbands. Our method utilizes the intrinsic sparsity and multi-scale structure of wavelet coefficients to achieve a tree-structured sampling and reconstruction, effectively capturing and highlighting the most important features within images. Specifically, the design of tree-structured reconstruction aims to capture the inter-dependencies among the multi-scale subbands, enabling the identification of both fine and coarse features, which can lead to a marked improvement in reconstruction quality. Furthermore, a wavelet domain adaptive sampling method is proposed to greatly improve the sampling capability, which is realized by assigning measurements to each wavelet subband based on its importance. Unlike pure deep learning methods that treat all components uniformly, our method introduces a targeted focus on important subbands, considering their energy and sparsity. This targeted strategy lets us capture key information more efficiently while discarding less important information, resulting in a more effective and detailed reconstruction. Extensive experimental results on various datasets validate the superior performance of our proposed method.

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

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