Compressive Sensing Framework Research Articles

An adaptive compressive sensing method on hybrid-field channel estimation for a massive MIMO system

Massive MIMO (Multiple-input-multiple output), crucial for 5 G and Beyond 5 G (B5G) networks, faces challenges with terahertz frequencies in B5G as the communication shifts from far-field to near-field. This shift disrupts traditional Massive MIMO channel estimation, leading to increased pilot overhead and limited performance. The current study used the hybrid-field orthogonal matching pursuit (HF-OMP) algorithm from the compressive sensing (CS) framework to estimate the channel with scatters from both far-field and near-field. The method, however, needs more flexibility regarding scatter location in the field of interest. Also, the usage of HF-OMP under a single measurement vector (SMV) scheme limits the overall performance of the existing method. To address these, we have proposed an adaptive hybrid-field simultaneous-OMP algorithm under multiple measurement vector (MMV) of the CS framework which selects multiple atoms having common support within a single iteration. This innovative approach tackles channel estimation for both far-field and near-field scatters while adapting to their varying distributions. Compared to classical methods, simulations show the new algorithm achieves up to a 14 % improvement in normalized mean square error within a 0 dB to 10 dB signal-to-noise ratio range. This translates to significant reductions in pilot overhead and enhanced channel reliability, paving the way for more efficient and robust wireless networks in the future.

LD-CSNet: A latent diffusion-based architecture for perceptual Compressed Sensing

Compressed Sensing (CS) is a groundbreaking paradigm in image acquisition, challenging the constraints of the Nyquist–Shannon sampling theorem. This enables high-quality image reconstruction using a minimal number of measurements. Neural Networks’ potent feature induction capabilities enable advanced data-driven CS methods to achieve high-fidelity image reconstruction. However, achieving satisfactory reconstruction performance, particularly in terms of perceptual quality, remains challenging at extremely low sampling rates. To tackle this challenge, we introduce a novel two-stage image CS framework based on latent diffusion, named LD-CSNet. In the first stage, we utilize an autoencoder pre-trained on a large dataset to represent natural images as low-dimensional latent vectors, establishing prior knowledge distinct from sparsity and effectively reducing the dimensionality of the solution space. In the second stage, we employ a conditional diffusion model for maximum likelihood estimates in the latent space. This is supported by a measurement embedding module designed to encode measurements, making them suitable for a denoising network. This guides the generation process in reconstructing low-dimensional latent vectors. Finally, the image is reconstructed using a pre-trained decoder. Experimental results across multiple public datasets demonstrate LD-CSNet’s superior perceptual quality and robustness to noise. It maintains fidelity and visual quality at lower sampling rates. Research findings suggest the promising application of diffusion models in image CS. Future research can focus on developing more appropriate models for the first stage.

Computer-Vision-Oriented Adaptive Sampling in Compressive Sensing.

Compressive sensing (CS) is recognized for its adeptness at compressing signals, making it a pivotal technology in the context of sensor data acquisition. With the proliferation of image data in Internet of Things (IoT) systems, CS is expected to reduce the transmission cost of signals captured by various sensor devices. However, the quality of CS-reconstructed signals inevitably degrades as the sampling rate decreases, which poses a challenge in terms of the inference accuracy in downstream computer vision (CV) tasks. This limitation imposes an obstacle to the real-world application of existing CS techniques, especially for reducing transmission costs in sensor-rich environments. In response to this challenge, this paper contributes a CV-oriented adaptive CS framework based on saliency detection to the field of sensing technology that enables sensor systems to intelligently prioritize and transmit the most relevant data. Unlike existing CS techniques, the proposal prioritizes the accuracy of reconstructed images for CV purposes, not only for visual quality. The primary objective of this proposal is to enhance the preservation of information critical for CV tasks while optimizing the utilization of sensor data. This work conducts experiments on various realistic scenario datasets collected by real sensor devices. Experimental results demonstrate superior performance compared to existing CS sampling techniques across the STL10, Intel, and Imagenette datasets for classification and KITTI for object detection. Compared with the baseline uniform sampling technique, the average classification accuracy shows a maximum improvement of 26.23%, 11.69%, and 18.25%, respectively, at specific sampling rates. In addition, even at very low sampling rates, the proposal is demonstrated to be robust in terms of classification and detection as compared to state-of-the-art CS techniques. This ensures essential information for CV tasks is retained, improving the efficacy of sensor-based data acquisition systems.

Enhanced hydrofoil pressure field reconstruction through phase-informed sensing and sensor optimization

This study proposes a cost-effective mixed-learning method for the cavitation behavior on hydrofoils, aiming to predict the global pressure field on the hydrofoil surface with sparse placed pressure sensors and the variation of the cavity outline captured by the high-speed cameras. The method integrates CS (compressed sensing) and deep learning techniques. Firstly, within the framework of CS, the Particle Swarm Optimization (PSO) algorithm is utilized to identify the best measuring points and achieve the initial reconstruction accordingly. Subsequently, in combination with the phase information, the final reconstructions are obtained within the deep learning framework. Through validation, the proposed mixed-learning model demonstrates significantly improved reconstruction performance compared to a single source of pressure information and an unoptimized measurement point position and significantly reduces the number of sensors. This provides a novel and effective approach for accurately predicting the pressure field on hydrofoil surfaces. Furthermore, the study evaluates the robustness concerning hydraulic sensor measurement errors, sensor placement deviations, missing measuring points, reconstruction performance under various cases and hydrofoil surface regions, and the contribution of optimized measuring points to the global field. Results show that the mixed-learning model exhibits robustness against typical measurement errors, position deviations of hydraulic sensors and missing measuring points on the suction side. Additionally, a positive correlation exists between the average pressure gradient under different conditions and regions and the reconstruction error, with the pressure side region significantly contributing to global field reconstruction. These findings underscore the mixed model's superiority in predicting pressure fields on hydrofoils and offer guidance for rational sensor installation.

Compressive sensing ISAR imaging with low-rank constraint and anisotropic spatial total variation processing

In order to suppress random noise and remove stripe interference in ISAR imaging, a Compressive Sensing method is proposed for super-resolution ISAR imaging in this paper, which is named LR-ASTV (Low-rank and Anisotropic Spatial Total Variation) algorithm here. In this algorithm, the original echo HRRP is transformed into echo HRRP of MMV model with radial interpolation processing at first. Subsequently, an optimization objective function based on Compressive Sensing framework is formulated which includes the sparsity constraint and low-rank constraint, and this optimization problem is solved by JLRS algorithm to generate an initial ISAR image from which the random noise has been eliminated. The initial image is then subjected to further refinement using the Anisotropic Spatial Total Variation (ASTV) processing, ultimately yielding the final ISAR image with stripe interference removed. To validate the effectiveness of the LR-ASTV algorithm, ISAR imaging experiments based on simulated and measured data at different SNRs are completed, and the imaging results of the LR-ASTV algorithm are compared with those of other three algorithms including the LSM-ME2 algorithm, the JLRS algorithm and the LRPB algorithm. It can be found that the LR-ASTV algorithm has obvious superiority in suppressing random noise and removing stripe interference, and can provide ISAR images of higher clarity. The quality evaluation for ISAR images also shows that the LR-ASTV algorithm has lower image entropy index and higher image contrast index than the other three ISAR imaging algorithms.

0.36 μW/channel capacitively-coupled chopper instrumentation amplifier in EEG recording wearable devices for compressed sensing framework

We evaluated the effectiveness of a low-current-consumption amplifier for a compressed-sensing (CS) framework in wearable electroencephalography (EEG) recording devices. The amplifier uses a capacitively coupled chopper instrumentation amplifier (CCIA) architecture which is often used for low-noise amplifier (LNA) to achieve low consumption and low-noise characteristics. According to measurements of the designed CCIA, the power consumption was 0.36 μW/channel, and the input referred noise (IRN) was 4.47 μVrms. The measured IRN and simulations were used to confirm the effect of CCIA noise on the CS-based EEG measurement framework. The difference in the normalized mean squared error at CR = 4 to the uncompressed conditions could be reduced to 0.008. The findings show that even with the LNA specialized for low power consumption, a slight signal degradation is observed when the compression ratio is increased up to 4 in the CS framework by utilizing the sparsity of EEG in the frequency domain.

The Optimally Designed Deep Autoencoder-Based Compressive Sensing Framework for 1D and 2D Signals

The Optimally Designed Deep Autoencoder-Based Compressive Sensing Framework for 1D and 2D Signals

A Wavelet-Domain Consistency-Constrained Compressive Sensing Framework Based on Memory-Boosted Guidance Filtering

A Wavelet-Domain Consistency-Constrained Compressive Sensing Framework Based on Memory-Boosted Guidance Filtering

Multidimensional compressed sensing to advance 23 Na multi-quantum coherences MRI.

Sodium (23 Na) multi-quantum coherences (MQC) MRI was accelerated using three-dimensional (3D) and a dedicated five-dimensional (5D) compressed sensing (CS) framework for simultaneous Cartesian single (SQ) and triple quantum (TQ) sodium imaging of in vivo human brain at 3.0 and 7.0 T. 3D 23 Na MQC MRI requires multi-echo paired with phase-cycling and exhibits thus a multidimensional space. A joint reconstruction framework to exploit the sparsity in all imaging dimensions by extending the conventional 3D CS framework to 5D was developed. 3D MQC images of simulated brain, phantom and healthy brain volunteers obtained from 3.0 T and 7.0 T were retrospectively and prospectively undersampled. Performance of the CS models were analyzed by means of structural similarity index (SSIM), root mean squared error (RMSE), signal-to-noise ratio (SNR) and signal quantification of tissue sodium concentration and TQ/SQ ratio. It was shown that an acceleration of three-fold, leading to less than min of scan time with a resolution of at 3.0 T, are possible. 5D CS improved SSIM by 3%, 5%, 1% and reduced RMSE by 50%, 30%, 8% for in vivo SQ, TQ, and TQ/SQ ratio maps, respectively. Furthermore, for the first time prospective undersampling enabled unprecedented high resolution from to MQC images of in vivo human brain at 7.0 T without extending acquisition time. 5D CS proved to allow up to three-fold acceleration retrospectively on 3.0 T data. 2-fold acceleration was demonstrated prospectively at 7.0 T to reach higher spatial resolution of 23 Na MQC MRI.

Compressed sensing framework for BCG signals based on the optical fiber sensor.

A compressed sensing (CS) framework is built for ballistocardiography (BCG) signals, which contains two parts of an optical fiber sensor-based heart monitoring system with a CS module and an end-to-end deep learning-based reconstruction algorithm. The heart monitoring system collects BCG data, and then compresses and transmits the data through the CS module at the sensing end. The deep learning-based algorithm reconstructs compressed data at the received end. To evaluate results, three traditional CS reconstruction algorithms and a deep learning method are adopted as references to reconstruct the compressed BCG data with different compression ratios (CRs). Results show that our framework can reconstruct signals successfully when the CR grows from 50% to 95% and outperforms other methods at high CRs. The mean absolute error (MAE) of the estimated heartbeat rate (HR) is lower than 1 bpm when the CR is below 95%. The proposed CS framework for BCG signals can be integrated into the IoMT system, which has great potential in health care for both medical and home use.

An efficient optimization of measurement matrix for compressive sensing

Compressive sensing (CS) is a new paradigm for signal acquisition and reconstruction, which can reconstruct the signal at less than the Nyquist sampling rate. The sampling of the signal occurs through a measurement matrix (MM); thus, MM generation is significant in the context of the CS framework. In this paper, an optimization algorithm is introduced for the generation of the MM of CS based on Restricted Isometric Property (RIP) mandates that eigenvalues of the sensing matrix fall within an interval also minimizes the mutual coherence of the sensing matrix (i.e. the product of the MM and sparsifying matrix). A novel gradient-based iterative optimization method is used to reduce the eigenvalues of the sensing matrix by SVD decomposition. Meanwhile, the proposed algorithm can also reduce the operational complexity. Experimental results and analysis prove that the optimized MM reduces the maximum mutual and average mutual coherence between the MM and the sparsifying basis, which shows the effectiveness of the proposed algorithm over some state-of-art works.

Active 3D Double-RIS-Aided Multi-User Communications: Two-Timescale-Based Separate Channel Estimation via Bayesian Learning

Double-reconfigurable intelligent surface (RIS) is a promising technique, achieving a substantial gain improvement compared to single-RIS techniques. However, in double-RIS-aided systems, accurate channel estimation is more challenging than in single-RIS-aided systems. This work solves the problem of double-RIS-based channel estimation based on active RIS architectures with only one radio frequency (RF) chain. Since the slow time-varying channels, i.e., the BS-RIS 1, BS-RIS 2, and RIS 1-RIS 2 channels, can be obtained with active RIS architectures, a novel multi-user two-timescale channel estimation protocol is proposed to minimize the pilot overhead. First, we propose an uplink training scheme for slow time-varying channel estimation, which can effectively address the double-reflection channel estimation problem. With channels’ sparisty, a low-complexity Singular Value Decomposition Multiple Measurement Vector-Based Compressive Sensing (SVD-MMV-CS) framework with the line-of-sight (LoS)-aided off-grid MMV expectation maximization-based generalized approximate message passing (M-EM-GAMP) algorithm is proposed for channel parameter recovery. For fast time-varying channel estimation, based on the estimated large-timescale channels, a measurements-augmentation-estimate (MAE) framework is developed to decrease the pilot overhead. Additionally, a comprehensive analysis of pilot overhead and computing complexity is conducted. Finally, the simulation results demonstrate the effectiveness of our proposed multi-user two-timescale estimation strategy and the low-complexity Bayesian CS framework.

Revisiting Model Order Selection: A Sub-Nyquist Sampling Blind Spectrum Sensing Scheme

Wideband spectrum sensing based on sub-Nyquist sampling is an attractive approach to advance dynamic spectrum sharing (DSS), which can improve frequency resource utilization while overcoming sampling bottlenecks. Under the Compressive Sensing (CS) framework, finding occupied subbands can be equivalent to computing the support set for the Multiple Measurement Vectors (MMV) problem. To guarantee the performance of joint support recovery in noisy environments, different kinds of prior information are required, one of which is sparsity, a time-varying parameter. To address the dependence of recovery performance on signal sparsity, this paper proposed a two-step scheme for blind wideband spectrum sensing using a Modulated Wideband Converter (MWC) sub-Nyquist sampling front-end. The scheme first adopts the model order selection (MOS) method to estimate sparsity from the compressed covariance matrix, and then uses the estimates to dynamically adjust joint support recovery. The complete theoretical derivation innovatively applies MOS to sub-Nyquist sampling and presents a design method for MOS penalty constant. Extensive simulation results show that the proposed scheme can not only achieve blind sensing under the spectrum occupancy up to 40%, reduce the overall computational complexity of iterative SOMP, but also significantly improve the false alarm performance, meeting the requirements of the IEEE 802.22 standard.

Capsule networks embedded with prior known support information for image reconstruction

Compressed sensing (CS) has been successfully applied to realize image reconstruction. Neural networks have been introduced to the CS of images to exploit the prior known support information, which can improve the reconstruction quality. Capsule Network (Caps Net) is the latest achievement in neural networks, and can well represent the instantiation parameters of a specific type of entity or part of an object. This study aims to propose a Caps Net with a novel dynamic routing to embed the information within the CS framework. The output of the network represents the probability that the index of the nonzero entry exists on the support of the signal of interest. To lead the dynamic routing to the most likely index, a group of prediction vectors is designed determined by the information. Furthermore, the results of experiments on imaging signals are taken for a comparation of the performances among different algorithms. It is concluded that the proposed capsule network (Caps Net) creates higher reconstruction quality at nearly the same time with traditional Caps Net.

Design of Robust Sensing Matrix for UAV Images Encryption and Compression

The sparse representation error (SRE) exists when the images are represented sparsely. The SRE is particularly large in unmanned aerial vehicles (UAV) images due to the disturbance of the harsh environment or the instability of its flight, which will bring more noise. In the compressed sensing (CS) system, the projected SRE in the compressed measurement will bring a significant challenge to the recovery accuracy of the images. In this work, a new SRE structure is proposed. Following the new structure, a lower sparse representation error (LSRE) is achieved by eliminating groups of sparse representation. With the proposed LSRE modeling, a robust sensing matrix is designed to compress and encrypt the UAV images. Experiments for UAV images are carried out to compare the recovery performance of the proposed algorithm with the existing related algorithms. The results of the proposed algorithm reveal superior recovery accuracy. The new CS framework with the proposed sensing matrix to address the scenario of UAV images with large SRE is dominant.

Sparse Reconstruction Using Hyperbolic Tangent as Smooth l1-Norm Approximation

In the Compressed Sensing (CS) framework, the underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find the sparsest possible solution, which is l0-norm minimization. However, finding an l0 norm solution out of infinitely many possible solutions is NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact that l0 norm penalty can be adequately estimated by l1 norm, which recasts a non-convex minimization problem to a convex problem. However, l1 norm non-differentiable and gradient-based minimization algorithms are not applicable, due to this very reason there is a need to approximate l1 norm by its smooth approximation. Iterative shrinkage algorithms provide an efficient method to numerically minimize l1-regularized least square optimization problem. These algorithms are required to induce sparsity in their solutions to meet the CS recovery requirement. In this research article, we have developed a novel recovery method that uses hyperbolic tangent function to recover undersampled signal/images in CS framework. In our work, l1 norm and soft thresholding are both approximated with the hyperbolic tangent functions. We have also proposed the criteria to tune optimization parameters to get optimal results. The error bounds for the proposed l1 norm approximation are evaluated. To evaluate performance of our proposed method, we have utilized a dataset comprised of 1-D sparse signal, compressively sampled MR image and cardiac cine MRI. The MRI is an important imaging modality for assessing cardiac vascular function. It provides the ejection fraction and cardiac output of the heart. However, this advantage comes at the cost of a slow acquisition process. Hence, it is essential to speed up the acquisition process to take the full benefits of cardiac cine MRI. Numerical results based on performance metrics, such as Structural Similarity (SSIM), Peak Signal to Noise Ratio (PSNR) and Root Mean Square Error (RMSE) show that the proposed tangent hyperbolic based CS recovery offers a much better performance as compared to the traditional Iterative Soft Thresholding (IST) recovery methods.

From Patch to Pixel: A Transformer-Based Hierarchical Framework for Compressive Image Sensing

The convolutional neural network (CNN)-based reconstruction methods have dominated the compressive sensing (CS) in recent years. However, existing CNN-based approaches show potential restrictions in capturing non-local similarity of images, because of the intrinsic characteristic of convolutional layers, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathit{i.e.}$</tex-math></inline-formula> , locality and weight sharing. In parallel, the emerging Transformer architecture shows fine capacity in modeling long-distance correlations onto embedded tokens for language and images. Yet vanilla Transformer does not exceed CNN-based networks considerably but shows roughly comparable performance, and the culprit can be the missing of sophisticated inductive bias regarding the local image structures. In this article, to eliminate the restrictions of the aforementioned paradigms, we propose a Transformer-based hierarchical framework, dubbed TCS-Net, for compressive image sensing (or image compressive sensing) with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathit{patch-to-pixel}$</tex-math></inline-formula> manner. Concretely, the proposed TCS-Net consists of an image acquisition module and a reconstruction module (includes two key decoding phases: a patch-wise decoding phase and a pixel-wise decoding phase). The acquisition module can implement data-driven image sampling by jointly learning with the decoding phases. By adjusting the Transformer architecture to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathit{patch-to-pixel}$</tex-math></inline-formula> multi-stage pattern, our reconstruction module can gradually decode the CS measurements from the patch-wise outlines to the pixel-wise textures, thereby building a high-precision mapping for image reconstruction. Extensive experiments on several datasets verify that the proposed TCS-Net outperforms existing state-of-the-art image CS methods by considerable margins.

ECG Signals Deep Compressive Sensing Framework Based on Multiscale Feature Fusion and SE Block

ECG Signals Deep Compressive Sensing Framework Based on Multiscale Feature Fusion and SE Block

Image Compressed Sensing Using Non-Local Neural Network

Deep network-based image Compressed Sensing (CS) has attracted much attention in recent years. However, the existing deep network-based CS schemes either reconstruct the target image in a block-by-block manner that leads to serious block artifacts or train the deep network as a black box that brings about limited insights of image prior knowledge. In this paper, a novel image CS framework using non-local neural network (NL-CSNet) is proposed, which utilizes the non-local self-similarity priors with deep network to improve the reconstruction quality. In the proposed NL-CSNet, two non-local subnetworks are constructed for utilizing the non-local self-similarity priors in the measurement domain and the multi-scale feature domain respectively. Specifically, in the subnetwork of measurement domain, the long-distance dependencies between the measurements of different image blocks are established for better initial reconstruction. Analogically, in the subnetwork of multi-scale feature domain, the affinities between the dense feature representations are explored in the multi-scale space for deep reconstruction. Furthermore, a novel loss function is developed to enhance the coupling between the non-local representations, which also enables an end-to-end training of NL-CSNet. Extensive experiments manifest that NL-CSNet outperforms existing state-of-the-art CS methods, while maintaining fast computational speed.

Physics-Guided Real-Time Full-Field Vibration Response Estimation from Sparse Measurements Using Compressive Sensing.

In civil, mechanical, and aerospace structures, full-field measurement has become necessary to estimate the precise location of precise damage and controlling purposes. Conventional full-field sensing requires dense installation of contact-based sensors, which is uneconomical and mostly impractical in a real-life scenario. Recent developments in computer vision-based measurement instruments have the ability to measure full-field responses, but implementation for long-term sensing could be impractical and sometimes uneconomical. To circumvent this issue, in this paper, we propose a technique to accurately estimate the full-field responses of the structural system from a few contact/non-contact sensors randomly placed on the system. We adopt the Compressive Sensing technique in the spatial domain to estimate the full-field spatial vibration profile from the few actual sensors placed on the structure for a particular time instant, and executing this procedure repeatedly for all the temporal instances will result in real-time estimation of full-field response. The basis function in the Compressive Sensing framework is obtained from the closed-form solution of the generalized partial differential equation of the system; hence, partial knowledge of the system/model dynamics is needed, which makes this framework physics-guided. The accuracy of reconstruction in the proposed full-field sensing method demonstrates significant potential in the domain of health monitoring and control of civil, mechanical, and aerospace engineering systems.