Compressive Sensing Research Articles

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.

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.

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%.

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 (PA) and the compressive sensing (CS) for spatial-undersampling 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 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 (BPF) has been observed in this study.

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.

Automatic Compressive Sensing of Shack–Hartmann Sensors Based on the Vision Transformer

Shack–Hartmann wavefront sensors (SHWFSs) are crucial for detecting distortions in adaptive optics systems, but the accuracy of wavefront reconstruction is often hampered by low guide star brightness or strong atmospheric turbulence. This study introduces a new method of using the Vision Transformer model to process image information from SHWFSs. Compared with previous traditional methods, this model can assign a weight value to each subaperture by considering the position and image information of each subaperture of this sensor, and it can process to obtain wavefront reconstruction results. Comparative evaluations using simulated SHWFS light intensity images and corresponding deformable mirror command vectors demonstrate the robustness and accuracy of the Vision Transformer under various guide star magnitudes and atmospheric conditions, compared to convolutional neural networks (CNNs), represented in this study by Residual Neural Network (ResNet), which are widely used by other scholars. Notably, normalization preprocessing significantly improves the CNN performance (improving Strehl ratio by up to 0.2 under low turbulence) while having a varied impact on the Vision Transformer, improving its performance under a low turbulence intensity and high brightness (Strehl ratio up to 0.8) but deteriorating under a high turbulence intensity and low brightness (Strehl ratio reduced to about 0.05). Overall, the Vision Transformer consistently outperforms CNN models across all tested conditions, enhancing the Strehl ratio by an average of 0.2 more than CNNs.

Hybrid Reconstruction Approach for Polychromatic Computed Tomography in Highly Limited-Data Scenarios

Conventional strategies aimed at mitigating beam-hardening artifacts in computed tomography (CT) can be categorized into two main approaches: (1) postprocessing following conventional reconstruction and (2) iterative reconstruction incorporating a beam-hardening model. While the former fails in low-dose and/or limited-data cases, the latter substantially increases computational cost. Although deep learning-based methods have been proposed for several cases of limited-data CT, few works in the literature have dealt with beam-hardening artifacts, and none have addressed the problems caused by randomly selected projections and a highly limited span. We propose the deep learning-based prior image constrained (PICDL) framework, a hybrid method used to yield CT images free from beam-hardening artifacts in different limited-data scenarios based on the combination of a modified version of the Prior Image Constrained Compressed Sensing (PICCS) algorithm that incorporates the L2 norm (L2-PICCS) with a prior image generated from a preliminary FDK reconstruction with a deep learning (DL) algorithm. The model is based on a modification of the U-Net architecture, incorporating ResNet-34 as a replacement of the original encoder. Evaluation with rodent head studies in a small-animal CT scanner showed that the proposed method was able to correct beam-hardening artifacts, recover patient contours, and compensate streak and deformation artifacts in scenarios with a limited span and a limited number of projections randomly selected. Hallucinations present in the prior image caused by the deep learning model were eliminated, while the target information was effectively recovered by the L2-PICCS algorithm.

Compressed sensing with smooth L0 constraints for moving force identification from bridge response measurements

Abstract Compressed sensing (CS), as an emerging information sampling technique, has been successfully applied in the field of moving force identification (MFI). However, existing MFI CS models often fail to obtain the optimal sparse solutions and frequently underestimate the amplitude of local impact forces. To effectively address this issue, a new CS method is proposed for MFI based on smooth L0 norm constraints and bridge response measurements. Firstly, a smooth function is used to approximate the L0 norm, establishing a noise CS reconstruction model for MFI. The introduction of the smoothing function can locally convexify the original MFI problem and enhance the smoothness and differentiability of the objective function, making the optimization problem easier to solve. Subsequently, the Polak–Ribiere–Polyak formula is adopted to point the descent direction of the new objective function, and the sparse solution is iteratively advanced through the conjugate gradient algorithm. Finally, the applicability and feasibility of the proposed method is confirmed by numerical simulations and vehicle–bridge interaction tests, respectively. The results show that the proposed method can accurately identify moving forces from limited measurements of bridge responses. Compared with existing methods, it can provide more precise sparse solutions with higher robustness to measurement noises, and address the issue of underestimating on the amplitude of local impact forces, which is expected to enhance the performance and in-situ applicability of MFI.

Research on the energy absorption performance of lattice filling structures based on homogenization analysis technique

The lattice structure has great application prospects in the field of energy absorption, but the high cost of numerical analysis makes it difficult to carry out related structural designs. Therefore, this article studies the feasibility of the homogenization analysis technique for the analysis of energy absorption processes in lattice-filled structures. In the study, compression experiments and numerical simulations were conducted for four different types of unit cells (including periodic truss-lattice cells and triply periodic minimal surface (TPMS cells). In the experiments, two compression samples with different numbers of periods were designed for the same unit cell structure. The research shows that the homogenized numerical model takes a lot less time to run than the classical beam and shell element models. The results of the simulation are also in line with the data from the experiments. On the other hand, the material curve constructed based on a small number of unit cell samples has excellent analytical accuracy. This means that relevant research can obtain the material experimental data required for homogenized analysis using lattice samples with low manufacturing costs. Understanding these phenomena can provide a basis for the design of energy absorption structures.

An adaptive parameter decoupling algorithm-based image reconstruction model (ADAIR) for rapid golden-angle radial DCE-MRI

Objective. The acceleration of magnetic resonance imaging (MRI) acquisition is crucial for both clinical and research applications, particularly in dynamic MRI. Existing compressed sensing (CS) methods, despite being effective for fast imaging, face limitations such as the need for incoherent sampling and residual noise, which restrict their practical use for rapid MRI.Approach. To overcome these challenges, we propose a novel image reconstruction framework that integrates the MRI physical model with a flexible, self-adjusting, decoupling data-driven model. We validated this method through experiments using both simulated andin vivodynamic contrast-enhanced MRI datasets.Main results. The experimental results demonstrate that the proposed framework achieves high spatial and temporal resolution reconstructions. Additionally, when compared to state-of-the-art image reconstruction approaches, our method significantly enhances acceleration capabilities, enabling sparse and rapid imaging with high resolution.Significance. Our proposed framework offers a promising solution for real-time imaging and image-guided radiation therapy applications by providing superior performance in achieving high spatial and temporal resolution reconstructions, thus addressing the limitations of existing CS schemes.

Channel estimation via compressed sampling matching pursuit for hybrid MIMO architectures in millimeter wave communication

ABSTRACT In recent times, there are considerable research efforts in utilising millimetre wave cellular system for meeting rising mobile traffic volume and escalating data rate demand. In this regard, several analytical models have been developed for obtaining Channel State Information (CSI) for the design of combiner and precoder architectures for millimetre wave communication. One prominent method that has caught the attention of most researchers is the Orthogonal Matching Pursuit (OMP) which performs poorly in noisy condition. As a result, this work introduces Compressed Sampling Matching Pursuit (CoSAMP) as alternative to OMP for obtaining CSI for the design of hybrid combiner. A comparative analysis of all the cases examined reveals that CoSAMP surpasses OMP and Least Square (LS) across SNR range of −30 dB to −10 dB, recording lowest Normalized Mean Square Error (NMSE), highest Spectral Efficiency (SE) and bit rate. For instance at −20 dB, NMSE of CoSAMP exhibits 95% and 86% gain over LS and OMP, respectively while SE and bit rate of CoSAMP are better than OMP and LS by 21% and 91%, respectively. It is therefore seen that CoSAMP is a better technique for estimating CSI and for combiner design in such condition.

ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} norm

The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

Exploiting Compress Sensing in Training of Deep Neural Network for Self-Noise Cancellation in Underwater Acoustics

Exploiting Compress Sensing in Training of Deep Neural Network for Self-Noise Cancellation in Underwater Acoustics