Compressed Sensing Reconstruction Algorithm Research Articles

An ISAR Imaging Method Based on Improved CAMP Algorithm

Compressed sensing (CS) provides a new idea for inverse synthetic aperture radar (ISAR) imaging. Complex approximate message passing (CAMP) algorithm, as a new CS reconstruction algorithm, has characteristics of fast convergence and good reconstruction, which is suitable for ISAR imaging. However, the off-grid problem is inevitable in ISAR imaging, which affects the reconstruction performance seriously and needs to be solved urgently. To solve the off-grid problem, a parametric CS ISAR imaging model is built in this paper, in which the off-grid is considered as an unknown parameter. To solve the joint optimization problem efficiently, first-order Taylor series approximation is used and the optimization problem is transformed into two least squares problems. To verify the effectiveness of the proposed method, it is applied into random sparse signals, complex sinusoids, quasi-real ISAR data and real ISAR data. Compared with the existing algorithms, the proposed method has got higher reconstruction signal-to-noise ratio (RSNR), smaller relative reconstruction error, smaller frequency position error and better imaging result. Therefore the proposed method is an effective CS ISAR imaging method which can solve the off-grid problem well.

A Task-Driven Invertible Projection Matrix Learning Algorithm for Hyperspectral Compressed Sensing

The high complexity of the reconstruction algorithm is the main bottleneck of the hyperspectral image (HSI) compression technology based on compressed sensing. Compressed sensing technology is an important tool for retrieving the maximum number of HSI scenes on the ground. However, the complexity of the compressed sensing algorithm is limited by the energy and hardware of spaceborne equipment. Aiming at the high complexity of compressed sensing reconstruction algorithm and low reconstruction accuracy, an equivalent model of the invertible transformation is theoretically derived by us in the paper, which can convert the complex invertible projection training model into the coupled dictionary training model. Besides, aiming at the invertible projection training model, the most competitive task-driven invertible projection matrix learning algorithm (TIPML) is proposed. In TIPML, we don’t need to directly train the complex invertible projection model, but indirectly train the invertible projection model through the training of the coupled dictionary. In order to improve the accuracy of reconstructed data, in the paper, the singular value transformation is proposed. It has been verified that the concentration of the dictionary is increased and that the expressive ability of the dictionary has not been reduced by the transformation. Besides, two-loop iterative training is established to improve the accuracy of data reconstruction. Experiments show that, compared with the traditional compressed sensing algorithm, the compressed sensing algorithm based on TIPML has higher reconstruction accuracy, and the reconstruction time is shortened by more than a hundred times. It is foreseeable that the TIPML algorithm will have a huge application prospect in the field of HSI compression.

Application of ultrasound molecular imaging based on compressed sensing reconstruction algorithm to phase change drug-loaded PLGA nanoparticles targeting breast cancer MCF-7 Cells.

Objectives:To study the ability of aptamer-modified nano-gold rods and liquid carbon-targeted PLGA nanoparticles to target in vitro using compressed sensing reconstruction algorithm, and observe the phenomenon of mediating ultrasound / photoacoustic imaging.Methods:PLGA nanoparticles were prepared by a double emulsification method, and the MUC1 aptamer was connected to the PLGA nanoparticles by the carbodiimide method to obtain an “aptamer-PLGA nanoparticle” targeted phase change contrast agent. Fluorescence microscopy was used to detect the in vitro targeting of breast cancer MCF-7 cells specifically identified by it, and three control groups were set up: the ordinary nanoparticle group, the aptamer interference group, and the HELA cell group. A photoacoustic instrument was used to observe the phenomenon of enhanced ultrasound / photoacoustic signal mediated in vitro.Results:Many targeted nanoparticles were clustered around MCF-7 cells and bound firmly, but no specific binding was observed in the non-targeted nanoparticles group, the aptamer interference group and the HELA cell group. After the targeted nanoparticle was excited by the photoacoustic instrument, the ultrasonic signal and the photoacoustic signal were significantly enhanced compared with before the excitation.Conclusion:The successfully prepared targeting nanoparticles have good targeting and specificity for breast cancer MCF-7 cells, and it has obvious effects on ultrasound / photoacoustic imaging, and has the potential to become a dual-mode ultrasound / photoacoustic targeted contrast agent. The various characteristics provide experimental basis for subsequent in vivo targeting experiments and are expected to become good target diagnostic molecular probes.

Hadamard Ghost Imaging Based on Compressed Sensing Reconstruction Algorithm

Hadamard Ghost Imaging Based on Compressed Sensing Reconstruction Algorithm

Downward-Looking Linear Array Three-Dimensional SAR Imaging Based on the Two-Dimensional Mismatch Compensation

For downward-looking linear array (DLLA) three-dimensional (3-D) synthetic aperture radar (SAR), it is necessary to realize the super-resolution in both azimuth and cross-track direction due to the limited lengths of the synthetic aperture and the linear array. As all the scatterers are assumed on the uniform grids, the cross-track super-resolution can be achieved by 1-D compressed sensing. In the real imaging system, however, the gridding error should be considered because the biased scatterers lead to the mismatch of the measurement matrix and affect the imaging performance. The 1-D mismatch in cross-track direction has been solved by atomic norm minimization and off-grid sparse Bayesian inference. With the development of the super-resolution methods, the 2-D super-resolution in both azimuth and cross-track direction is realized by the 2-D compressed sensing (CS) algorithms. To solve the 2-D mismatch problem, a novel 2-D mismatch compensation method for DLLA 3-D SAR is proposed. Instead of converting the 2-D matrix signals to the 1-D vectors, the proposed method directly processes the 2-D mismatch with 2-D joint model. Furthermore, the 2-D joint model with 2-D mismatch is simplified as a normal sparse linear model, which is suitable for most of the CS reconstruction algorithms. It can not only provide better reconstruction performance but also reduce the memory cost and computation load. Finally, the simulation experiments are shown to demonstrate the validity of the proposed method.

Analyzing cross-validation in compressed sensing with Poisson noise

In many compressive sensing reconstruction algorithms, a good choice of important parameters such as the optimal number of measurements (which is dependent upon the unknown signal sparsity) or the regularization parameter, is critical for successful signal recovery. Cross-validation provides a principled method of doing so, by dividing the measurements into a ‘reconstruction set’ to recover the signal given each candidate parameter value, and a ‘cross-validation set’ to determine in a purely data-driven manner as to which candidate parameter value is optimal. In previous work, such a technique has been theoretically analyzed for the case of noiseless compressive measurements or for the case of additive i.i.d. Gaussian noise in the measurements. This paper presents the first theoretical analysis of this technique for compressed sensing when the measurements are corrupted by Poisson noise, the dominant noise distribution in optical systems. Using two different methods, we present different types of theoretical bounds in the form of confidence intervals on the actual (unobservable) recovery error in terms of the (observable) cross-validation error. We show in particular that these bounds become tighter with increase in the underlying signal intensity or number of cross-validation measurements (if other factors are held constant). We validate our theoretical bounds with simulations and experimental results for Poisson compressed sensing with the widely used Lasso estimator.

Research on mechanical vibration monitoring based on wireless sensor network and sparse Bayes

Mechanical vibration monitoring for rotating mechanical equipment can improve the safety and reliability of the equipment. The traditional wired monitoring technology faces problems such as high-frequency signal pickup and high-precision data collection. Therefore, this paper proposes optimization techniques for mechanical vibration monitoring and signal processing based on wireless sensor networks. First, the hardware design uses high-performance STM32 as the control center and Si4463 as the wireless transceiver core. The monitoring node uses a high-precision MEMS acceleration sensor with a 16-bit resolution ADC acquisition chip to achieve high-frequency, high-precision acquisition of vibration signals. Then, the bearing vibration signal optimization method is studied, and the sparse Bayes algorithm is proposed as a compressed sensing reconstruction algorithm. Finally, the difference in reconstruction accuracy between this method and the traditional reconstruction algorithm is compared through experiments and the effect of this method on the reconstruction performance is analyzed when different parameters are selected.

Iterative Selection and Correction Based Adaptive Greedy Algorithm for Compressive Sensing Reconstruction

Compressive sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. Therefore in this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward–Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms, as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. To evaluate the AFB’s reconstruction performance, we used two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward–Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.

Far-field acoustic subwavelength imaging with structured illumination

In the past decade, subwavelength imaging technologies have attracted a lot of interest for breaking the diffraction limit. While localization-based methods are able to image isolated subwavelength objects, differentiating objects with subwavelength distances in the far field is still challenging. To solve this problem, it has been proposed in optical microscopy to exploit structured or blind structured illumination, where the spatial frequency mixing between the objects and the illumination converts evanescent waves to propagating waves that can reach far field. Here, we propose an acoustic analogy and demonstrate a framework, both theoretically and experimentally, for performing far-field acoustic subwavelength imaging using structured illumination generated by scattering media with subwavelength features. A scattering medium is placed behind subwavelength objects. The excitation wave is first diffracted by the scattering medium before it further passes through the objects and reaches the receiver in the far field. By utilizing a compressive sensing reconstruction algorithm, the image of the objects can be reconstructed with multiple measurements that are obtained by shifting or rotating the scattering medium. The proposed framework has great potential in medical imaging, non-destructive testing, and underwater acoustic imaging for improving imaging resolution of objects far away from the sensors.

100,000 frames-per-second compressive imaging with a conventional rolling-shutter camera by random point-spread-function engineering.

We demonstrate an approach that allows taking videos at very high frame-rates of over 100,000 frames per second by exploiting the fast sampling rate of the standard rolling-shutter readout mechanism, common to most conventional sensors, and a compressive-sampling acquisition scheme. Our approach is directly applied to a conventional imaging system by the simple addition of a diffuser to the pupil plane that randomly encodes the entire field-of-view to each camera row, while maintaining diffraction-limited resolution. A short video is reconstructed from a single camera frame via a compressed-sensing reconstruction algorithm, exploiting the inherent sparsity of the imaged scene.

Deep Unfolding With Weighted ℓ₂ Minimization for Compressive Sensing

Compressive sensing (CS) aims to accurately reconstruct high-dimensional signals from a small number of measurements by exploiting signal sparsity and structural priors. However, signal priors utilized in existing CS reconstruction algorithms rely mainly on hand-crafted design, which often cannot offer the best sparsity-undersampling tradeoff because high-order structural priors of signals are hard to be captured in this manner. In this article, a new recovery guarantee of the unified CS reconstruction model-weighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization (WL1M) is derived, which indicates universal priors could hardly lead to the optimal selection of the weights. Motivated by the analysis, we propose a deep unfolding network for the general WL1M model. The proposed deep unfolding-based WL1M (D-WL1M) integrates universal priors with learning capability so that all of the parameters, including the crucial weights, can be learned from training data. We demonstrate the proposed D-WL1M outperforms several state-of-the-art CS-based methods and deep learning-based methods by a large margin via the experiments on the Caltech-256 image data set.

Efficient Optical MIMO–OFDM Channel Estimation Based on Correntropy Compressive Sensing

The compressive sensing (CS) technique is widely used in the field of radio-frequency channel estimation. However, in optical wireless channel (OWC) estimation, CS needed to be adapted to cope with the nonlinear distortion resultant from the electrical-to-optical and optical-to-electrical conversion process of the OWC. Therefore, a robust CS channel estimation technique is proposed for the optical MIMO–OFDM system. The proposed CS channel estimation technique is based on higher-order statistics (HOS). In which, the correntropy is exploited as a HOS similarity measurement instead of the second-order statistics euclidean distance (ED) used with the conventional CS to handle the OWC nonlinear distortion. Herein, the ED is the most popular iterative CS algorithms such as orthogonal matching pursuits, sparsity adaptive matching pursuit, and self-aware step size sparsity adaptive matching pursuit is efficiently replaced by the HOS correntropy based CS to show the effectiveness of the proposed algorithm. Moreover, the most recent visible light communication system GLIM-OFDM is considered here to test the proposed technique. However, the pre-estimated channel state information (CSI) obtained from the previous OFDM frame is exploited as initial information in estimating the CSI of the current OFDM frame, which improves overall system performance. A comparison with the conventional CS reconstruction algorithms is conducted via extensive simulation analysis. The simulation results show the superiority of the bit error rate of the proposed correntropy based CS channel estimation scheme compared to the conventional CS-based channel estimation algorithms.

SFIM Detector Based on Joint-Sparse Index Removal for MIMO-OFDM-CR System

This letter proposes a joint-sparse index removal (JSIR) based algorithm to detect the index of space-frequency index modulation (SFIM) signal for MIMO-OFDM cognitive radio (MIMO-OFDM-CR) system. At first, the proposed algorithm calculates the inner-product matrix of the received signal and channel gain to measure the index information of each subcarrier on each antenna. Then, an antenna index metric is computed through a definition which is given by summing the metrics of all subcarriers on the antenna. According to the metric, the silent antenna indices are acquired by comparing the metric with a threshold derived from statistical distribution. Next, the index detection problem is simplified by removing the silent antenna indices, i.e., the joint-sparse indices of SFIM signal matrix. At last, the indices of active subcarriers on active antennas are obtained through solving the simplified problem via a compressed sensing reconstruction algorithm. The complexity analysis shows that the proposed JSIR algorithm has lower complexity under certain conditions, compared with other related methods. The simulation results verify the accuracy of the proposed method in terms of bit error rate (BER).

Deep-learning-based single-photon-counting compressive imaging via jointly trained subpixel convolution sampling.

The combination of single-pixel-imaging and single-photon-counting technology can achieve ultrahigh-sensitivity photon-counting imaging. However, its applications in high-resolution and real-time scenarios are limited by the long sampling and reconstruction time. Deep-learning-based compressive sensing provides an effective solution due to its ability to achieve fast and high-quality reconstruction. This paper proposes a sampling and reconstruction integrated neural network for single-photon-counting compressive imaging. To effectively remove the blocking artefact, a subpixel convolutional layer is jointly trained with a deep reconstruction network to imitate compressed sampling. By modifying the forward and backward propagation of the network, the first layer is trained into a binary matrix, which can be applied to the imaging system. An improved deep-reconstruction network based on the traditional Inception network is proposed, and the experimental results show that its reconstruction quality is better than existing deep-learning-based compressive sensing reconstruction algorithms.

Trends in Compressive Sensing for EEG Signal Processing Applications.

The tremendous progress of big data acquisition and processing in the field of neural engineering has enabled a better understanding of the patient’s brain disorders with their neural rehabilitation, restoration, detection, and diagnosis. An integration of compressive sensing (CS) and neural engineering emerges as a new research area, aiming to deal with a large volume of neurological data for fast speed, long-term, and energy-saving purposes. Furthermore, electroencephalography (EEG) signals for brain–computer interfaces (BCIs) have shown to be very promising, with diverse neuroscience applications. In this review, we focused on EEG-based approaches which have benefited from CS in achieving fast and energy-saving solutions. In particular, we examine the current practices, scientific opportunities, and challenges of CS in the growing field of BCIs. We emphasized on summarizing major CS reconstruction algorithms, the sparse basis, and the measurement matrix used in CS to process the EEG signal. This literature review suggests that the selection of a suitable reconstruction algorithm, sparse basis, and measurement matrix can help to improve the performance of current CS-based EEG studies. In this paper, we also aim at providing an overview of the reconstruction free CS approach and the related literature in the field. Finally, we discuss the opportunities and challenges that arise from pushing the integration of the CS framework for BCI applications.

Learnable Sparse Transformation-Based Massive MIMO CSI Recovery Network

In frequency division duplex massive Multiple-Input Multiple-Output (MIMO) systems, plenty of Channel State Information (CSI) needs to be fed back. By exploiting the correlation of channel coefficients, the channel matrix can be transformed into a sparse form for compression. In this letter, we propose a model-based sparse recovery network that combines the advantages of compressed sensing reconstruction algorithms and neural networks, to perform CSI compression and reconstruction fast and accurately. Moreover, considering that the CSI is not strictly sparse in the discrete Fourier transform basis, we introduce a sparse autoencoder in our network to learn sparse transformations. Extensive experiments show that our model outperforms traditional compressed sensing algorithms and network-based methods.

Sparse Analyzer Tool for Biomedical Signals.

The virtual (software) instrument with a statistical analyzer for testing algorithms for biomedical signals’ recovery in compressive sensing (CS) scenario is presented. Various CS reconstruction algorithms are implemented with the aim to be applicable for different types of biomedical signals and different applications with under-sampled data. Incomplete sampling/sensing can be considered as a sort of signal damage, where missing data can occur as a result of noise or the incomplete signal acquisition procedure. Many approaches for recovering the missing signal parts have been developed, depending on the signal nature. Here, several approaches and their applications are presented for medical signals and images. The possibility to analyze results using different statistical parameters is provided, with the aim to choose the most suitable approach for a specific application. The instrument provides manifold possibilities such as fitting different parameters for the considered signal and testing the efficiency under different percentages of missing data. The reconstruction accuracy is measured by the mean square error (MSE) between original and reconstructed signal. Computational time is important from the aspect of power requirements, thus enabling the selection of a suitable algorithm. The instrument contains its own signal database, but there is also the possibility to load any external data for analysis.

Single Sensor Compressive Light Field Video Camera

AbstractThis paper presents a novel compressed sensing (CS) algorithm and camera design for light field video capture using a single sensor consumer camera module. Unlike microlens light field cameras which sacrifice spatial resolution to obtain angular information, our CS approach is designed for capturing light field videos with high angular, spatial, and temporal resolution. The compressive measurements required by CS are obtained using a random color‐coded mask placed between the sensor and aperture planes. The convolution of the incoming light rays from different angles with the mask results in a single image on the sensor; hence, achieving a significant reduction on the required bandwidth for capturing light field videos. We propose to change the random pattern on the spectral mask between each consecutive frame in a video sequence and extracting spatio‐angular‐spectral‐temporal 6D patches. Our CS reconstruction algorithm for light field videos recovers each frame while taking into account the neighboring frames to achieve significantly higher reconstruction quality with reduced temporal incoherencies, as compared with previous methods. Moreover, a thorough analysis of various sensing models for compressive light field video acquisition is conducted to highlight the advantages of our method. The results show a clear advantage of our method for monochrome sensors, as well as sensors with color filter arrays.

Low Complexity FFT Factorization for CS Reconstruction

In this paper is presented a novel area efficient Fast Fourier transform (FFT) for real-time compressive sensing (CS) reconstruction. Among various methodologies used for CS reconstruction algorithms, Greedy-based orthogonal matching pursuit (OMP) approach provides better solution in terms of accurate implementation with complex computations overhead. Several computationally intensive arithmetic operations like complex matrix multiplication are required to formulate correlative vectors making this algorithm highly complex and power consuming hardware implementation. Computational complexity becomes very important especially in complex FFT models to meet different operational standards and system requirements. In general, for real time applications, FFT transforms are required for high speed computations as well as with least possible complexity overhead in order to support wide range of applications. This paper presents an hardware efficient FFT computation technique with twiddle factor normalization for correlation optimization in orthogonal matching pursuit (OMP). Experimental results are provided to validate the performance metrics of the proposed normalization techniques against complexity and energy related issues. The proposed method is verified by FPGA synthesizer, and validated with appropriate currently available comparative analyzes.

A Machine Condition Monitoring Framework Using Compressed Signal Processing.

The vibration monitoring of ball bearings of a rotating machinery is a crucial aspect for smooth functioning and sustainability of plants. The wireless vibration monitoring using conventional Nyquist sampling techniques is costly in terms of power consumption, as it generates lots of data that need to be processed. To overcome this issue, compressive sensing (CS) can be employed, which directly acquires the signal in compressed form and hence reduces power consumption. The compressive measurements so generated can easily be transmitted to the base station and the original signal can be recovered there using CS reconstruction algorithms to diagnose the faults. However, the CS reconstruction is very costly in terms of computational time and power. Hence, this conventional CS framework is not suitable for diagnosing the machinery faults in real time. In this paper, a bearing condition monitoring framework is presented based on compressed signal processing (CSP). The CSP is a newer research area of CS, in which inference problems are solved without reconstructing the original signal back from compressive measurements. By omitting the reconstruction efforts, the proposed method significantly improves the time and power cost. This leads to faster processing of compressive measurements for solving the required inference problems for machinery condition monitoring. This gives a way to diagnose the machinery faults in real-time. A comparison of proposed scheme with the conventional method shows that the proposed scheme lowers the computational efforts while simultaneously achieving the comparable fault classification accuracy.