Efficient Compressive Sensing Research Articles

A Highly Efficient Compressive Sensing Algorithm Based on Root-Sparse Bayesian Learning for RFPA Radar

Off-grid issues and high computational complexity are two major challenges faced by sparse Bayesian learning (SBL)-based compressive sensing (CS) algorithms used for random frequency pulse interval agile (RFPA) radar. Therefore, this paper proposes an off-grid CS algorithm for RFPA radar based on Root-SBL to address these issues. To effectively cope with off-grid issues, this paper derives a root-solving formula inspired by the Root-SBL algorithm for velocity parameters applicable to RFPA radar, thus enabling the proposed algorithm to directly solve the velocity parameters of targets during the fine search stage. Meanwhile, to ensure computational feasibility, the proposed algorithm utilizes a simple single-level hierarchical prior distribution model and employs the derived root-solving formula to avoid the refinement of velocity grids. Moreover, during the fine search stage, the proposed algorithm combines the fixed-point strategy with the Expectation-Maximization algorithm to update the hyperparameters, further reducing computational complexity. In terms of implementation, the proposed algorithm updates hyperparameters based on the single-level prior distribution to approximate values for the range and velocity parameters during the coarse search stage. Subsequently, in the fine search stage, the proposed algorithm performs a grid search only in the range dimension and uses the derived root-solving formula to directly solve for the target velocity parameters. Simulation results demonstrate that the proposed algorithm maintains low computational complexity while exhibiting stable performance for parameter estimation in various multi-target off-grid scenarios.

Efficient Compressed Sensing Reconstruction Algorithm for Nonnegative Vectors in Wireless Data Transmission

With the rapid development of 5G communication and wireless Internet of Things technology, the application of intelligent wearable devices based on wireless data transmission technology is becoming more and more popular. However, due to the bandwidth of wireless data transmission nodes and the power consumption of the device system, the use time and data storage of wearable devices are severely restricted. The compressed sensing (CS) technology has become an effective method to tackle this problem. CS technology includes data compressive sensing at the transmission end and data reconstruction at the receiving end. In this paper, we consider the reconstruction of nonnegative sparse vectors, an important problem in the area of CS for wireless data transmission. It is known that the interval-passing (IP) algorithm is a low-complexity message-passing type method for the problem. However, the reconstruction performance of the IP algorithm is inferior to that of the other state-of-the-art CS reconstruction algorithms such as the orthogonal matching pursuit (OMP) algorithm. In order to address the problem, we propose a two-stage reconstruction algorithm in this paper. The proposed algorithm applies the IP algorithm for the first stage of reconstruction. If the reconstruction fails, the OMP algorithm is then used on the basis of the results in the first stage. The proposed algorithm is evaluated and compared with other state-of-the-art algorithms by the probability of perfect reconstruction under the given sparsity order value. Simulation results suggest that the proposed two-stage algorithm can greatly improve the reconstruction performance of the IP algorithm and can even outperform the OMP algorithm. In addition, the low-complexity advantages of the IP algorithm are maintained in the proposed algorithm.

A Compact and Highly Efficient Compressive Sensing Imaging System Using In-Fiber Grating

Serial time-encoded amplified microscopy can achieve ultrafast imaging speed within varied dynamic regimes. However, it has two challenges: the high-throughput data issue and low-efficiency diffraction issue. Here, we report a compact and highly efficient ultrafast optical imaging system based on compressive sensing and in-fiber grating. Our proposal is confirmed by the proof-of-principle experiment and obtains a minimum data compression ratio of 5% with a continuous ultrafast imaging speed of 10 Mfps at a field of view of 0.5 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{\ast} 1.6$ </tex-math></inline-formula> mm. A barcode with a moving speed of 4m/s is also demonstrated for imaging and an imaging speed of 1.25 Mfps is obtained. The proposed optical imaging system overcomes the big data issue, increases energy efficiency, and paves the way for compact and highly efficient ultrafast optical imaging within dynamic scenarios.

A Modified Normalized Channel Estimation Method for Efficient Compressive Sensing Based SWA by 2D Frequency Characterization

A Modified Normalized Channel Estimation Method for Efficient Compressive Sensing Based SWA by 2D Frequency Characterization

Energy Efficient Compressive Sensing based Multi-focus Image Fusion Scheme for WVSN

Energy Efficient Compressive Sensing based Multi-focus Image Fusion Scheme for WVSN

Efficient Compressed Sensing for Wireless Neural Recording: A Deep Learning Approach

Data compression is crucial for resource-constrained wireless neural recording applications with limited data bandwidth, and compressed sensing (CS) theory has successfully demonstrated its potential in neural recording applications. Based on deep learning theory, this paper presents a binarized autoencoder scheme for CS, in which a binary sensing matrix and a noniterative recovery solver are jointly optimized. Experimental results on synthetic dataset reveal that the proposed approach outperforms the state-of-the-art CS-based methods both in terms of recovery quality and computation time.

Efficient Compressive Sensing Detectors for Generalized Spatial Modulation Systems

Generalized spatial modulation (GSM) is a novel multiple-input–multiple-output (MIMO) technique, which relies on a sparse use of radio-frequency (RF) front ends at the transmitter. In this paper, low-complexity and compressive-sensing (CS)-based detectors for GSM systems are proposed. First, an extension of the normalized CS detector (E-NCS) based on the orthogonal matching pursuit (OMP) algorithm is proposed, which is shown to be suitable for large-scale GSM implementations, due to its low complexity. Furthermore, to mitigate the error floor effect of the E-NCS detector, two efficient CS (ECS) detectors based on the OMP algorithm are designed with the aid of a preset threshold. Specifically, different searching algorithms are designed, whose objective is to balance computational complexity and system performance. An upper bound for the average bit error probability (ABEP) of the first ECS detector is derived and used to optimize the preset threshold. Simulation results show that the proposed ECS detectors are capable of achieving a considerable reduction in computational complexity, compared with other near-optimal algorithms, with a negligible performance loss.

Efficient Compressed Sensing Method for Moving-Target Imaging by Exploiting the Geometry Information of the Defocused Results

Compressed sensing (CS) has been increasingly used in the synthetic aperture radar ground moving-target indication system, particularly for imaging the moving targets, which satisfy the sparse precondition of the CS method. However, efficient moving-target imaging is a key challenge for current CS methods, since the redundant basis brings heavy computation load. In this letter, by exploiting the geometry information of the defocused results, we present an efficient fractional Fourier transform (FRFT) to estimate the Doppler rate and image the moving targets by only two times FRFT rather than time-consuming searching operation. Then, the concept is extended into an efficient CS (ECS) imaging method by two bases consisting of two discrete FRFT matrices rather than the redundant basis. Simulations and real-data process are provided to demonstrate the effectiveness of the ECS method. The proposed ECS method can achieve accurate parameter estimation and imaging performance with low computational complexity.

Simple and Efficient Compressed Sensing Encoder for Wireless Body Area Network

Compressed sensing (CS) is an emerging signal processing technique that enables sub-Nyquist measurement of signals having sparse representations in certain bases. Since most physiological signals treated within a wireless body area network (WBAN) are sparse, CS can be applied to WBANs to reduce the number of measurements and minimize the energy consumption of the sensor nodes. In this paper, we propose a simple and efficient CS encoder device used to measure signals within sensor nodes of a WBAN. A digital and an analog models of the proposed CS encoder are presented. As the CS encoder and decoder are tightly coupled, a model of the overall acquisition chain is required in the first stages of development and validation. To do this, we propose a virtual prototyping of the system with SystemC-AMS. A SPICE model and a hardware prototype of the proposed CS encoder are also presented. The simulation results of both models show that the proposed encoder was able to compressively measure an electrocardiogram (ECG) and an electroencephalogram signals with compression ratios of 6:1 and 4:1, respectively, which save 82.9% and 75% of the energy consumption of transceivers. The experiment results were consistent with those of the model and show that the hardware prototype was able to compressively measure an ECG signal with a compression ratio of 8:1. Comparison with a random demodulator (RD) was carried out and shows that the proposed encoder outperformed RD in terms of compression ratio and reconstruction quality.

Fast and Efficient Compressive Sensing Using Structurally Random Matrices

This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the transform coefficients as the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable with that of completely random sensing matrices. Numerical simulation results verify the validity of the theory as well as illustrate the promising potentials of the proposed sensing framework.

Efficient and Robust Compressed Sensing Using Optimized Expander Graphs

Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -dimensional vector that is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -sparse can be fully recovered using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ) measurements and only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ) simple recovery iterations. In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">/</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> and show that, with the same number of measurements, only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> ) recovery iterations are required, which is a significant improvement when <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> is large. In fact, full recovery can be accomplished by at most <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</i> very simple iterations. The number of iterations can be reduced arbitrarily close to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , and the recovery algorithm can be implemented very efficiently using a simple priority queue with total recovery time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> log( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ))). We also show that by tolerating a small penalty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come up with explicit measurement matrices for this method. We compare our result with other recently developed expander-graph-based methods and argue that it compares favorably both in terms of the number of required measurements and in terms of the time complexity and the simplicity of recovery. Finally, we will show how our analysis extends to give a robust algorithm that finds the position and sign of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> significant elements of an almost <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -sparse signal and then, using very simple optimization techniques, finds a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -sparse signal which is close to the best <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -term approximation of the original signal.