Sparse Signal Reconstruction Research Articles

Derivative-free MLSCD conjugate gradient method for sparse signal and image reconstruction in compressive sensing

Finding the sparse solution to under-determined or ill-condition equations is a fundamental problem encountered in most applications arising from a linear inverse problem, compressive sensing, machine learning and statistical inference. In this paper, inspired by the reformulation of the ?1-norm regularized minimization problem into a convex quadratic program problem by Xiao et al. (Nonlinear Anal Theory Methods Appl, 74(11), 3570-3577), we propose, analyze, and test a derivative-free conjugate gradient method to solve the ?1-norm problem arising from the reconstruction of sparse signal and image in compressive sensing. The method combines the MLSCD conjugate gradient method proposed for solving unconstrained minimization problem by Stanimirovic et al. (J Optim Theory Appl, 178(3), 860-884) and a line search method. Under some mild assumptions, the global convergence of the proposed method is established using the backtracking line search. Computational experiments are carried out to reconstruct sparse signal and image in compressive sensing. The numerical results indicate that the proposed method is stable, accurate and robust.

High-Resolution Radar Imaging of Off-Grid Maneuvering Targets Based on Parametric Sparse Bayesian Learning

In high-resolution radar imaging, the time-varying Doppler induced by maneuvering targets generally invalidates traditional methods. Although sparse signal reconstruction methods can be applied to achieve better performance, the off-grid problem embedded in these methods still prohibits well-focused imaging. In this article, we propose to perform high-resolution radar imaging of maneuvering targets with off-grid scattering centers in a Bayesian framework. First, the statistical model with a parametric dictionary is established, in which the Doppler frequencies of scattering centers are treated as unknown model parameters instead of being discretized into the grid. To be consistent with the physical characteristics, the posterior of the Doppler is approximated by the von Mises distribution. Then, the model parameters and rotation parameters are estimated iteratively by variational inference (VI) and the Newton method. Experiments have demonstrated that the proposed method provides an effective way for high-resolution and well-focused radar imaging of maneuvering targets with off-grid scattering centers in complex scenarios, such as incomplete data and low signal-to-noise ratio.

Off-Grid Error and Amplitude–Phase Drift Calibration for Computational Microwave Imaging With Metasurface Aperture Based on Sparse Bayesian Learning

Computational microwave imaging (CMI) based on the frequency diversity metasurface apertures (FDMAs) is an emerging technology and has attracted wide attention. FDMA based CMI (FDMA-CMI) can be considered as microwave compressive sensing imaging with the frequency diversity pattern of the FDMA being the sensing matrix and solved by sparse signal reconstruction algorithms. However, the imaging quality is affected by the sensing matrix error and off-grid error seriously. In this paper, we propose a novel algorithm for FDMA-CMI, referred to as OGSISBL, by taking both the off-grid error and sensing matrix error into account. Firstly, we establish the measurement model with both the off-grid error and sensing matrix error. Specifically, the off-grid error is represented as a set of parameters to be estimated in the measurement model and the sensing matrix error is represented as the amplitude-phase drift of the transceiver channels of the imaging system due to the principle of the FDMA. Then, under the framework of the sparse Bayesian learning, a robust imaging algorithm OGSISBL is developed via the variational Bayesian expectation maximization (VBEM), which can not only recover the amplitude and position of the return of the scattered, but also simultaneously calibrate the amplitude-phase drift of the transceiver channels and the off-grid error. The performance of the proposed algorithm is evaluated by both the simulation data and the measured data collected by the self-designed experimental FDMA-CMI system, and the results validate the effectiveness and robustness of the proposed method.

Compressive hard thresholding pursuit algorithm for sparse signal recovery

<abstract><p>Hard Thresholding Pursuit (HTP) is one of the important and efficient algorithms for reconstructing sparse signals. Unfortunately, the hard thresholding operator is independent of the objective function and hence leads to numerical oscillation in the course of iterations. To alleviate this drawback, the hard thresholding operator should be applied to a compressible vector. Motivated by this idea, we propose a new algorithm called Compressive Hard Thresholding Pursuit (CHTP) by introducing a compressive step first to the standard HTP. Convergence analysis and stability of CHTP are established in terms of the restricted isometry property of a sensing matrix. Numerical experiments show that CHTP is competitive with other mainstream algorithms such as the HTP, Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms both in the sparse signal reconstruction ability and average recovery runtime.</p></abstract>

Reversible image authentication scheme with blind content reconstruction based on compressed sensing

Reversible image authentication (RIA) schemes embed fragile watermarks to protect images against tampering attacks. If a marked image is not attacked, watermarks can be completely extracted and eliminated to obtain the original cover image. Tampered image regions can be reconstructed by including recovery information as part of the watermarks. In this paper, we introduce a novel blind RIA scheme for tampering localization and reconstruction. The proposed scheme is based on compressed sensing technique to obtain reference values, which are embedded into the cover image to perform sparse signal reconstruction using only the embedded information. Signal sparsity is enhanced in the discrete cosine transform (DCT) domain by omitting some high-frequency coefficients. Experimental results indicate that better sparse signal approximations can be obtained when some DCT coefficients are omitted, improving image reconstructions. The proposed scheme outperforms similar state-of-the-art works when reconstructing tampered image regions, especially when the damaged area size is increased.

Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, which encompass many important modern optimization problems arising from diverse areas such as the recently proposed scale-invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for solving this optimization model and show that the iterated sequence generated by the algorithm is bounded and that any one of its limit points is a stationary point of the model problem. The choice of our extrapolation parameter is flexible and includes the popular extrapolation parameter adopted in the restarted fast iterative shrinking-threshold algorithm (FISTA). By providing a unified analysis framework of descent methods, we establish the convergence of the full sequence under the assumption that a suitable merit function satisfies the Kurdyka–Łojasiewicz property. Our algorithm exhibits linear convergence for the scale-invariant sparse signal reconstruction problem and the Rayleigh quotient problem over spherical constraint. When the denominator is the maximum of finitely many continuously differentiable weakly convex functions, we also propose another extrapolated proximal subgradient algorithm with guaranteed convergence to a stronger notion of stationary points of the model problem. Finally, we illustrate the proposed methods by both analytical and simulated numerical examples.

Sparsity Signal Detection for Indoor GSSK-VLC System

In this article, the signal detection problem in indoor visible light communication (VLC) system aided by generalized space shift keying (GSSK) is modeled as a sparse signal reconstruction problem, which has lower computational complexity by exploiting the sparse reconstruction algorithms in compressed sensing (CS). In order to satisfy the measurement matrix property to perform sparse signal reconstruction, a preprocessing approach of measurement matrix is proposed based on singular value decomposition (SVD), which theoretically guarantees the feasibility of utilizing CS based sparse signal detection method in indoor GSSK-VLC system. Then, by adopting classical orthogonal matching pursuit (OMP) algorithm and compressed sampling matching pursuit (CoSaMP) algorithm, the GSSK signals are efficiently detected in the considered indoor GSSK-VLC system. Furthermore, a more efficient detection algorithm combined with OMP and maximum likelihood (ML) is also presented especially for SSK scenario. Finally, the effectiveness of the proposed sparsity aided detection algorithms in indoor GSSK-VLC system are verified by computer simulations. The results show that the proposed algorithms can achieve better bit error rate (BER) and lower computation complexity than ML based detection method. Specifically, a signal-to-noise ratio (SNR) gain as high as 12 dB is observed in the SSK scenario and about 5 dB in case of a GSSK scenario upon employing our proposed detection methods.

Sparse Signal Reconstruction on Fixed and Adaptive Supervised Dictionary Learning for Transient Stability Assessment

Fixed and adaptive supervised dictionary learning (SDL) is proposed in this paper for wide-area stability assessment. Single and hybrid fixed structures are developed based on impulse dictionary (ID), discrete Haar transform (DHT), discrete cosine transform (DCT), discrete sine transform (DST), and discrete wavelet transform (DWT) for sparse features extraction and online transient stability prediction. The fixed structures performance is compared with that obtained from transient K-singular value decomposition (TK-SVD) implemented while adding a stability status term to the optimization problem. Stable and unstable dictionary learning are designed based on datasets recorded by simulating thousands of contingencies with varying faults, load, and generator switching on the IEEE 68-bus test system. This separate supervised learning of stable and unstable scenarios allows determining root mean square error (RMSE), useful for online stability status assessment of new scenarios. With respect to the RMSE performance metric in signal reconstruction-based stability prediction, the present analysis demonstrates that [DWT], [DHT|DWT] and [DST|DHT|DCT] are better stability descriptors compared to K-SVD, [DHT], [DCT], [DCT|DWT], [DHT|DCT], [ID|DCT|DST], and [DWT|DHT|DCT] on test datasets. However, the K-SVD approach is faster to execute in both off-line training and real-time playback while yielding satisfactory accuracy in transient stability prediction (i.e., 7.5-cycles decision window after fault-clearing).

Time-Frequency Sparse Reconstruction of Non-Uniform Sampling for Non-Stationary Signal

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

SGCS: a signal reconstruction method based on Savitzky-Golaysgz filtering and compressed sensing for wavelength modulation spectroscopy.

The residual oxygen concentration in pharmaceutical glass vial variously threatens the aseptic properties of encapsulated agents. The demodulated 2nd harmonic signals in the wavelength modulation spectroscopy (WMS) detection system, the data basis of the inversion of oxygen concentration, are inevitably destroyed by various time-varying industrial noises. In this work, we propose a signal reconstruction method based on self-correcting Savitzky-Golaysgz filter and compressed sensing (namely SGCS) for the urgent signal denoising task, which is a dual-step lightweight denoising scheme. First, in order to avoid the influence of glitch noise on sparse signal reconstruction, Savitzky-Golay (S-G) filter is used to smooth the 2nd harmonic signal while retaining the change information effectively. Then, the well-tuned measurement matrix of compressed-sensing (CS) is applied to aggressively fetch the sparse principal components while bypassing most residual dynamic noises. Finally, the orthogonal matching pursuit (OMP) is used to reconstruct the 2nd harmonic signal according to sparsity constrain and the sparse principal components. Experimental results show that the performance of SGCS method is superior. Compared with other competitive methods the operation time of SGCS is the shortest. When the normalized SNR is 1, the average correct discrimination rate is 98.57%. Even if SNR reduces from 1 to 0.55, the WMS detection system still survives well, with the highest average correct discrimination rate of 89.34%.

Two dimensional sparse signal reconstruction via 2D inverse-free sparse Bayesian learning

Two dimensional sparse signal reconstruction via 2D inverse-free sparse Bayesian learning

A comparative study of multi-objective optimization algorithms for sparse signal reconstruction

A comparative study of multi-objective optimization algorithms for sparse signal reconstruction

A dai-liao hybrid conjugate gradient method for unconstrained optimization

One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algorithm is shown to converge globally using standard assumptions. The numerical experimentation of the scheme demonstrated that the proposed method is robust and promising than some known methods applying the performance profile Dolan and Mor´e on 250 unrestricted problems. Numerical assessment of the tested CG algorithms with sparse signal reconstruction and image restoration in compressive sensing problems, file restoration, image video coding and other applications. The result shows that these CG schemes are comparable and can be applied in different fields such as temperature, fire, seismic sensors, and humidity detectors in forests, using wireless sensor network techniques.

Perfect reconstruction of sparse signals with piecewise continuous nonconvex penalties and nonconvexity control

We consider a reconstruction problem of sparse signals from a smaller number of measurements than the dimension formulated as a minimization problem of nonconvex sparse penalties: smoothly clipped absolute deviations and minimax concave penalties. The nonconvexity of these penalties is controlled by nonconvexity parameters, and the ℓ 1 penalty is contained as a limit with respect to these parameters. The analytically-derived reconstruction limit overcomes that of the ℓ 1 limit and is also expected to overcome the algorithmic limit of the Bayes-optimal setting when the nonconvexity parameters have suitable values. However, for small nonconvexity parameters, where the reconstruction of the relatively dense signals is theoretically expected, the algorithm known as approximate message passing (AMP), which is closely related to the analysis, cannot achieve perfect reconstruction leading to a gap from the analysis. Using the theory of state evolution, it is clarified that this gap can be understood on the basis of the shrinkage in the basin of attraction to the perfect reconstruction and also the divergent behavior of AMP in some regions. A part of the gap is mitigated by controlling the shapes of nonconvex penalties to guide the AMP trajectory to the basin of the attraction.

Structured sparsity learning for large-scale fuzzy cognitive maps

Fuzzy cognitive map (FCM) as a kind of intelligent soft computing method, by combining the advantages of neural network and fuzzy logic, can be used to mine the causal relationships between concepts and make reasoning. However, how to effectively learn the large-scale FCMs is still an open problem. In this article, by means of structured sparsity learning, a robust learning method for large-scale FCMs based on iterative smoothing algorithm is proposed. Firstly, in terms of sparse signal reconstruction, the objective function of learning method is constructed by using elastic and total variation (TV) penalties, which can be conducive to capture the sparse structure information of FCM and improve the robustness of network reconstruction. Due to the non-smoothness of the TV penalty, Nesterov’s smoothing technique is used to solve the non-smooth problem, thus transforming the problem into a convex optimization problem. Subsequently, in order to quickly solve the convex optimization, the algorithm based on proximal gradient descent is applied. In the experiment part, synthetic FCM models with different densities, sizes and noises are used to evaluate the proposed method, and the experimental results demonstrate the proposed method can make full use of the observations to learn the structural information of FCM. Moreover, the real-world data from the gene regulatory networks (GRNs) are further used to evaluate the effect of network reconstruction, and a higher reconstruction accuracy can be verified.

A novel sparse reconstruction method based on multi-objective Artificial Bee Colony algorithm

Compressed sensing is a signal processing method that performs the compressing and sensing processes at the same time. Sparse signal reconstruction is one of the most important issues of compressed sensing. The developments in sparse signal reconstruction methods directly affect the performance of the compressed sensing process. Many sparse signal reconstruction methods have been proposed in the literature. In general, these algorithms are classified as convex optimization, non-convex optimization, and greedy algorithms. In addition, multi-objective optimization algorithms have started to be used in sparse signal reconstruction lately. A sparse signal reconstruction method based on a Multi-objective Artificial Bee Colony algorithm is proposed in this study. The proposed algorithm optimizes the sparsity and measurement error at the same time. Furthermore, it uses the iterative half thresholding algorithm to improve the convergence acceleration of the method. The proposed method was evaluated by using various test signals. Additionally, it was compared with other sparse signal reconstruction algorithms. According to the obtained results, the proposed method has some superiority over the compared algorithms.

Two-Dimensional ISAR Fusion Imaging of Block Structure Targets

The range resolution and azimuth resolution are restricted by the limited transmitting bandwidth and observation angle in a monostatic radar system. To improve the two-dimensional resolution of inverse synthetic aperture radar (ISAR) imaging, a fast linearized Bregman iteration for unconstrained block sparsity (FLBIUB) algorithm is proposed to achieve multiradar ISAR fusion imaging of block structure targets. First, the ISAR imaging echo data of block structure targets is established based on the geometrical theory of the diffraction model. The multiradar ISAR fusion imaging is transformed into a signal sparse representation problem by vectorization operation. Then, considering the block sparsity of the echo data of block structure targets, the FLBIUB algorithm is utilized to achieve the block sparse signal reconstruction and obtain the fusion image. The algorithm further accelerates the iterative convergence speed and improves the imaging efficiency by combining the weighted back-adding residual and condition number optimization of the basis matrix. Finally, simulation experiments show that the proposed method can effectively achieve block sparse signal reconstruction and two-dimensional multiradar ISAR fusion imaging of block structure targets.

Moving target inverse synthetic aperture radar image resolution enhancement based on two‐dimensional block sparse signal reconstruction

To achieve the high-resolution inverse synthetic aperture radar (ISAR) imaging of moving targets, the range Doppler method and compressed sensing technique can be used. However, those methods are generally faced with the problem of migration through range cells and basis mismatch problems, and the imaging results can be improved. To solve these problems and improve the image quality, the problem of ISAR imaging is termed as a block-sparse signal recovery problem by utilizing the block-sparse structure of the ISAR images. A localized low-rank promoting (LLP) method is introduced and extended to the complex case for the recovery of range compressed block-sparse signals. The sparse recovery problem is solved by minimizing another function, which is the surrogate function that can be solved more effectively. Based on the LLP method, the coefficients of the range compressed echo signal are reconstructed and some 2 × 2 matrices can be obtained. And then the log-determinant function is introduced to find the low rankness solutions for these matrices. Then the LLP method is also used in the cross-range domain to reconstruct the ISAR image. Experimental results show that the proposed method can recover better focused and higher quality ISAR images compared with the traditional methods.

Pilot design for underwater MIMO cosparse channel estimation based on compressed sensing

In multiple-input multiple-output–orthogonal frequency-division multiplexing underwater acoustic communication systems, the correlation of the sampling matrix is the key of the channel estimation algorithm based on compressed sensing. To reduce the cross-correlation of the sampling matrix and improve the channel estimation performance, a pilot design algorithm for co-sparse channel estimation based on compressed sensing is proposed in this article. Based on the time-domain correlation of the channel, the channel estimation is modeled as a common sparse signal reconstruction problem. When replacing each pilot indices position, the algorithm selects multiple pilot indices with the least cross-correlation from the alternative positions to replace the current pilot indices position, and it uses the inner and outer two-layer loops to realize the bit-by-bit optimal replacement of the pilot. The simulation results show that the channel estimation mean squared error of pilot design algorithm for co-sparse channel estimation based on compressed sensing can be reduced by approximately 18 dB compared with the least square algorithm. Compared with the genetic algorithm and search space size methods, the structural sequence search proposed by pilot design algorithm for co-sparse channel estimation based on compressed sensing is used to design the pilot to complete the channel estimation. Thus, the mean squared error of the channel estimation can be reduced by 2 dB. At the same bit error rate of 0.03, the signal-to-noise ratio can be decreased by approximately 7 dB.

ECG compression using wavelet-based compressed sensing with prior support information

Electrocardiogram (ECG) signal compression is a vital signal processing area, especially with the growing usage of wireless body sensor networks (WBSN). ECG signals need to be compressed for efficient storage or transmission. Traditional compression methods acquire the ECG signal and perform compression in the sensors, where most of the computations are performed. Therefore, sensors have significant complexity and power consumption. On the other hand, compressed sensing transfers the complexity from the encoder to the decoder, thus allowing for cheap, low-power sensors, with longer lifetime. In this paper, we propose the adaptive reduced-set matching pursuit with partially known support (ARMP-PKS) compressed sensing reconstruction algorithm. ARMP-PKS performs sparse signal reconstruction at very high accuracy and speed. Furthermore, it takes advantage of prior support information, which further improves the performance. Our proposed algorithm achieves 35 dB reconstruction SNR at 50% compression and about 22.5 dB at 25%, significantly faster than related algorithms.