Sparsity-based Algorithm Research Articles

A mixed-field sources localization algorithm based on high-order cumulant matrix reconstruction for general symmetric array

Sparse arrays are able to generate more lags to extend the array aperture, which is a distinct advantage in mixed-field localization. To exploit these lags, existing algorithms in the known literature can be mainly divided into two types: the subspace-based algorithm and the sparsity-based algorithm. However, the former algorithm cannot fully utilize the time delay information provided by sparse array, and the second algorithm has basis mismatch problem. In this paper, an interpolation processing method based on atomic norm is proposed to solve the sparse array localization problem. The high-order cumulant matrix is reconstructed by the interpolation method to generate an augmented cumulant matrix without holes, which can make full use of all the lags. Then, the atomic norm minimization method is used to recover the sparse matrix after interpolation in a gridless way. The matrix after recovery enables gridless direction-of-arrival (DOA) estimation. After the interpolation reconstruction, more lags can be exploited, the degrees of freedom are further increased. The proposed algorithm can not only make full use of the array receiving information but also avoid the base mismatch problem, and the accuracy of DOA estimation is improved. Numerical simulations verify the superiority of the proposed algorithm compared with the existing algorithms.

A total variation and group sparsity-based algorithm for nuclear radiation-contaminated video restoration

ABSTRACT Nuclear radiation-contaminated video deblurring is an important issue of the robot vision system and has been widely studied. In this paper, a hybrid radiation-contaminated video frame enhancement algorithm is proposed that utilizes both intra-frame and inter-frame correlation by a two-stage strategy. In the first stage, total variation (TV) transformation are used to locate the spot areas, and then local TV is employed to restore spot areas. The preliminary deblurring result not only enhances the video frame and similar patch matching accuracy but also provides reliable estimates of filtering parameters. In the second stage, visual group technology and improved k-nearest neighbours (k-NN) method is used to select similar frames and reference patches respectively. The final enhanced video frame is obtained by a novel patch-based group sparse method. Experimental results clearly show that the proposed method outperforms other state-of-the-art methods in both quantitative evaluation indices and visual quality measurements.

Recovery of 21-cm intensity maps with sparse component separation

ABSTRACT 21-cm intensity mapping has emerged as a promising technique to map the large-scale structure of the Universe. However, the presence of foregrounds with amplitudes orders of magnitude larger than the cosmological signal constitutes a critical challenge. Here, we test the sparsity-based algorithm generalized morphological component analysis (GMCA) as a blind component separation technique for this class of experiments. We test the GMCA performance against realistic full-sky mock temperature maps that include, besides astrophysical foregrounds, also a fraction of the polarized part of the signal leaked into the unpolarized one, a very troublesome foreground to subtract, usually referred to as polarization leakage. To our knowledge, this is the first time the removal of such component is performed with no prior assumption. We assess the success of the cleaning by comparing the true and recovered power spectra, in the angular and radial directions. In the best scenario looked at, GMCA is able to recover the input angular (radial) power spectrum with an average bias of ${\sim} 5{{\ \rm per\ cent}}$ for ℓ > 25 ($20\!-\!30 {{\ \rm per\ cent}}$ for $k_{\parallel } \gtrsim 0.02 \, h^{-1}$ Mpc), in the presence of polarization leakage. Our results are robust also when up to $40{{\ \rm per\ cent}}$ of channels are missing, mimicking a radio-frequency interference (RFI) flagging of the data. Having quantified the notable effect of polarization leakage on our results, in perspective we advocate the use of more realistic simulations when testing 21-cm intensity mapping capabilities.

Hierarchical Frequency-Domain Sparsity-Based Algorithm for Fault Feature Extraction of Rolling Bearings

Rolling bearings are the crucial parts in rotating machines and its fault detection is indispensable for ensuring operational reliability of entire mechanical system. To accurately extract fault-induced fault features from vibration signal, this article proposes a hierarchical frequency-domain sparsity-based algorithm (HFDSA). Concretely, the algorithm is established based on the frequency-domain sparsity property of bearing fault features, in which a customized penalty function incorporating weighting strategy is introduced for hierarchically penalizing sparse coefficients. In addition, an iterative convergence algorithm is deduced to solve optimization problem in the proposed method HFDSA and parameter selection method is discussed in detail. Finally, the effectiveness of the HFDSA is verified through the simulation analysis and case studies. The results demonstrate that the HFDSA can efficiently extract fault transients in noisy vibration signal and achieve fault detection of rolling bearings.

Double-frame tomographic PTV at high seeding densities

A novel method performing 3D PTV from double frame multi-camera images is introduced. Particle velocities are estimated by following three steps. Firstly, separate particle reconstructions with a sparsity-based algorithm are performed on a fine grid. Secondly, they are expanded on a coarser grid on which 3D correlation is performed, yielding a predictor displacement field that allows to efficiently match particles at the two time instants. As these particles are still located on a voxel grid, the third, final step achieves particle position refinement to their actual subvoxel position by a global optimization process, also accounting for their intensities. As it strongly leverages on principles from tomographic reconstruction, the technique is termed Double-Frame Tomo-PTV (DF-TPTV). Synthetic tests on a complex turbulent flow show that the method achieves high particle and vector detection efficiency, up to seeding densities of around 0.08 particles per pixel (ppp), while its root-mean-square error of velocity estimation is lower to that of state-of-the-art similar methods. Results from an experimental campaign on a transitional round air jet at Reynolds number 4600 are also presented. During the tests, seeding density varies from 0.06 to 0.03 ppp on average. Associated to an outlier rejection scheme based on temporal statistics, DF-TPTV vector fields truthfully correspond to the instantaneous jet dynamics. Quantitative performance assessment is provided by introducing statistics performed by bin averaging, upon assuming statistical axisymmetry of the jet. Mean and fluctuating axial velocity components in the jet near-field are compared with reference results obtained from planar PIV at higher seeding density.

Sparsity-Based Algorithm for Condition Assessment of Rotating Machinery Using Internal Encoder Data

This article proposes a novel three-stage condition assessment scheme of rotating machinery using internal encoder data rather than traditional external vibration data. In this article, periodical group sparse derivatives (PGSD)-based signal denoising method is proposed to suppress the background noise, which incorporates the periodical group sparse derivative property of encoder signal and can be considered as an optimization problem. Moreover, the convexity condition of optimization problem is thoroughly investigated and an effective iterative algorithm is derived. After the PGSD-based signal denoising method, difference method (DM), and autoregressive (AR) filter are employed to convert the denoised encoder signal into intelligible speed information and remove the operation-related harmonic components. With the proposed method PGSD-DMAR, the periodical transient features are effectively extracted and the health condition of rotating machinery is successfully identified. The effectiveness and superiority of the PGSD-DMAR are verified via simulated signal and experimental data.

A Constrained Sparse Representation Model for Hyperspectral Anomaly Detection

In this paper, we propose a novel sparsity-based algorithm for anomaly detection in hyperspectral imagery. The algorithm is based on the concept that a background pixel can be approximately represented as a sparse linear combination of its spatial neighbors while an anomaly pixel cannot if the anomalies are removed from its neighborhood. To be physically meaningful, the sum-to-one and nonnegativity constraints are imposed to abundance vector based on the linear mixture model, and the upper bound constraint on sparsity level is removed for better recovery of the test pixel. First, the proposed method utilizes the redundant background information to automatically remove anomalies from the background dictionary. Then, the reconstruction error obtained by the new background dictionary is directly used for anomaly detection. Moreover, a kernel version of the proposed method is also derived to completely exploit the nonlinear feature of hyperspectral data. An important advantage of the proposed methods is their capability to adaptively model the background even when some anomaly pixels are involved. Extensive experiments have been conducted on three real hyperspectral data sets. It is demonstrated that the proposed detectors achieve a promising detection performance with a relatively low computational cost.

Sparsity-based continuous wave terahertz lens-free on-chip holography with sub-wavelength resolution.

We demonstrate terahertz (THz) lens-free in-line holography on a chip in order to achieve 40 μm spatial resolution corresponding to ~0.7λ with a numerical aperture of ~0.87. We believe that this is the first time that sub-wavelength resolution in THz holography and the 40 μm resolution were both far better than what was already reported. The setup is based on a self-developed high-power continuous wave THz laser at 5.24 THz (λ = 57.25 μm) and a high-resolution microbolometer detector array (640 × 512 pixels) with a pitch of 17 μm. This on-chip in-line holography, however, suffers from the twin-image artifacts which obfuscate the reconstruction. To address this problem, we propose an iterative optimization framework, where the conventional object constraint and the L1 sparsity constraint can be combined to efficiently reconstruct the complex amplitude distribution of the sample. Note that the proposed framework and the sparsity-based algorithm can be applied to holography in other wavebands without limitation of wavelength. We demonstrate the success of this sparsity-based on-chip holography by imaging biological samples (i.e., a dragonfly wing and a bauhinia leaf).

A Sparsity-Based Adaptive Channel Estimation Algorithm for Massive MIMO Wireless Powered Communication Networks

Compressed sensing (CS) based channel estimation methods can effectively acquire channel state information for Massive MIMO wireless powered communication networks. In order to solve the problem that the existing sparsity-based adaptive matching pursuit (SAMP) channel estimation algorithm is unstable under low signal to noise ratio (SNR), an optimized adaptive matching pursuit (OAMP) algorithm is proposed in this paper. First, the channel is pre-estimated. Next, the energy entropy-based order determination is raised to optimize the reconstruction performance of the algorithm. Then, a staged adaptive variable step size method is put forward to further promote the accuracy of channel estimation. Finally, theoretical analysis and simulation results demonstrate that the proposed OAMP algorithm improves the accuracy at the expense of a small amount of time complexity, does not require a priori knowledge of sparsity and its comprehensive performance is superior to other existing channel estimation algorithms.

Temporal diagnostics of femtosecond electron bunches with complex structures using sparsity-based algorithm

Femtosecond electron bunches with complex temporal structures play a crucial role in THz generation, free-electron lasers and plasma wakefield accelerators. The ultrashort electron pulse duration can be reconstructed from the coherent transition radiation (CTR) spectrum based on prior knowledge. A weighted greedy sparse phase retrieval (WGESPAR) algorithm is developed to reduce the ambiguities for reconstructing the distribution of the beam current. This algorithm achieves better performance than iterative algorithms, especially for truncated noisy spectra of multibunch structures. Based on the WGESPAR algorithm, the complex temporal structures of femtosecond electron bunches generated from laser wakefield accelerators can be successfully reconstructed.

Denoising of Microscopy Images: A Review of the State-of-the-Art, and a New Sparsity-Based Method.

This paper reviews the state-of-the-art in denoising methods for biological microscopy images and introduces a new and original sparsity-based algorithm. The proposed method combines total variation (TV) spatial regularization, enhancement of low-frequency information, and aggregation of sparse estimators and is able to handle simple and complex types of noise (Gaussian, Poisson, and mixed), without any a priori model and with a single set of parameter values. An extended comparison is also presented, that evaluates the denoising performance of the thirteen (including ours) state-of-the-art denoising methods specifically designed to handle the different types of noises found in bioimaging. Quantitative and qualitative results on synthetic and real images show that the proposed method outperforms the other ones on the majority of the tested scenarios.

A Content-Adaptively Sparse Reconstruction Method for Abnormal Events Detection With Low-Rank Property

This paper presents a content-adaptively sparse reconstruction method for abnormal events detection by exploiting the low-rank property of video sequences. In dictionary learning phase, the bases which describe more important characteristics of the normal behavior patterns are assigned with lower reconstruction costs. Based on the low-rank property of the bases captured by the low-rank approximation, a weighted sparse reconstruction method is proposed to measure the abnormality of testing samples. Multiscale 3-D gradient features, which encode the spatiotemporal information, are adopted as the low level descriptors. The benefits of the proposed method are threefold: first, the low-rank property is utilized to learn the underlying normal dictionaries, which can represent groups of similar normal features effectively; second, the sparsity-based algorithm can adaptively determine the number of dictionary bases, which makes it a preferable choice for representing the dynamic scene semantics; and third, based on the weighted sparse reconstruction method, the proposed method is more efficient for detecting the abnormal events. Experimental results on the public datasets have shown that the proposed method yields competitive performance comparing with the state-of-the-art methods.

Transfer orthogonal sparsifying transform learning for phase retrieval

The phase retrieval (PR) problem of recovering an image from its Fourier magnitudes is an important issue. Several PR algorithms have been proposed to address this problem. Recent efforts of exploiting sparsity were developed to improve the performance of PR algorithms, such as the reconstruction quality, robustness to noise, and convergence behavior. In this paper, we propose a novel sparsity-based algorithm, which can adaptively learn an orthogonal sparsifying transform, and reconstruct the image simultaneously from the Fourier magnitudes. However, the estimated images at the early iterations are extremely bad. Training samples from these images cannot provide much useful information for sparsifying transform learning. To avoid unnecessary updating, an orthogonal sparsifying transform learning method based on transfer learning is proposed. Through transfer learning, we transfer the fixed sparsifying transform to an adaptive one. We apply this new sparsifying transform learning method to PR, and exploit the alternating directions method of multipliers (ADMM) technique to solve the formulated problem. Since the learnt sparsifying transform is adaptive to data, it favors better sparsity. Using this learnt sparsifying transform for image reconstruction can improve the reconstruction quality at low oversampling ratios. Experimental results show that the proposed PR algorithm can improve nearly 6 dB compared with the recently proposed PR-TIHP-l1 algorithm in terms of the average PSNR (Peak Signal to Noise Ratio) at oversampling ratio 2.47, 2.53, 2.59. Moreover, our algorithm is robust to noise and has better convergence behavior heuristically.

Hyperspectral Image Classification via Basic Thresholding Classifier

We propose a lightweight sparsity-based algorithm, namely, the basic thresholding classifier (BTC), for hyperspectral image (HSI) classification. BTC is a pixelwise classifier which uses only the spectral features of a given test pixel. It performs the classification using a predetermined dictionary consisting of labeled training pixels. It then produces the class label and residual vector of the test pixel. Since incorporating spatial and spectral information in HSI classification is quite an effective way of improving classification accuracy, we extend our proposal to a three-step spatial–spectral framework. First, every pixel of a given HSI is classified using BTC. The resulting residual vectors form a cube which could be interpreted as a stack of images representing residual maps. Second, each residual map is filtered using an averaging filter. Finally, the class label of each test pixel is determined based on minimal residual. Numerical results on public data sets show that our proposal outperforms well-known support vector machine-based techniques and sparsity-based greedy approaches like simultaneous orthogonal matching pursuit in terms of both classification accuracy and computational cost.

Reducing streak artifacts in computed tomography via sparse representation in coupled dictionaries.

Reducing the number of acquired projections is a simple and efficient way to reduce the radiation dose in computed tomography (CT). Unfortunately, this results in streak artifacts in the reconstructed images that can significantly reduce their diagnostic value. This paper presents a novel algorithm for suppressing these artifacts in 3D CT. The proposed algorithm is based on the sparse representation of small blocks of 3D CT images in learned overcomplete dictionaries. It learns two dictionaries, the first dictionary (D(a)) is for artifact-full images that have been reconstructed from a small number (approximately 100) of projections. The other dictionary (D(c)) is for clean artifact-free images. The core idea behind the proposed algorithm is to relate the representation coefficients of an artifact-full block in D(a) to the representation coefficients of the corresponding artifact-free block in D(c). The relation between these coefficients is modeled with a linear mapping. The two dictionaries and the linear relation between the coefficients are learned simultaneously from the training data. To remove the artifacts from a test image, small blocks are extracted from this image and their sparse representation is computed in D(a). The linear map is then used to compute the corresponding coefficients in D(c), which are then used to produce the artifact-suppressed blocks. The authors apply the proposed algorithm on real cone-beam CT images. Their results show that the proposed algorithm can effectively suppress the artifacts and substantially improve the quality of the reconstructed images. The images produced by the proposed algorithm have a higher quality than the images reconstructed by the FDK algorithm from twice as many projections. The proposed sparsity-based algorithm can be a valuable tool for postprocessing of CT images reconstructed from a small number of projections. Therefore, it has the potential to be an effective tool for low-dose CT.

Classification via ensembles of basic thresholding classifiers

The authors present a sparsity‐based algorithm, basic thresholding classifier (BTC), for classification applications which is capable of identifying test samples extremely rapidly and performing high classification accuracy. They introduce a sufficient identification condition (SIC) under which BTC can identify any test sample in the range space of a given dictionary. By using SIC, they develop a procedure which provides a guidance for the selection of threshold parameter. By exploiting rapid classification capability, they propose a fusion scheme in which individual BTC classifiers are combined to produce better classification results especially when very small number of features is used. Finally, they propose an efficient validation technique to reject invalid test samples. Numerical results in face identification domain show that BTC is a tempting alternative to sparsity‐based classification algorithms such as greedy orthogonal matching pursuit and l1‐minimisation.

Sparsity-based algorithm for detecting faults in rotating machines

This paper addresses the detection of periodic transients in vibration signals so as to detect faults in rotating machines. For this purpose, we present a method to estimate periodic-group-sparse signals in noise. The method is based on the formulation of a convex optimization problem. A fast iterative algorithm is given for its solution. A simulated signal is formulated to verify the performance of the proposed approach for periodic feature extraction. The detection performance of comparative methods is compared with that of the proposed approach via RMSE values and receiver operating characteristic (ROC) curves. Finally, the proposed approach is applied to single fault diagnosis of a locomotive bearing and compound faults diagnosis of motor bearings. The processed results show that the proposed approach can effectively detect and extract the useful features of bearing outer race and inner race defect.

Recursive Sparsity-based MVDR Algorithm for Interference Cancellation in Sensor Arrays

ABSTRACTIn this paper, an improved sparsity-based interference cancellation algorithm for beamforming in sensor arrays is proposed, which improves the conventional Minimum Variance Distortionless Response (MVDR) algorithms. The key point in this algorithm is to divide the stress on the minimum variance term in the conventional algorithms with a term that uses no additional information than those used in conventional algorithms. The goal in this algorithm is to find the sparsest array response in the angles other than the Direction Of Arrival (DOA) of the Signal Of Interest (SOI). Also, a global convergence proof for this algorithm is presented. The results show that by this algorithm, some reduction in sidelobe levels, deeper nulls, less sensitivity to the DOA of the SOI and no sensitivity to data length are achieved.

Information integration for ground-based cloud classification using joint consistent sparse coding in heterogeneous sensor network

Although sparsity-based algorithm has emerged as an extremely powerful tool for information integration, it neglects the relationship of heterogeneous features and coding coefficients from the same class in the training stage, which may cause declining of the classification performance. In this paper, we focus on information integration for ground-based cloud classification in heterogeneous sensor network (HSN), and propose a novel coding strategy named joint consistent sparse coding (JCSC) to overcome the drawbacks of traditional sparse coding. In order to integrate information effectively, we add a joint sparse regularization to learn the relationship of heterogeneous features. Moreover, we utilize the consistent constraint on coding coefficients. In this way, coding coefficients from the same class can be forced to their mean vector, and therefore they are more compact and discriminative. The experimental results demonstrate that our method achieves better performance than the state-of-the-art methods.

Direct Data Domain Sparsity-Based STAP Utilizing Subaperture Smoothing Techniques

We propose a novel direct data domain (D3) sparsity-based space-time adaptive processing (STAP) algorithm utilizing subaperture smoothing techniques for airborne radar applications. Different from either normal sparsity-based STAP or D3 sparsity-based STAP, the proposed algorithm firstly uses only the snapshot in the cell under test (CUT) to generate multiple subsnapshots by exploiting the space-time structure of the steering vector and the uncorrelated nature of the components of the interference covariance matrix. Since the interference spectrum is sparse in the whole angle-Doppler plane, by employing a sparse regularization, the generated multiple subsnapshots are jointly used to recover the interference spectrum. The interference covariance matrix is then estimated from the interference spectrum, followed by the space-time filtering and the target detection. Simulation results illustrate that the proposed algorithm outperforms the generalized forward/backward method, the conventional D3 least squares STAP algorithm, and the existing D3 sparsity-based STAP algorithm. Furthermore, compared with the normal sparsity-based STAP algorithm using multiple snapshots, the proposed algorithm can also avoid the performance degradation caused by discrete interferers merely appearing in the CUT.