Orthogonal Matching Pursuit Method Research Articles

Sparse-Bayesian-Learning-Based Wideband Spectrum Sensing With Simplified Modulated Wideband Converter

Wideband spectrum sensing is an important aspect of cognitive radio systems. In current models of wide spectrum sensing, a discrete frequency denotes a continuous frequency band. This type of model is divorced from practice and cannot reflect the reality of spectrum occupation. In this paper, we propose a novel wideband spectrum sensing scheme in terms of a modulated wideband converter (MWC) and sparse Bayesian learning (SBL). By exploiting the MWC, a practical wideband signal denoted by a block-sparse model is sampled to acquire the compressed measurements. We then employ SBL to directly extract the relevant information from the compressed measurements for estimating the support set. The estimated support set is chosen as the test statistic to facilitate spectrum sensing and analyze the detection performance. For applications in actual situations of support sets, different matching criteria are presented according to the requirements imposed by wideband spectrum sensing. Finally, we analyze the detection performance when a frequency band’s location is given as well as when it is randomly generated by conducting simulations. These simulations show that the proposed method outperforms the MWC-based orthogonal matching pursuit method, and the best performance can be achieved under matching criterion 3.

Parametric Sparse SAR Imaging of Ground Moving Targets Integrated With Motion Compensation

Using the array technique, the multi-channel synthetic aperture radar (SAR) has the capability of high-resolution imaging, detection, and location of the ground moving targets, which is a powerful tool during the remote sensing of smart city. Recently, the theory of compressive sensing has been applied to radar imaging with data of compressive sampling, which can effectively reduce the burden of current radar system. In this paper, we focus on SAR moving targets imaging from sparse aperture (SA) data with accurate target motion compensation. The procedure of motion compensation is decomposed into two steps: the SPECAN processing in the range frequency and azimuth time domain is first applied and then followed by the residue component correction embedded into sparse imaging. To overcome the SA and target motion, a novel parametric sparse imaging approach is proposed by addressing the problems of Doppler ambiguity and phase errors. In the scheme, a parametric and dynamic dictionary is used to include these two important issues. Then, a modified orthogonal matching pursuit method is presented for high-quality imaging with Doppler ambiguity number estimation and phase error correction, which can deal with the case of multiple moving targets. Finally, experimental analysis is performed to confirm the effectiveness of the proposed algorithm.

Pulsar time delay estimation method based on two-level compressed sensing

In the traditional compressed sensing algorithms, the precision of the time delay estimation is closely related to the number of atoms in the dictionary. The bigger the atom number, the smaller the atomic interval becomes, thus the higher the accuracy of the time delay estimation will be. However, the bigger atom number leads to a higher calculation load. Considering the limited calculation capacity of on-board computer, in order to fast obtain high-accuracy time delay estimation value of the integrated pulsar profile of pulsar in the X-ray pulsar-based navigation, we propose a time delay estimation method based on two-level compression sensing. Compressed sensing mainly includes three parts:the dictionary, the measurement matrix, and the recovery algorithm. Among them, the dictionary size is one of the most important factors that affect the estimation accuracy of the compressed sensing. Aiming to solve the problem of the greater computational load with the increase of the atom number in the dictionary of compressed sensing while improving the accuracy of estimation, we combine the rough estimation with the precision estimation as a two-level dictionary. In the first level, the global phase estimation of the low-dimensional integrated pulsar profile is carried out by making use of the feature of the large atomic interval and the small atomic amount of the rough estimation dictionary. Specifically, first, construct a coarse estimation dictionary according to the low-dimensional standard pulsar profile. Then make dimension reduction sampling on the low-dimensional integrated pulsar profile by the rough estimation measurement matrix based on low-dimensional Hadamard matrix. Finally, use an orthogonal matching pursuit method to obtain the predictive estimation of delay value. In the second level, by taking advantage of the small atomic intervals and numbers of the precise estimation dictionary which are suitable for local estimation, the exact time delay estimation of the high dimensional integrated pulsar profile is performed. Specifically, the original position is first corrected by using the predictive estimation of time delay value, that is, shifting the initial high-dimensional integrated pulsar profile as the input signal of the second level. Then the precise estimation dictionary is constructed according to the partial signal of the length of the high dimension standard pulse profile, using the precise estimation measurement matrix sampling on high-dimensional integrated pulsar profile to obtain measurement value. Finally, the optimal matching position is obtained through the recovery algorithm, which is then combined with the predictive estimation of delay value to calculate the prcis time delay estimation value. Theoretical analysis and experimental results show that the quantity of data in the two level dictionary is two orders of magnitude smaller than in the traditional dictionary. The proposed method reduces the computational complexity greatly compared with traditional compression sensing method in the same time delay estimation accuracy. Therefore, this method has the advantages of high precision and small calculation load.

FOMP algorithm for Direction of Arrival estimation

Adaptive antennas and antenna array processing are much significant issues for improving the performance of wireless communication systems. One of the most important applications of adaptive antenna systems is the Direction of Arrival (DOA) estimation. Recently, compressive sensing algorithms, including convex relaxation methods and greedy algorithms, have been recognized as a type of novel DOA estimation methods. The Orthogonal Matching Pursuit (OMP) is an example of compressive sensing methods. Using the OMP method for DOA estimation has many advantages in comparison to other algorithms. In spite of these advantages, the DOA estimation by OMP algorithm has a substantial challenge. The OMP algorithm cannot distinguish between two adjacent signal sources. In the DOA estimation by OMP algorithm, when there are two adjacent sources, the mutual coherent condition of the compressive sensing methods is violated. The situation gets worse when there are two sources from two adjacent DOAs. In this situation, the beam former has a single peak. In this paper, we propose the Focused Orthogonal Matching Pursuit (FOMP) algorithm for estimation of DOA. The FOMP algorithm is an improved version of the OMP algorithm. It can detect two signal sources exactly when they are very close and beam former has a single peak corresponding to a direction between right directions. Simulation results demonstrate the advantages of the proposed scheme. It can be observed the FOMP algorithm could detect very close signal sources with a negligible error.

Compressive Sensing and Reconstruction of Crop Growth Environmental Information

The crop growth environmental information in farmland such as temperature and humidity has a gentle variation amplitude in a certain time or space domain, and is sparse in the discrete cosine transform domain. Based on compression sensing, we construct the approach to crop growth environmental information monitoring. The reconstruction error for crop growth environmental information is validated through the simulation experiment. By exploiting orthogonal matching pursuit method, it is found that the reconstructed environmental information data are consistent with the measured data.

Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method

This article investigates parameter and order identification of a block-oriented Hammerstein system by using the orthogonal matching pursuit method in the compressive sensing theory which deals with how to recover a sparse signal in a known basis with a linear measurement model and a small set of linear measurements. The idea is to parameterize the Hammerstein system into the linear measurement model containing a measurement matrix with some unknown variables and a sparse parameter vector by using the key variable separation principle, then an auxiliary model based orthogonal matching pursuit algorithm is presented to recover the sparse vector. The standard orthogonal matching pursuit algorithm with a known measurement matrix is a popular recovery strategy by picking the supporting basis and the corresponding non-zero element of a sparse signal in a greedy fashion. In contrast to this, the auxiliary model based orthogonal matching pursuit algorithm has unknown variables in the measurement matrix. For a K-sparse signal, the standard orthogonal matching pursuit algorithm takes a fixed number of K stages to pick K columns (atoms) in the measurement matrix, while the auxiliary model based orthogonal matching pursuit algorithm takes steps larger than K to pick K atoms in the measurement matrix with the process of picking and deleting atoms, due to the gradually accurate estimates of the unknown variables step by step. The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.

Incipient Fault Diagnosis of Rolling Bearings Based on Impulse-Step Impact Dictionary and Re-Weighted Minimizing Nonconvex Penalty Lq Regular Technique

The periodical transient impulses caused by localized faults are sensitive and important characteristic information for rotating machinery fault diagnosis. However, it is very difficult to accurately extract transient impulses at the incipient fault stage because the fault impulse features are rather weak and always corrupted by heavy background noise. In this paper, a new transient impulse extraction methodology is proposed based on impulse-step dictionary and re-weighted minimizing nonconvex penalty Lq regular (R-WMNPLq, q = 0.5) for the incipient fault diagnosis of rolling bearings. Prior to the sparse representation, the original vibration signal is preprocessed by the variational mode decomposition (VMD) technique. Due to the physical mechanism of periodic double impacts, including step-like and impulse-like impacts, an impulse-step impact dictionary atom could be designed to match the natural waveform structure of vibration signals. On the other hand, the traditional sparse reconstruction approaches such as orthogonal matching pursuit (OMP), L1-norm regularization treat all vibration signal values equally and thus ignore the fact that the vibration peak value may have more useful information about periodical transient impulses and should be preserved at a larger weight value. Therefore, penalty and smoothing parameters are introduced on the reconstructed model to guarantee the reasonable distribution consistence of peak vibration values. Lastly, the proposed technique is applied to accelerated lifetime testing of rolling bearings, where it achieves a more noticeable and higher diagnostic accuracy compared with OMP, L1-norm regularization and traditional spectral Kurtogram (SK) method.

Feature extraction of vibration signal using OMP-NWE method

Feature extraction is one of the core problems in condition monitoring and fault diagnosis of mechanical equipment. In this study, an OMP-NWE method of feature extraction is proposed, aiming at the problem of low accuracy of existing feature extraction method. The OMP-NWE method integrates the strengths of orthogonal matching pursuit (OMP) algorithm with the benefits of nonparametric waveform estimation (NWE). Signal feature extraction model is constructed by design of filter bank and adaptive template signal. Then the vibration signal is linearly decomposed into a set of best matching waveform, which solves the problem that the basis function must be chosen in advance in OMP algorithm. The OMP-NWE method is applied to the feature extraction of the simulation and experimental vibration signal of rolling bearing, compared with the traditional OMP algorithm. Results show that the SNR of the extracted feature signal using OMP-NWE method increased by 19.22 % compared with that using the OMP method, which illustrates that OMP-NWE method has a higher accuracy in the feature extraction of unknown complex vibration signals. This work provides a new idea and a successful example for the feature extraction of vibration signal in the condition monitoring and fault diagnosis of mechanical equipment.

A novel threshold based compressed channel sensing in OFDM system

High speed data transmission for wireless communication in orthogonal frequency division multiplexing (OFDM) system requires effective channel state information (CSI). CSI should be precisely estimated with low consumption of spectral resources and acceptable computational cost. To realize this goal, an effective compressed sensing (CS) based channel estimation scheme is proposed for sparse channels with large delay spreads, without prior knowledge of channel statistics and noise standard deviation. By fully considering the rank of the measurement matrix, a novel algorithm based on orthogonal matching pursuit (OMP) and least squares (LS) methods with a new threshold is proposed for effective channel estimation. Simulation results show that with fewer number of pilots, the proposed method outperforms the compared existing channel estimation methods in a comprehensive way and approaches the optimal channel estimation performance.

Real-time characterization of FM-AM modulation in a high-power laser facility using an RF-photonics system and a denoising algorithm

FM-AM modulation of high-power lasers significantly affects laser performance. Therefore, precise measurement of the FM-AM modulation depth is necessary. The subsequent FM-AM modulation generated by group velocity dispersion when the laser pulse propagates through a fiber affects the measurement accuracy. In order to eliminate this effect, a waveform-acquisition module is proposed that converts a broad-spectrum pulse of 1053 nm to a narrow-spectrum pulse of 1550 nm, without affecting the waveform. In addition, a signal-processing algorithm based on the orthogonal matching pursuit method is implemented to remove the sampling noise from the waveform. In this way, the signal-to-noise ratio of the measurement can be readily improved. Both theoretical and experimental results indicate that the proposed FM-AM modulation detection system is effective and economical. It can measure the FM-AM modulation depth precisely, and therefore shows considerable promise for future applications in high-power lasers.

DEM Estimation for LASAR Based on Variational Model

This paper discusses the digital elevation model (DEM) estimation problem for the linear array synthetic aperture radar based on the variational model. Compared with the sparse recovery model, the one-to-one mapping between the horizontal grid nodes and the elevations is preserved explicitly, which is important for the topographic surveying and mapping mission. During the research, we find that since the mean square error criterion is insensitive to the amount of the elevation offsets, the numerical method by solving the Euler-Lagrange equation is unreliable and the global optimization method is necessary to solve the variational problem. With the ambiguity function localization and the sliding-window architecture, the global optimal path can be obtained by solving a series of local optimization problems provided that the observation matrix is row full rank. Furthermore, the local optimization problem can be relaxed as a sparse recovery problem and can be solved by a modified orthogonal matching pursuit (OMP) method (named as Var-OMP), whose computational cost is acceptable for the actual data processing. By a series of numerical experiments, we show that the performance of Var-OMP is influenced by both the resolution enhancement factor (L) and the signal-to-noise ratio (SNR). The larger the SNR is, the better the performance is; the smaller L is, the more stable and faster the Var-OMP algorithm is. Compared with the sparse recovery methods, the variational model and the Var-OMP algorithm are more suitable for the DEM estimation application in the face of all kinds of terrains.

A New Generalized Orthogonal Matching Pursuit Method

To improve the reconstruction performance of the generalized orthogonal matching pursuit, an improved method is proposed. Columns are selected from the sensing matrix by generalized orthogonal matching pursuit, and indices of the columns are added to the estimated support set to reconstruct a sparse signal. Those columns contain error columns that can reduce the reconstruction performance. Therefore, the proposed algorithm adds a backtracking process to remove the low-reliability columns from the selected column set. For any k-sparse signal, the proposed method firstly computes the correlation between the columns of the sensing matrix and the residual vector and then selects s columns that correspond to the s largest correlation in magnitude and adds their indices to the estimated support set in each iteration. Secondly, the proposed algorithm projects the measurements onto the space that consists of those selected columns and calculates the projection coefficient vector. When the size of the support set is larger than k, the proposed method will select k high-reliability indices using a search strategy from the support set. Finally, the proposed method updates the estimated support set using the selected k high-reliability indices. The simulation results demonstrate that the proposed algorithm has a better recovery performance.

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound.

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal as a linear superposition of as few spectral components as possible, without affecting the quality of the reproduction. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the fast Fourier transform. The achieved sparsity is theoretically equivalent to that rendered by the orthogonal matching pursuit (OMP) method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard OMP algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral representation is illustrated by comparison with the traditional method, in the line of the short time Fourier transform, involving only the corresponding orthonormal trigonometric basis.

Vandermonde transform for complex residual based on complex speech analysis

Vandermonde transform using the orthogonal basis is a time-frequency transform method that can describe a speech and audio signal to be uncorrelated and sparse, and can be considered to be also effective in speech processing. In particular, when applied to the residual considered to be effective in a pitch estimation of speech and speaker recognition. On the other hand, we have already proposed Time-Varying Complex AR (TV-CAR) speech analysis for an analytic signal. The TV-CAR analysis can improve spectral estimation accuracy in the low frequencies and it can estimate the complex AR coefficients for each sample. As a result, in the estimated complex residual signal, formant components are more subtracted from speech signal. It can perform better on pitch estimation, or so on. In this paper, we evaluated the time-frequency analysis using the Vandermonde transform based on an Orthogonal Matching Pursuit (OMP) method of the literature using the complex AR residual. The performance is evaluated for several orthogonal basis such as Fourier basis, Cos basis, K-L transform, and Gabor basis. Furthermore, the Ramanujan-sum is also introduced as the basis function to realize time-frequency transform.

On the reconstruction of derivative sampling method of band-limited signal

In this paper, the reconstruction methods of the derivative sampling methods of bandlimited signals are presented. First, the conventional Nyquist uniform sampling method and the derivative sampling method are reviewed briefly. Then, the reconstruction filters are designed by converting the analog filter bank structure in derivative sampling method to an equivalent discrete-time filter bank structure preceded by Nyquist uniform sampling and followed by impulse modulation and lowpass filtering. Next, the first-order derivative sampling method is extended to fractional-order derivative sampling method and the designs of its reconstruction filter bank are also studied. To reduce the implementation complexity, the orthogonal matching pursuit method is used to design the sparse digital filter bank in the proposed reconstruction structure. Finally, some numerical examples are used to show the effectiveness of the proposed reconstruction methods of the derivative sampling schemes.

Robust Online Object Tracking with a Structured Sparse Representation Model

As one of the most important issues in computer vision and image processing, online object tracking plays a key role in numerous areas of research and in many real applications. In this study, we present a novel tracking method based on the proposed structured sparse representation model, in which the tracked object is assumed to be sparsely represented by a set of object and background templates. The contributions of this work are threefold. First, the structure information of all the candidate samples is utilized by a joint sparse representation model, where the representation coefficients of these candidates are promoted to share the same sparse patterns. This representation model can be effectively solved by the simultaneous orthogonal matching pursuit method. In addition, we develop a tracking algorithm based on the proposed representation model, a discriminative candidate selection scheme, and a simple model updating method. Finally, we conduct numerous experiments on several challenging video clips to evaluate the proposed tracker in comparison with various state-of-the-art tracking algorithms. Both qualitative and quantitative evaluations on a number of challenging video clips show that our tracker achieves better performance than the other state-of-the-art methods.

Pseudo-inverses of difference matrices and their application to sparse signal approximation

We derive new explicit expressions for the components of Moore–Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial differential equations. The columns of the Moore–Penrose inverse then serve as elements of a dictionary that allow a sparse signal approximation. In order to find a set of suitable data points for signal representation we apply the orthogonal matching pursuit (OMP) method.

Design of Wideband Fractional-Order Differentiator Using Interlaced Sampling Method

In this paper, the design of a wideband digital fractional-order differentiator (FOD) is investigated. First, conventional FOD designs are reviewed, and the reconstruction formula of the interlaced sampling method is used to design the proposed wideband FOD by index substitution and the Grunwald---Letnikov fractional derivative. Because a closed-form window design is obtained, the filter coefficients are easily computed. Then, the weighted least squares and convex optimization methods are applied to design non-sparse digital FODs that are optimal in the least squares or min---max sense. Next, the iterative hard thresholding and orthogonal matching pursuit methods are used to design sparse digital FODs to reduce the implementation complexity. Finally, several numerical examples are presented to show that the proposed FODs have smaller design errors in the high-frequency band than conventional digital FODs that do not use the auxiliary interlaced sampling signal.

Wideband digital fractional Hilbert transformer designs based on interlaced and derivative sampling methods

In this paper, the design of wideband digital fractional Hilbert transformer (FHT) is presented. First, the wideband digital FHT is designed by using the reconstruction formula of interlaced sampling method and derivative sampling method. The closed-form design is obtained, so the filter coefficients are easily calculated. Then, the Lp-norm minimization method is applied to design digital wideband FHT whose solution can be obtained by using convex optimization tool. Next, the orthogonal matching pursuit method is used to design sparse digital FHT for reducing arithmetic complexity. Finally, several examples are demonstrated to show that the proposed FHT has smaller design error in high frequency band than the conventional digital FHT.

<inline-formula> <tex-math notation="LaTeX">$\ell _{p}$ </tex-math></inline-formula>-Regularized Least Squares <inline-formula> <tex-math notation="LaTeX">$(0<p<1)$ </tex-math></inline-formula> and Critical Path

This paper elucidates the underlying structures of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -regularized least squares problems in the nonconvex case of 0 <; p <; 1. The difference between two formulations is highlighted (which does not occur in the convex case of p = 1): 1) an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -constrained optimization (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ) and 2) an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -penalized (unconstrained) optimization (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ). It is shown that the solution path of (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ) is discontinuous and also a part of the solution path of (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ). As an alternative to the solution path, a critical path is considered, which is a maximal continuous curve consisting of critical points. Critical paths are piecewise smooth, as can be seen from the viewpoint of the variational method, and generally contain non-optimal points, such as saddle points and local maxima as well as global/local minima. Our study reveals multiplicity (non-monotonicity) in the correspondence between the regularization parameters of (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ) and (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> ). Two particular paths of critical points connecting the origin and an ordinary least squares (OLS) solution are studied further. One is a main path starting at an OLS solution, and the other is a greedy path starting at the origin. Part of the greedy path can be constructed with a generalized Minkowskian gradient. This paper of greedy path leads to a nontrivial close-link between the optimization problem of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -regularized least squares and the greedy method of orthogonal matching pursuit.