A block orthogonal matching pursuit algorithm based on sensing dictionary

In this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block 𝐾-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of the nonzero elements of the block 𝐾-sparse signals, we prove that the support of the block 𝐾-sparse signals can be exactly recovered by the BOMP algorithm in the case of ℓ 2 \ell_{2} and ℓ 2 / ℓ ∞ \ell_{2}/\ell_{\infty} bounded total noise if 𝑨 satisfies the BRIP of order K + 1 K+1 with δ K + 1 < 1 K + 1 ⁢ ( 1 + ϵ A ( K + 1 ) ) 2 + 1 ( 1 + ϵ A ( K + 1 ) ) 2 - 1 . \delta_{K+1}<\frac{1}{\sqrt{K+1}(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}+\frac{1}{(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1. In addition, we also show that this is a sharp condition for exactly recovering any block 𝐾-sparse signal with the BOMP algorithm. Moreover, we also give the reconstruction upper bound of the error between the recovered block-sparse signal and the original block-sparse signal. In the noiseless and perturbed case, we also prove that the BOMP algorithm can exactly recover the block 𝐾-sparse signal under some constraints on the block 𝐾-sparse signal and δ K + 1 < 2 + 2 2 ⁢ ( 1 + ϵ A ( K + 1 ) ) 2 - 1 . \delta_{K+1}<\frac{2+\sqrt{2}}{2(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1. Finally, we compare the actual performance of perturbed OMP and perturbed BOMP algorithm in the numerical study. We also present some numerical experiments to verify the main theorem by using the completely perturbed BOMP algorithm.

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

In this paper, a block version of the orthogonal matching pursuit with thresholding algorithm is proposed. Compared with the block version of the orthogonal matching pursuit algorithm, the block orthogonal matching pursuit algorithm works in a less greedy fashion in order to improve support estimating efficiency in each iteration. The lower and upper bounds of the threshold are theoretical derived for exact recovering the block-sparse signal in noiseless environment. When the noise is bounded with unknown distribution, the algorithm can also estimate the support exactly under certain ssumptions. Experimental results are provided to illustrate the validity of our main results.

Spectrum sensing is an important task in Cognitive radio networks (CRN). In this paper, we focus on estimating wide band frequency spectrum using compressed sensing. In particular, we compare the spectrum estimation performance of greedy algorithms Orthogonal Matching Pursuit (OMP) and Block Orthogonal Matching Pursuit (BOMP) using compressed sensing. Our results show that the BOMP algorithm can outperform OMP in estimating sparse frequency spectrum if the exact frequency usage bands are known. For spectrum access in a dynamic environment where frequency subbands are not known apriori, we propose a greedy algorithm in this paper that recovers the frequency spectrum along with the subbands. Simulation results show that the spectrum estimation performance of the proposed algorithm lies in between OMP and BOMP algorithms.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

Sparse signal approximations have become a new tool in signal processing with wide ranging applications from source separation to signal acquisition. Recently, many algorithms for sparse signal reconstruction have been developed, however, greedy algorithms, such as Orthogonal Matching Pursuit algorithm, can have better performance than the other algorithms. Approximate orthogonal matching pursuit algorithms, such as gradient pursuit algorithm and conjugate gradient pursuit algorithm, can lead to fast approximations to Orthogonal Matching Pursuit. In this paper Newton pursuit algorithm for sparse signal reconstruction is proposed. The algorithm is a kind of directional pursuit algorithms with the same computational complexity compared to orthogonal matching pursuit algorithm, but it can have better performance than approximate orthogonal matching pursuit algorithms.

FOMP algorithm for Direction of Arrival estimation

Aiming at the problem of anomaly detection of hyperspectral imagery sub-pixel targets, this paper proposes a novel algorithm of kernel sparse representation. The key idea is that background pixels can be sparsely represented by their neighborhoods, whereas anomalous pixels cannot, and the algorithm can be solved by orthogonal matching pursuit algorithm. The algorithm introduced the kernel method to map the original data to high-dimensional space, and derived the kernel orthogonal matching pursuit(KOMP) algorithm to solve the pixel non-linear mixed problem. Through the introduction of sum to one constraint, the detection value of anomalous pixels and background pixels is increased, which is more conducive to detection. The regularization model is added to make the solution of kernel orthogonal matching pursuit algorithm more stable. Finally, this algorithm is compared with other algorithms on the actual hyperspectral data set, and achieved good results.

Acoustic emission(AE) dynamic monitoring of HRB400 welding specimens during tension process will collect a large number of mixed noise data, increasing the storage space and transmission time of data. And the sparsity of the signal changes with the change of ambient noise, which affects the reconstruction performance of the orthogonal matching pursuit (OMP) algorithm under fixed sparse degree. An adaptive threshold piecewise weak orthogonal matching pursuit (SWOMP) algorithm is proposed to reconstruct the signal, which is solved the problem of data quantity and guarantees the quality of real-time monitoring and reconstruction. The simulation results show that the reconstruction error of SWOMP and OMP algorithm decreases with the increase of measurement value, and the reconstruction performance of SWOMP algorithm is obviously better than that of OMP algorithm. The reconstructed quality of OMP algorithm fluctuates greatly when reconstructing multi-segment signals, while the reconstructed error of SWOMP algorithm is stable at about 0.05, which can reconstruct signals effectively and has high adaptability.

Power-line noise is mainly comes from power systems and has become one of the most common noises during the acquisition of magnetotelluric (MT) signal, its components including a fundamental frequency signal and a lot of odd harmonics. There are trap circuits designed in most of the acquisition instruments to separate these noise, however, the fundamental frequency of the power line noise will fluctuate with the changing of load current, but the center frequency of the trap circuits are fixed, hence the MT data are still seriously disturbed by the power line noise. To mitigate the disturbance of power line noise, a novel denoising method was proposed based on orthogonal matching pursuit (OMP) algorithm. Semisynthetic experiments and real data obtained from Lu-Zong ore-concentration district illustrate that the proposed method can effectively suppress the power line noise while remain the useful MT signal, the apparent resistivity and phase curves are greatly improved over previous.

A methodology for automatic incipient broken rotor bar detection in induction motors (IMs) is presented. Sparse representations of signals are applied as a diagnosis technique. The novelty of this technique is that it can analyze the frequency spectra from vibration signals even when the differences among signals are small. This representation allows decomposing or reconstructing signals through a trained dictionary that has learned the features of one specific group/class. The main feature of this paper is the use of over-complete dictionaries trained from sets of signals with faults to be detected. In this way, trained dictionaries perform the decomposition of signals using the orthogonal matching pursuit (OMP) algorithm. The decomposition is evaluated and classified by error-based criteria and a majority decision classifier, allowing the detection of early damage, ranging from 1 mm to one broken bar. The detection is performed by the decomposition of vibration signals from three axes (x, y, and z) of IMs under three load conditions (unloaded, half loaded, and three-fourths loaded) and different levels of damage (healthy or 0 mm, 1-9 mm, and one broken bar). These signals are processed by the Fourier transform and the spectrum obtained is evaluated by the OMP algorithm. Finally, the retrieved information is evaluated and the diagnosis is given. All algorithms are developed in MATLAB software and the detection accuracy is higher than 90% for damages as small as 1 mm.

For the millimeter wave (mmWave) time-varying system, beamforming poses a formidable challenge for huge power overhead. In this paper, an adaptive step-size prediction joint orthogonal matching pursuit (OMP) algorithm (ASP-OMP), is proposed for beam tracking. With the direction of arrival (DOA) information obtained by OMP algorithm, kalman filter is used to predict the beamforming vector during N time slots to avoid huge sampling loss. In addition, we propose to determine the prediction step-size with outlier identification and eliminate the beam tracking error through data fusion based on Bayesian estimation. The simulation results demonstrate that the proposed algorithm can converge quickly and have a good performance for mmWave beam tracking.

This brief presents a new variant of the orthogonal matching pursuit (OMP) algorithm for reducing the computational complexity of the digital predistortion (DPD) behavioral model in the forward path. The proposed spectral weighting OMP (SW-OMP) algorithm focuses on selecting the most relevant basis functions to compensate for the out-of-band residual distortion which may eventually be masked by the dominant in-band residual error. This basis selection is carried out in an off-line process that does not affect the computational complexity of the real-time closed-loop DPD but, on the contrary, reduces its complexity while enhancing the robustness. Experimental results show that by selecting the DPD coefficients with the SW-OMP, the inherent ACLR and NMSE degradation suffered when reducing the number of coefficients is mitigated under strong nonlinear operation, when compared to using the basis functions selected by the classical OMP algorithm.