Forward Backward Pursuit Research Articles

Adaptive stepsize forward–backward pursuit and acoustic emission-based health state assessment of high-speed train bearings

Compressed sensing (CS) is a promising tool for data compression reconstruction. However, fault diagnosis methods for high-speed train bearings based on CS and acoustic emission (AE) technologies have not been reported yet. Notably, the accuracy and speed of CS two-stage reconstruction methods are affected and restricted by prior initial conditions. Therefore, this article proposes adaptive dynamic thresholds applicable to adaptive stepsize forward–backward pursuit (ASFBP), and bearing health state assessment method. First, the adaptive dynamic thresholds for atom selection and deletion are constructed based on the residual feedback mechanism and the atom quality distribution law, which enables ASFBP to realize high-precision rapid reconstruction of signal without any atom priori initial conditions. Second, the initial dictionary length is improved based on the AE hit characteristics. Furthermore, a damage state comprehensive evaluation index (DSCEI) is established using principal component analysis based on AE time-domain hit parameters and compression-domain energy parameter. Compared with the kurtosis index and permutation entropy index, the DSCEI demonstrates better monotonicity and stability in the quantitative evaluation of high-speed train bearing condition. Finally, the validity and stability of the method are verified by testing under complex test conditions resembling actual high-speed train lines, providing valuable insights for the CS-based data-driven bearing fault diagnosis.

High-precision bearing signal recovery based on signal fusion and variable stepsize forward-backward pursuit

In multi-sensor, long-distance fault monitoring of rolling bearings, the bearing signals are compressively sampled, transmitted, and reconstructed according to the theory of compressive sensing. However, the reconstruction accuracy and speed are limited and are affected by the noise afflicting the collected signals. In this paper, a high-precision signal recovery method, based on signal fusion and the variable stepsize forward–backward pursuit (VSFBP) algorithm, is proposed. First, the method adaptively adjusts the best estimate of the traditional random weighted fusion algorithm, by using the relative fluctuation value, which can fuse variable signals and reduce the noise component of the detection signal. Second, two fuzzy parameters are used to control the step sizes of the atom selection and deletion in the two-stage matching pursuit algorithm; this improves the reconstruction accuracy and speed of the algorithm under a high compression ratio. Finally, to prevent excessive backtracking, in the two-stage matching pursuit algorithm, the observation matrix is updated after each iteration, which improves the reconstruction accuracy of the algorithm further. Simulation and experimental results are compared to verify the effectiveness of the proposed method.

Long-Term Channel Statistic Estimation for Highly-Mobile Hybrid MmWave Multi-User MIMO Systems

Channel estimation is crucial to beamforming techniques in directional millimetre wave (mmWave) communications, which is generally designed based on channel state information static. However, due to the Doppler effect caused by the mobility of users, such as unmanned aerial vehicles, high-speed trains and autonomous vehicles, the mmWave channel is changing rapidly. Spatial channel covariance, defined by long-term statistic information of channels, is a promising solution to reduce channel estimation frequency and can be used to design hybrid precoders. In this paper, we first proposed a highly mobile hybrid mmWave multi-user (MU) multiple input multiple output (MIMO) system based on transition probabilities which can represent moving action of the MU. Secondly, we investigate compressive sensing based spatial channel covariance estimation based on the proposed dynamic system. We then propose a dynamic covariance forward-backward pursuit (DCFBP) algorithm which introduces forward and backward mechanisms to reconstruct the Hermitian sparse covariance matrix. We further explore the constructed MU sensing matrix quality for conventional sparse Bayesian learning (SBL) framework. The updated sparse Bayesian learning (Updated-SBL) algorithm is developed to reduce the total squared coherence of a constructed sensing matrix with updated receive precoder. Numerical analysis demonstrates the proposed DCFBP method outperforms the benchmark methods. The total squared coherence of the proposed Updated-SBL algorithm is dramatically reduced. and the superiority of this algorithm is validated compared with other benchmark methods with comparable computation complexity.

Iterative Selection and Correction Based Adaptive Greedy Algorithm for Compressive Sensing Reconstruction

Compressive sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. Therefore in this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward–Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms, as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. To evaluate the AFB’s reconstruction performance, we used two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward–Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.

Iterative selection and correction based adaptive greedy algorithm for compressive sensing reconstruction

Compressive Sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. A lot of researches have been proposed to address this challenge, however most of the existing techniques start with the same forward step which does not provide the best reconstruction performance. In this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward-Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. We evaluated the AFB’s reconstruction performance using two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward-Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.

Improved adaptive forward-backward matching pursuit algorithm to compressed sensing signal recovery

As a novel two-stage greedy approximation algorithm, Forward-Backward Pursuit (FBP) algorithm attracts wide attention because of its high reconstruction accuracy and no need for sparsity as a priori information. However, the FBP algorithm has to spend much more time to get a higher accuracy. In view of this, an Improved Adaptive Forward-Backward Matching Pursuit (IAFBP) algorithm is proposed in this paper. In the forward stage, the IAFBP algorithm uses an adaptive threshold to select the appropriate number of atoms into support set, so that the number of selected atoms is more random. In the backward stage, the projection coefficient of the atoms is taken as the basis of rejection, and the deletion threshold is introduced to reject the atoms adaptively, so that more right atoms are retained in each iteration and the reconstruction speed can be accelerated. At the same time, it overcomes the excessive backtracking phenomenon existing in the adaptive process and improves the accuracy of the algorithm. The simulation results of one-dimensional sparse signals and two-dimensional images show that the IAFBP algorithm has more advantages than the FBP algorithm in reconstruction performance and computational time.

Massive MIMO-OFDM Channel Estimation via Distributed Compressed Sensing

Massive multiple-input multiple-output orthogonal frequency division multiplexing (mMIMO-OFDM) channel estimation is considered recently utilizing compressed sensing (CS) based methods. Here, we proposed to use the joint sparsity of mMIMO-OFDM channels using stage-wise forward backward pursuit (StFBP) algorithm. In order to increase the speed of convergence and accuracy of estimation, we proposed to gather multiple good atoms in each step and to exploit common sparsity in the system model, respectively. Furthermore, the backward steps improve the accuracy by omitting bad previously gathered atoms. Simulation results represent the superiority of the proposed StFBP approach rather than the conventional CS-based and non-CS-based approaches.

Quaternion-Based Sparse Model for Pan-Sharpening of IRS Satellite Images

This paper considers the pan-sharpening problem of the IRS satellite images from the perspective of vector sparse representation model using quaternion matrix analysis. It selects the sparse basis in quaternion space, which uniformly transforms the color channels into an orthogonal color space. Moreover, the proposed quaternion model for pan-sharpening is more efficient than the conventional sparse model as the hyper-complex representation of color channels conserves the interrelationship among the chromatic channels. This paper also proposes a quaternion forward–backward pursuit algorithm that preserves the inherent chromatic structures in terms of spatial and spectral details during the vector reconstruction. The experimental result validates the efficacy of the proposed quaternion model and shows its potential as a powerful pan-sharpening tool for IRS data even for cloudy multispectral data.

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

In solving the partial Fourier Multiple Measurement Vectors (FMMV) problem, existing greedy pursuit algorithms such as Simultaneous Orthogonal Matching Pursuit (SOMP), Simultaneous Subspace Pursuit (SSP), Hybrid Matching Pursuit (HMP), and Forward-Backward Pursuit (FBP) suffer from low recovery ability or need sparsity as a prior information. This paper combines SOMP and FBP to propose a Hybrid Orthogonal Forward-Backward Pursuit (HOFBP) algorithm. As an iterative algorithm, each iteration of HOFBP consists of two stages. In the first stage, α indices selected by SOMP are added to the support set. In the second stage, the support set is shrank by removing β indices. The choice of α and β is critical to the performance of this algorithm. The simulation results showed that, by using proper parameters, HOFBP has better performance than other greedy pursuit algorithms at the expense of more computing time in some cases. HOFBP does not need sparsity as a prior knowledge.

Fusion Forward–Backward Pursuit Algorithm for Compressed Sensing

The Forward–Backward Pursuit (FBP), which is a recently proposed method, receives wide attention due to the high reconstruction accuracy. In this paper, we use the fusion strategy and propose the Fusion Forward–Backward Pursuit (FFBP) algorithm. This strategy only needs the reconstruction information of two FBP with different parameters. According to the termination conditions of the FBP algorithm, FFBP adopts different operation strategies, during the signal reconstruction. Without other priori information, FFBP effectively improves the exact reconstruction rate, compared with the original algorithm. Moreover, FFBP, which fuses two FBP with non-optimal parameter, can reconstruct a better signal than a single FBP with optimal parameter. We demonstrate the advantage of the proposed method through numerical simulations.

Forward-Backward Synergistic Acceleration Pursuit Algorithm Based on Compressed Sensing

We propose the Forward-Backward Synergistic Acceleration Pursuit (FBSAP) algorithm in this paper. The FBSAP algorithm inherits the advantages of the Forward-Backward Pursuit (FBP) algorithm, which has high success rate of reconstruction and does not necessitate the sparsity level as a priori condition. Moreover, it solves the problem of FBP that the atom can be selected only by the fixed step size. By mining the correlation between candidate atoms and residuals, we innovatively propose the forward acceleration strategy to adjust the forward step size adaptively and reduce the computation. Meanwhile, we accelerate the algorithm further in backward step by fusing the strategy proposed in Acceleration Forward-Backward Pursuit (AFBP) algorithm. The experimental simulation results demonstrate that FBSAP can greatly reduce the running time of the algorithm while guaranteeing the success rate in contrast to FBP and AFBP.

Improvement of Forward-Backward Pursuit Algorithm Based on Weak Selection

Forward-backward pursuit (FBP) algorithm is a novel two-stage greedy approach. However once its forward and backward steps were determined during iteration, it would make computing time increased and affected the reconstruction efficiency. This paper presents a algorithm called forward-backward pursuit algorithm based on weak selection (SWFBP) by introducing threshold strategy into FBP algorithm, and in view of that in the first few iterations, most of the atoms which are selected are right, so this part of atoms are directly incorporated into support set instead of using backward strategy to reduce them. Flexible forward and backward steps accelerate the speed of atom selecting and improve the reconstruction accuracy. We compared SWFBP and FBP algorithm via one-dimensional signal and two-dimensional image reconstruction experiments. The simulation results demonstrate that compared with FBP, SWFBP algorithm has superior performance, including higher PSNR, faster computing speed and lower recovery time.

Forward-backward pursuit method for distributed compressed sensing

In this paper, a forward-backward pursuit method for distributed compressed sensing (DCSFBP) is proposed. In contrast to existing distributed compressed sensing (DCS), it is an adaptive iterative approach where each iteration consists of consecutive forward selection and backward removal stages. And it not needs sparsity as prior knowledge and multiple indices are identified at each iteration for recovery. These make it a potential candidate for many practical applications, when the sparsity of signals is not available. Numerical experiments, including recovery of random sparse signals with different nonzero coefficient distributions in many scenarios, in addition to the recovery of sparse image and the real-life electrocardiography (ECG) data, are conducted to demonstrate the validity and high performance of the proposed algorithm, as compared to other existing DCS algorithms.

Data-Driven Forward–Backward Pursuit for Sparse Signal Reconstruction

In recent years, compressed sensing has received considerable attention from the signal processing community because of its ability to represent sparse signals with a number of samples much less than that is required by the Nyquist sampling theorem. $$\ell _{1}$$l1-minimization is a powerful tool for sparse signal reconstruction from few measured samples, but its computational complexity is a burden for real applications. Recently, a number of greedy algorithms based on orthogonal matching pursuit (OMP) have been proposed, and they have near $$\ell _{1}$$l1-minimization performance with much less processing time. In this work, a new OMP-type two-stage sparse signal reconstruction algorithm, namely data-driven forward---backward pursuit (DD-FBP), is proposed. It is based on a former work called forward---backward pursuit (FBP). DD-FBP iteratively expands and shrinks the estimated support set, and these constitute the forward and backward stages. In DD-FBP, unlike FBP, the forward and backward step sizes are not constants, but they are dependent on the correlation and projection values, respectively, which are calculated in each iteration. The recovery performance by using noiseless and noisy sparse signal ensembles, as well as a natural sparse image, indicates that DD-FBP surpasses the other methods in terms of success rate and processing time.

Forward-backward pursuit algorithm for Cerenkov luminescence tomography.

Cerenkov luminescence tomography (CLT) is a powerful imaging technique that allows dynamically and three-dimensionally resolving the metabolic process of radiopharmaceuticals. It uses optical method to detect radiopharmaceuticals with low cost and high sensitivity. However, because of the strong absorption and scatter of biological tissues, the reconstruction of CLT is always converted to an ill-posed linear system which is hard to solve. An accurate and fast reconstruct algorithm becomes a current issue. The traditional reconstruction algorithm based on l2 norm regularization is too smooth and with low accuracy. Some novel sparse reconstruction algorithm has satisfying accuracy and convergence rate, but lose its accuracy for multi-source situation. In this work, a novel CLT method based on forward-backward greedy algorithm is proposed to solve the ill-posed problem. Digital simulations and in vivo experiment were conducted to test the algorithm. The reconstruct results were compared with traditional orthogonal matching pursuit (OMP) algorithm and Tikhonov algorithm. Both the Digital simulations and in vivo experiment show that this approach can reconstruct the distribution of radiopharmaceuticals effectively and accurately.

Iterative Forward-Backward Pursuit Algorithm for Compressed Sensing

It has been shown that iterative reweighted strategies will often improve the performance of many sparse reconstruction algorithms. Iterative Framework for Sparse Reconstruction Algorithms (IFSRA) is a recently proposed method which iteratively enhances the performance of any given arbitrary sparse reconstruction algorithm. However, IFSRA assumes that the sparsity level is known. Forward-Backward Pursuit (FBP) algorithm is an iterative approach where each iteration consists of consecutive forward and backward stages. Based on the IFSRA, this paper proposes the Iterative Forward-Backward Pursuit (IFBP) algorithm, which applies the iterative reweighted strategies to FBP without the need for the sparsity level. By using an approximate iteration strategy, IFBP gradually iterates to approach the unknown signal. Finally, this paper demonstrates that IFBP significantly improves the reconstruction capability of the FBP algorithm, via simulations including recovery of random sparse signals with different nonzero coefficient distributions in addition to the recovery of a sparse image.

Compressed sensing signal recovery via forward–backward pursuit

Recovery of sparse signals from compressed measurements constitutes an l0 norm minimization problem, which is unpractical to solve. A number of sparse recovery approaches have appeared in the literature, including l1 minimization techniques, greedy pursuit algorithms, Bayesian methods and nonconvex optimization techniques among others. This manuscript introduces a novel two stage greedy approach, called the Forward-Backward Pursuit (FBP). FBP is an iterative approach where each iteration consists of consecutive forward and backward stages. The forward step first expands the support estimate by the forward step size, while the following backward step shrinks it by the backward step size. The forward step size is larger than the backward step size, hence the initially empty support estimate is expanded at the end of each iteration. Forward and backward steps are iterated until the residual power of the observation vector falls below a threshold. This structure of FBP does not necessitate the sparsity level to be known a priori in contrast to the Subspace Pursuit or Compressive Sampling Matching Pursuit algorithms. FBP recovery performance is demonstrated via simulations including recovery of random sparse signals with different nonzero coefficient distributions in noisy and noise-free scenarios in addition to the recovery of a sparse image.