Kernel Sparse Representation for Anomaly Detection in Hyperspectral Imagery

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.

FOMP algorithm for Direction of Arrival estimation

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.

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.

With the proliferation of unmanned aerial vehicles (UAVs) in both commercial and military use, the public is paying increasing attention to UAV identification and regulation. The micro-Doppler characteristics of a UAV can reflect its structure and motion information, which provides an important reference for UAV recognition. The low flight altitude and small radar cross-section (RCS) of UAVs make the cancellation of strong ground clutter become a key problem in extracting the weak micro-Doppler signals. In this paper, a clutter suppression method based on an orthogonal matching pursuit (OMP) algorithm is proposed, which is used to process echo signals obtained by a linear frequency modulated continuous wave (LFMCW) radar. The focus of this method is on the idea of sparse representation, which establishes a complete set of environmental clutter dictionaries to effectively suppress clutter in the received echo signals of a hovering UAV. The processed signals are analyzed in the time-frequency domain. According to the flicker phenomenon of UAV rotor blades and related micro-Doppler characteristics, the feature parameters of unknown UAVs can be estimated. Compared with traditional signal processing methods, the method based on OMP algorithm shows advantages in having a low signal-to-noise ratio (-10 dB). Field experiments indicate that this approach can effectively reduce clutter power (-15 dB) and successfully extract micro-Doppler signals for identifying different UAVs.

The recovery algorithm is a crucial issue of the compressed sensing (CS). This paper presents a greedy algorithm called optimized orthogonal matching pursuit (OOMP) for sparse signal recovery. The OOMP algorithm improves the orthogonal matching pursuit (OMP) algorithm via providing the projection onto the subspace generated by the selected measurements and minimizing the corresponding residual error at each iteration. Compared with the OMP algorithm, the simulation results show that the proposed algorithm provides a better approximation of a given signal and reduces measurements needed to recover the signal accurately.

In this paper, we present a novel architecture based on field-programmable gate arrays (FPGAs) for the reconstruction of compressively sensed signal using the orthogonal matching pursuit (OMP) algorithm. We have analyzed the computational complexities and data dependence between different stages of OMP algorithm to design its architecture that provides higher throughput with less area consumption. Since the solution of least square problem involves a large part of the overall computation time, we have suggested a parallel low-complexity architecture for the solution of the linear system. We have further modeled the proposed design using Simulink and carried out the implementation on FPGA using Xilinx system generator tool. We have presented here a methodology to optimize both area and execution time in Simulink environment. The execution time of the proposed design is reduced by maximizing parallelism by appropriate level of unfolding, while the FPGA resources are reduced by sharing the hardware for matrix-vector multiplication across the data-dependent sections of the algorithm. The hardware implementation on the Virtex6 FPGA provides significantly superior performance in terms of resource utilization measured in the number of occupied slices, and maximum usable frequency compared with the existing implementations. Compared with the existing similar design, the proposed structure involves 328 more DSP48s, but it involves 25,802 less slices and 1.85 times less computation time for signal reconstruction with N = 1024, K = 256, and m = 36, where N is the number of samples, K is the size of the measurement vector, and m is the sparsity. It also provides a higher peak signal-to-noise ratio value of 38.9 dB with a reconstruction time of 0.34 s, which is twice faster than the existing design. In addition, we have presented a performance metric to implement the OMP algorithm in resource constrained FPGA for the better quality of signal reconstruction.

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.

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.

A block version of the orthogonal matching pursuit (OMP) algorithm, termed BOMP, can yield better reconstruction performance for block-sparse signals than conventional algorithms. However, the redundant dictionaries for block sparse signals are block coherent in the particle applications. In this paper, we consider a modified version of BOMP by introducing the concept of sensing dictionary. Exploiting the alternating projection (AP), we propose a method to design sensing dictionary for this modified BOMP. Simulation results show that the modified BOMP with sensing dictionary provides significant improvement for the recovery performance in the case of block coherent dictionary. Key words: Block-sparsity, sensing dictionary, orthogonal matching pursuit, sparse reconstruction.