RPCA based time-frequency signal separation algorithm for narrow-band interference suppression

Narrow-band interference (NBI) is a critical issue for synthetic aperture radar (SAR), in which the imaging quality can be degraded severely. To suppress NBI effectively, a novel interference suppression algorithm using robust principal component analysis (RPCA) based signal separation in time-frequency domain is proposed. The RPCA algorithm is introduced for signal separation in the time-frequency domain for the first time. The fundamental assumption of RPCA is that a matrix can be modeled as a combination of a low-rank matrix and a sparse counterpart. In terms of the SAR echo, the short time Fourier transformation (STFT) matrix of mixed signals (i.e., useful SAR signals and NBIs) well fits the assumption of RPCA. Based on this property, radar echoes are first transformed into the time-frequency domain by STFT to form an STFT matrix. Then, the RPCA algorithm is used to decompose the STFT matrix into a low-rank matrix (i.e., NBIs) and a sparse matrix (i.e., useful signals). Finally, the NBIs can be reconstructed and subtracted from the echoes to realize the interference suppression. The experimental results of simulated and measured data demonstrate that the proposed algorithm not only can suppress interference effectively, but also preserve the useful information as much as possible.

Principal component analysis (PCA) is widely used to extract features and reduce dimensionality in various computer vision and image/video processing tasks. Conventional approaches either lack robustness to outliers and corrupted data or are designed for one-dimensional signals. To address this problem, we propose a robust PCA model for two-dimensional images incorporating structured sparse priors, referred to as structured sparse 2D-PCA. This robust model considers the prior of structured and grouped pixel values in two dimensions. As the proposed formulation is jointly nonconvex and nonsmooth, which is difficult to tackle by joint optimization, we develop a two-stage alternating minimization approach to solve the problem. This approach iteratively learns the projection matrices by bidirectional decomposition and utilizes the proximal method to obtain the structured sparse outliers. By considering the structured sparsity prior, the proposed model becomes less sensitive to noisy data and outliers in two dimensions. Moreover, the computational cost indicates that the robust two-dimensional model is capable of processing quarter common intermediate format video in real time, as well as handling large-size images and videos, which is often intractable with other robust PCA approaches that involve image-to-vector conversion. Experimental results on robust face reconstruction, video background subtraction data set, and real-world videos show the effectiveness of the proposed model compared with conventional 2D-PCA and other robust PCA algorithms.

A comparison between two robust PCA algorithms

This paper presents a novel data-oriented unsupervised machine learning-based theft detection approach for efficiently identifying the fraudster consumers. It accomplishes the above-mentioned objective by exploiting the intelligence of the robust principal component analysis (ROBPCA) algorithm in conjunction with the outlier removal clustering (ORC) algorithm. To avoid the irregularities in acquired consumers’ data from a power utility, the statistical features are extracted from each consumer's consumption patterns using an anomalous time series extension. Based on the extracted features, the consumers with most similar features are initially grouped into two categories using the ROBPCA algorithm. In order to evade any overlapping between the two newly formed groups, the ORC algorithm is utilized to categorize the consumers distinctly as “suspicious” and “non-suspicious”. Finally, a very selective onsite inspection is proposed, thus, saving the considerable time, resources, and overall cost of the utilities. The effectiveness of the proposed theft detection method is validated by comparing its performance with nine most widely used outlier detection methods on the basis of seven of the most prominent performance metrics. The accuracy and detection rate of the proposed technique are found as 94.34% and 92.52%, respectively, which is significantly higher than that of other studied conventional methods.

Due to the spread of the Internet and improvement of the audio compression technology, we need technologies to handle a large number of audio files. Separating singing voice from music is one of them and it is used in many applications, such as lyric retrieval and singer recognition. Recently, robust principal component analysis (RPCA) has been proposed, which makes use of repetition of a phrase in an accompaniment. We assume that there are some points to be improved in RPCA. In this paper, we propose a developed method based on the RPCA algorithm. First, we propose the extended RPCA algorithm that makes use of the two features of the spectrogram. Second, we apply simple post-processing to remove noise effectively. Lastly, we experiment our algorithm using the MIR-1K dataset and confirm that the proposed algorithm shows better separation performance than the conventional RPCA method.

Wide-band interference (WBI) is a critical issue for synthetic aperture radar (SAR), which may severely affect the imaging quality of SAR systems. To suppress WBI effectively, a novel interference suppression algorithm based on robust principal component analysis (RPCA) in time-frequency-pulse (TF-P) domain is proposed. For SAR echoes in TF-P domain, there are two useful properties: 1) The TF characteristic of useful signal in adjacent pulse are similar, indicating that useful signal has low-rank property; 2) Due to its variation of position and sparsely distrusted in TF-P domain, WBI has sparse characteristic. According to these properties, RPCA method is applied to decompose the TF-P matrix into a low-rank matrix (i.e. useful signal) and a sparse matrix (i.e. WBI). Finally, the WBIs can be reconstructed and subtracted from the echoes to realize the interference suppression. The experimental results of simulated data demonstrate that the proposed algorithm not only can suppress interference effectively, but also preserve the useful information as much as possible.

In this paper, an improved algorithm for narrow-band interference suppression is described for global navigation satellite system software receiver based on frequency-domain algorithm. The threshold of the interference in navigation signal is determined though N-sigma algorithm. This paper introduces the principle and flowchart of the algorithm. Performance comparison between this algorithm and other algorithms is also given based on simulation results. The results show that the improved algorithm has better anti-interference ability than other methods. This algorithm is suitable to eliminate the narrowband interference in global navigation satellite system software receiver.

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to have strong mutual coherence with a large number of data points. By contrast, outliers either do not admit low dimensional structures or form small clusters. In either case, an outlier is unlikely to bear strong resemblance to a large number of data points. Given that, CoP sets an outlier apart from an inlier by comparing their coherence with the rest of the data points. The mutual coherences are computed by forming the Gram matrix of the normalized data points. Subsequently, the sought subspace is recovered from the span of the subset of the data points that exhibit strong coherence with the rest of the data. As CoP only involves one simple matrix multiplication, it is significantly faster than the state-of-the-art robust PCA algorithms. We derive analytical performance guarantees for CoP under different models for the distributions of inliers and outliers in both noise-free and noisy settings. CoP is the first robust PCA algorithm that is simultaneously non-iterative, provably robust to both unstructured and structured outliers, and can tolerate a large number of unstructured outliers.

Chaos through-wall imaging radar has attracted wide attention due to its inherent low probability of detection/interception, strong anti-jamming, and high resolution. However, the target response is usually overwhelmed by strong clutter. This paper proposes an imaging-then-decomposition method based on two-stage robust principal component analysis (RPCA) to remove the clutter and recover the target image. The proposed method firstly focuses the energy of the preprocessing data by the back-projection imaging algorithm; then, it performs matrix decomposition on the full and the sparse component of the focused data, in succession, by the RPCA algorithm. Simulation and experimental results show that the proposed method can suppress the clutter dramatically and indicate human targets distinctly. Compared with the traditional methods, it has effectiveness and superiority in improving the signal-to-clutter ratio.

A new algorithm for narrowband interference suppression in direct-sequence spread-spectrum (DS-SS) communications is presented. The algorithm combines the undecimated wavelet packet transform (UWPT) with frequency shifts to confine the interference energy in a subband that is subsequently eliminated. Computer simulation shows a robust performance that appears to be independent of the interference frequency

Nowadays, in the electromagnetism environment, the complex interferences, including the narrowband interferences (NBIs) and wideband interferences (WBIs), may severely affect the imaging quality of synthetic aperture radar (SAR) systems. Most traditional methods can only tackle with one kind of isolated interferences, NBIs or WBIs, which are widely distributed in the 1-D range frequency domain or 2-D range time-frequency domain. In this paper, we propose a complex tensor robust principal component analysis (CT-RPCA) method based on a novel 3-D range-azimuth-space tensor model to mitigate continuously distributed NBIs and WBIs simultaneously. The main contributions of this paper are summarized in three aspects. First, we strictly prove the low-rank property of the isolated NBIs and WBIs in the range-azimuth domain. Second, we use multiple views of the signal to construct a novel 3-D range-azimuth-space tensor model, where both the NBI tensor and the WBI tensor have spatial low-rank property due to the approximately stable frequency bands along the spatial dimension. Third, the CT-RPCA method is employed to efficiently suppress NBIs and WBIs simultaneously by solving the tensor RPCA problem. Finally, the real SAR data with simulated complex interferences are employed to demonstrate the effectiveness of the proposed method.

Interference suppression (IS) algorithms have been extensively discussed for it can reveal the target signals among the interference. Numerous IS algorithms have been proposed for passive sonar. To appropriately apply them in different scenarios, a novel category is proposed in this paper to analyze them and classify them into three methods (the adaptive array processing technology based nulling method, the subspace separation based IS method and the joint time-space-frequency based IS method). In the meantime, the complexity, applicable occasions, strengths and weaknesses of three types of IS algorithms are analyzed.

Narrow-band interference (NBI) suppression is an important technique in the low-frequency synthetic aperture radar (SAR). NBI sources either intentional or unintentional can mask the SAR signals and cause image degradation. According to the different characteristics of the spectra between the NBI and the SAR signals, a new method using subband spectral cancellation is applied to suppress the NBI. In contrast to the conventional suppression method performed on the raw data, this letter deals with the focused SAR image. By subtracting different range subband spectra of the SAR image, the NBIs are obtained and cancelled. The proposed method does not need to detect and estimate the parameters of the NBI and is easy to put in practice. Its performance is tested on the real data acquired by an experimental SAR system at P-band.

Separating vocal and accompaniment signals from a monaural music signal is a challenging task. Recently, robust principal component analysis (RPCA) has been proposed for use in the magnitude spectrogram domain to separate the low-rank and sparse residual matrices, which are assumed to represent the accompaniment and vocal signals, respectively. In this paper, we propose two extended methods based on the RPCA algorithm for more effective vocal separation. First, we extend the conventional RPCA and propose to use in the spectrogram decomposition framework Schatten p- and lp-norms, which are generalized versions of the nuclear norm and l1-norm used in RPCA, respectively. Second, we apply proper scale compression to the magnitude spectrogram, making it a more appropriate representation for the decomposition. Experiments using the MIR-1K dataset show that the proposed methods yield significantly better separation performance than the conventional RPCA.

This paper presents a novel nonlinear estimation algorithm based on hidden Markov models for narrowband interference suppression in CDMA spread spectrum systems. The proposed algorithm combines a recursive hidden Markov model estimator, a Kalman filter and a recursive prediction error parameter estimation algorithm. It is shown that the proposed algorithm not only outperforms the nonlinear filtering techniques for narrowband interference suppression presented in Rusch and Poor (1994), but that it outperforms and has faster, more robust convergence properties than the cross-coupled expectation maximization based algorithm presented in Logothetis and Krishnamurthy.