Vocal separation using improved robust principal component analysis and post-processing

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.

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.

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.

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.

Narrow-band interference (NBI) is a common jamming signal against 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 time-frequency signal separation is proposed. The RPCA algorithm is introduced for time-frequency signal separation for the first time. 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.

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.

Blind monaural singing voice separation using rank-1 constraint robust principal component analysis and vocal activity detection

This paper presents a proposed extension of robust principal component analysis (RPCA) with weighting (WRPCA) based on gammatone auditory filterbank for singing voice separation. Although the conventional RPCA is an effective method to separate singing voice and music accompaniment, it makes some strong assumptions. For example, drums may lie in the sparse subspace instead of being low-rank, which decreases the separation performance in many real-world applications, especially for drums existing in the mixture music signal. Accordingly, the proposed WRPCA method utilizes different weighted values between sparse (singing voice) and low-rank matrices (music accompaniment). In addition, we developed an extended RPCA on cochleagram using an alternative time-frequency (T-F) representation based on gammatone auditory filterbank. We also applied IBM/IRM estimation to improve the separation results. Evaluation results show that WRPCA achieves better separation performance than the conventional RPCA, especially for the IBM estimation method.

Recent advances in optical coherence tomography (OCT) lead to the development of OCT angiography to provide additional helpful information for diagnosis of diseases like basal cell carcinoma. In this paper, we investigate how to extract blood vessels of human skin from full-field OCT (FF-OCT) data using the robust principal component analysis (RPCA) technique. Specifically, we propose a short-time RPCA method that divides the FF-OCT data into segments and decomposes each segment into a low-rank structure representing the relatively static tissues of human skin and a sparse matrix representing the blood vessels. The method mitigates the problem associated with the slow-varying background and is free of the detection error that RPCA may have when dealing with FF-OCT data. Both short-time RPCA and RPCA methods can extract blood vessels from FF-OCT data with heavy speckle noise, but the former takes only half the computation time of the latter. We evaluate the performance of the proposed method by comparing the extracted blood vessels with the ground truth vessels labeled by a dermatologist and show that the proposed method works equally well for FF-OCT volumes of different quality. The average F-measure improvements over the correlation-mapping OCT method, the modified amplitude-decorrelation OCT angiography method, and the RPCA method, respectively, are 0.1835, 0.1032, and 0.0458.

Chemical exchange saturation transfer (CEST) MRI requires the acquisition of multiple saturation-weighted images and can last several minutes. Misalignments among these images, which are often due to the inevitable motion of the subject, will corrupt CEST contrast maps and result in large quantification errors. Therefore, the registration of the CEST series is critical. However, registration is challenging since common intensity-based registration algorithms may fail to differentiate CEST signals from motion artifacts. Herein, we studied how different patterns of motion affect CEST quantification and proposed a cascaded two-step registration scheme by utilizing features extracted from the entire Z-spectral image series instead of direct registration to a single image. The proposed approach is conducted in two stages: during the first coarse registration, the Z-spectral image series is decomposed by robust principal component analysis (RPCA) to separate CEST contrast from motion. The recomposed image series using only the low-rank component, which contains minimized motion, are averaged to generate a reference for the alignment of the image series. To further remove residual misalignments, the coarse registration is followed by a refinement stage, which uses PCA iteratively to generate motionless synthetic reference series with the first few principal components (PCs) that correspond to CEST contrast. In the end, the quality check is performed to exclude the images with unsuccessful registration. The proposed registration scheme (RPCA + PCA_R) was assessed by both phantom experiments and in vivo data of tumor-bearing mouse brain, with simulated random rigid motion in different patterns applied to the acquired static Z-spectral image series. For comparison, previous correction schemes using an explicit image [either S0 or Ssat(∆ω)] as registration reference were also performed, named as S0_R and Ssat_R respectively. To illustrate the advantage of combination of RPCA and PCA, registration was also exploited using either only the RPCA-based method (RPCA_R) or only the PCA-based one (PCA_R). Compared with the above four methods, RPCA + PCA_R allowed for more accurate correction of the corrupted Z-spectral images, exhibiting smaller MTRasym(∆ω) error maps and lower residual Z-spectra referring to the static data. Among all the five correction methods, the corrected Z-spectral image series by RPCA + PCA_R and the resulting MTRasym(∆ω) maps achieved the highest correlation coefficients (CC) with respect to the static ones. The registration scheme of RPCA + PCA_R provides robust motion correction between two specific Z-spectral images and among an entire image series, through extraction of the static component from the entire Z-spectra set and inclusion of a PCA-based refinement step. Therefore, this method can help improve CEST acquisition and quantification.

Video background recovery is a very important task in computer vision applications. Recent research offers robust principal component analysis (RPCA) as a promising approach for solving video background recovery. RPCA works by decomposing a data matrix into a low-rank matrix and a sparse matrix. Our previous work shows that when the desired rank of the low-rank matrix is known, fixing the rank in the algorithm called FrALM (fixed-rank ALM) yields more robust and accurate results than existing RPCA algorithms. However, application of RPCA to video background recovery requires that each frame in the video is encoded as a column in the data matrix. This is impractical in real applications because the videos can be easily larger than the amount of memory in a computer. This paper presents an algorithm called iFrALM (incremental fixed-rank ALM) that computes fixed-rank RPCA incrementally by splitting the video frames into an initial batch and an incremental batch. Comprehensive tests show that iFrALM uses less memory and time compared to FrALM. Moreover, the initial batch size and batch quality can be carefully selected to ensure that iFrALM reduces memory and time complexity without sacrificing accuracy.KeywordsBackground recoveryIncremental SVDFixed-rank robust PCA

Due to the severe interference of background noise, the signal-to-noise ratio of desert seismic data is extremely low. In addition, due to low-frequency characteristics of sand in the Tarim desert region, the background noise in desert seismic data is mainly distributed in low-frequency band, so that the frequency spectrum aliasing of effective signals and background noise is more serious than the general land seismic data. Thus, conventional filtering methods cannot effectively suppress background noise in desert seismic data and recover effective signals. In order to overcome the problem that low-frequency background noise in desert seismic data is hard to suppress, a new method called R-TNRD based on robust principal component analysis (RPCA) algorithm and trainable nonlinear reaction diffusion (TNRD) network is proposed in this paper. By using the good sparsity of RPCA, the input noisy desert seismic data are decomposed into a low-rank matrix and a sparse matrix, and these two matrices contain background noise and effective signals. Due to the serious spectrum aliasing of desert seismic data, conventional thresholds have been unable to extract effective signals from the two matrices obtained by RPCA effectively. Therefore, we introduce TNRD network into desert seismic data denoising. By network training with a low-frequency noise set, the optimisation of TNRD network can be achieved, so as to accurately extract the effective signals from the low-rank matrix and the sparse matrix. In the experimental part, we test the performance of R-TNRD on both synthetic and real seismic data. The results demonstrate that the proposed method can suppress background noise more effectively than conventional methods.

In this paper, we propose an efficient singing voice extraction method from a music sound consisting of a singing voice and a drum sound. The proposed method is based on robust principal component analysis (RPCA) which is a technique to separate a given matrix into a sparse matrix and a low rank matrix. Dealing with a spectrogram of the music sound as the given matrix, RPCA gives an extracted singing voice spectrogram as a sparse spectrogram. We improve the capability of RPCA method by removing a residual drum sound from the sparse spectrogram. The residual drum sound is estimated as spectral components which repeatedly arise in the sparse spectrogram. Removing the estimated residual drum sound spectrogram from the sparse spectrogram gives an improved singing voice spectrogram. Simulation results show that the proposed method can improve 10dB of GNSDR as compared with the conventional RPCA singing voice extraction method.