Separating More Sources Than Sensors Using Time-Frequency Distributions

This paper presents a new approach for blind separation of nonstationary frequency-modulated (FM) sources in the underdetermined case (i.e., more sources than sensors) using their time-frequency distributions (TFDs). The underlying idea of the proposed blind source separation (BSS) method is based on the observation that a monocomponent FM signal is represented by a linear feature corresponding to the 'energy concentration points' in the time-frequency (TF) image. Therefore, we propose to adapt an existing 'road network extraction' method [Tupin et al., (1998)] for the detection and separation of the source signal components from the spatially averaged TF image of their mixtures. The sources spatial signatures are then used to group together (classify) the components of the same source (or equivalently, the same spatial direction). Simulation examples are provided to assess the performance of the proposed algorithm in various scenarios.

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

Recently, many researches have been done to solve the speech separation problems in the underdetermined cases, and the Two-step method is widely used, which estimates the mixing matrix first and then separates the sources. Subspace projection is an effective method for signal separation, whereas it has some limitations because it fixes the active number at the Time-Frequency (TF) point as a constant. A commonly used solution is to add an extra step to estimate the active source number at every TF point, which will increase the computation cost greatly. This paper provides a new convex-model-based subspace projection method with enhanced functionality, which can be used for Underdetermined Blind Source Separation (UBSS). The model takes into account both projection and size of the signal's subspace, without estimating the real source numbers at the TF points. Simulation results show that the proposed method overcomes the shortage of conventional subspace method and achieves higher separation performance. Furthermore, the proposed algorithm can be employed as a preprocessing technology in the fields of acoustic signals enhancement, recognition, and biomedical images, etc.

Time-frequency (TF) analysis (TFA) to nonstationary signals can reveal the nonlinearly changing instantaneous frequencies (IFs) of signals; it is, therefore, widely used for rotating machinery fault diagnosis under time-varying speed conditions. However, the traditional TFA methods may only reveal the outline of IFs due to the extra TF diffusion caused by limited TF resolution, hindering the fault diagnosis of rotating machinery. To enhance the readability of the time-frequency representation (TFR) of the signals with IF trajectories linearly time-varying, linear chirplet transform has been proved effective. To effectively tackle the signal with nonlinearly changing IFs, a string of chirp-rates is preferred, where the final TFR is obtained by superposition of each corresponding sub-TFR at each TF point. However, the extra cross-term interferences resulted from a string of chirp-rates cannot be neglected on TFRs. Aiming at alleviating the cross-terms from the TFR, matching and reassignment based TF enhancement strategy is proposed, where only the appropriate chirp-rate and its corresponding TFR slice is retained at each time instant. The appropriate chirp-rate is adaptively selected by the index—spectral kurtosis. To further increase the readability of the resulting TFR, a reassignment technique synchrosqueezing transform is integrated with the proposed matching strategy. By iteratively employing reassignments, TFR with the enhanced energy and sharp IF ridges can be generated. The effectiveness of the proposed method is validated by both simulated and experimental analyses. It is shown that the proposed method is effective in processing time-varying signals and can provide more accurate IF estimation, which paves the way for rotating machinery fault diagnosis under nonstationary speed conditions.

Blind separation of non-stationary sources using continuous density hidden Markov models

In this paper, we propose a novel method for the detection of road accidents by analyzing audio streams for road surveillance application. In the last decade, due to the increase in a number of people and transportation vehicles, traffic accidents have become one of a major public issue worldwide. The vast number of injuries and death due to road traffic accident reveals the story of a global crisis of road safety. A total of 52,160 road traffic accidents (RTA), 1130 injuries and 85 fatalities were registered during the year 2000, in the state of Qatar. An increase in the number of transportation vehicles around cities has risen the need for more security and safety in public environments. The most obvious reason for a person's death during accidents is the absence or prolong response time of the first aid facility, which is due to the delay in the information of the accident being reached to the police, hospital or ambulance team. In the last couple of years, several surveillance systems have been proposed based on image and video processing for automatically detecting road accidents and car crashes to ensure a quick response by emergency teams. However, in some situations such as adverse weather conditions or cluttered environments, the visual information is not sufficient enough, whereas analyzing the audio tracks can significantly improve the overall reliability of surveillance systems. In this paper we propose a novel method that automatically identifies hazardous situations such as tire skidding and car crashes in presence of background noises, by analyzing the audio streams. Previous studies show that methods for the detection, estimation, and classification of nonstationary signals can be enhanced by utilizing the time-frequency (TF) characteristics of such signals. The TF-based techniques have been proved to outperform classical techniques based on either time or frequency domains, in analyzing real-life nonstationary signals. Time-frequency distributions (TFDs) give additional information about signals that cannot be extracted from either the time domain or frequency domain representations, i.e. the instantaneous frequency of the components of a signal. In order to utilize this extra information provided by TF domain representation, the proposed approach extracts TF image features from quadratic time-frequency distributions (QTFDs), for the detection of audio anomalies. The extended modified-B distribution (EMBD) is utilized to transform a 1-dimensional audio signal into 2-dimensional TF representation which is interpreted as an image. The image descriptors based features are then extracted from the TF representation to classify visually the audio signals into background or abnormal activity patterns in the TF domain. The proposed features are based on Haralick's texture features extracted from the TF representation of audio signals considered and processed as a textured image. These features are used to characterize and hence classify audio signals into M classes. This research study demonstrates that a TF image pattern recognition approach offers significant advantages over standard signal classification methods that utilize either t-domain only or f-domain only features. The proposed method has been experimentally validated on a large open source database of sounds, including several kinds of background noise. The events to be recognized are superimposed on different background sounds of roads and traffic jam. The obtained results are compared with a recent study, utilizing the same large and complex data set of audio signals, and the same experimental setup. The overall classification results confirm the superior performance of the proposed approach with accuracy improvement up to 6%.

The paper discusses the application of the new concept of spatial time-frequency distribution (STFD), and more generally the spatial arbitrary joint-variable distribution, to key array signal processing problems including blind source separations and high resolution direction finding of narrowband and broadband sources with stationary and nonstationary temporal characteristics. The STFD can be formulated based on the widely used class of time-frequency distributions, namely Cohen's class, or it can be devised by incorporating other classes of quadratic distributions, such as the Hyperbolic class and the Affine class. The paper delineates the fundamental offerings of STFDs, presents three examples of array signal processing using the localization properties of time-frequency distributions of the impinging signals, and summarizes recent contributions in this area.

This paper explores three groups of time–frequency distributions: the Cohen’s, affine, and reassigned classes of time–frequency representations (TFRs). This study provides detailed insight into the theory behind the selected TFRs belonging to these classes. Extensive numerical simulations were performed with examples that illustrate the behavior of the analyzed TFR classes in the joint time–frequency domain. The methods were applied both on synthetic and real-life non-stationary signals. The obtained results were assessed with respect to time–frequency concentration (measured by the Rényi entropy), instantaneous frequency (IF) estimation accuracy, cross-term presence in the TFRs, and the computational cost of the TFRs. This study gives valuable insight into the advantages and limitations of the analyzed TFRs and assists in selecting the proper distribution when analyzing given non-stationary signals in the time–frequency domain.

This chapter presents a comprehensive treatment of the hybrid area of time-frequency distributions (TFDs) and array signal processing. The application of quadratic ‘l’F’Ds to sensor signal processing has recently become of interest, and it was necessitated by the need to address important problems related to processing nonstationary signals incident on multiantenna receivers. Over the past few years, major contributions have been made to improve direction finding and blind source separation using time-frequency signatures. This improvement has cast quadratic TFDs as a key tool for source localization and signal recovery, and put bilinear transforms at equal footing with second-order and higher-order statistics as bases for effective spatial-temporal signal processing. This chapter discusses the advances made through time-frequency analysis in direction-of-arrival estimation, signal synthesis, and near-field source characterization.

An empirical signal separation algorithm for multicomponent signals based on linear time-frequency analysis

The extraction of single train signal is necessary in wayside fault diagnosis because the acoustic signal acquired by a microphone is composed of multiple train bearing signals and noises. However, the Doppler distortion in the signal acquired by a microphone effectively hinders the signal separation and fault diagnosis. To address this issue, we propose a novel method based on the generalized S-transform, morphological filtering, and time–frequency amplitude matching-based resampling time series for multiple-Doppler-acoustic-source signal separation and correction. First, the original time–frequency distribution is constructed by applying generalized S-transform to the raw signal acquired by a microphone. Based on a morphological filter, several time–frequency distributions corresponding to different single source Doppler fault signals are extracted from the original time–frequency distribution. Subsequently, the time–frequency distributions are reverted to time signals by inverse generalized S-transform. Then, a resampling time series is built by time–frequency amplitude matching to obtain the correct signals without Doppler distortion. Finally, the bearing fault is diagnosed by the envelope spectrum of the correction signal. The effectiveness of this method is verified by simulated and practical signals.

Decomposition of biomedical signals for enhancement of their time–frequency distributions

Two high-resolution direction of arrival (DOA) estimation approaches of non-stationary narrowband signals based on matching pursuit (MP) are developed. The first sensor output is considered as the reference and decomposed by MP. As the MP is a linear decomposition, the obtained MP coefficients contain the steering vector information. So, the MP coefficients corresponding to the leading decomposition atoms are used to develop the MP-MUSIC algorithm for the DOA estimation. In addition, the chosen MP atoms are used to implement the modified spatial time–frequency distribution (STFD) based on Wigner Ville (WV) distribution as well, and this method named MP-WV. It has been demonstrated that these two methods can be applied for underdetermined problems and are robust against Gaussian and impulsive noises. The authors show that using either coefficients or chosen atoms to estimate the DOA in array processing by considering the source discriminative capability outperforms the conventional MUSIC and STFD. Some simulation results showing the performance of the two proposed approaches based on MP, conventional MUSIC and STFD are presented.

Enhanced Cohen class time–frequency methods based on a structure tensor analysis: Applications to ISAR processing

In recent years, much research has been focused on separating acoustic sources from their mixtures. Degenerate Unmixing Estimation Technique (DUET) is one of the widely popular methods of Blind Source Separation (BSS) in underdetermined scenarios. DUET is based on a signal recovery sparsity algorithm whose performance is strongly influenced by sparsity in the Time-Frequency (TF) domain. Noises and an several sources in mixtures limit the sparsity resulting in performance degradation in DUET. Here an enhanced strategy has been adopted by combining DUET with adaptive noise cancellation utilising the Dual-Tree Complex Wavelet Transform (DTCWT) as a pre-processor and TF refinement utilising Synchroextracting Transform (SET) as a post-processor. This improves the sparsity of sources and energy concentrations in a TF representation. Results of the signal separation performance evaluation reveal that the proposed algorithm outperforms conventional DUET in signal separation, especially in real-time scenarios.