Sparse Time-frequency Research Articles

A sparse time-frequency reconstruction approach from the synchroextracting domain

Synchroextracting, including frequency-extracting and transient-extracting, offers a sparse time-frequency (TF) representation for multi-component signals. However, it is susceptible to amplitude modulation (AM) and frequency modulation (FM) when reconstructing the raw signal through the TF ridge. This paper proposes a new signal reconstruction approach (SRA) in the synchroextracting domain to address this limitation. This approach performs synchroextracting on the short-time Fourier transform (STFT) domain. We incorporate the extracting operator in the inverse STFT to establish the mathematical relationship between the synchroextracting representation and the retrieved signal, thus enabling the reconstruction of each mode in the synchroextracting domain. The proposed SRA is theoretically derived, and its reconstruction performance is evaluated in the frequency-extracting and transient-extracting domains. Two synthetic signals are utilized to demonstrate that compared with some advanced reconstruction methods, the SRA has a high reconstruction accuracy, strong noise robustness, and is less affected by AM-FM features and the window length. The application of the bat signal further clarifies the advantages of the SRA and its feasibility in practical applications. Moreover, this study also provides a new reconstruction framework and reference for other synchroextracting-type methods.

Exploiting Time–Frequency Sparsity for Dual-Sensor Blind Source Separation

This paper explores the important role of blind source separation (BSS) techniques in separating M mixtures including N sources using a dual-sensor array, i.e., M=2, and proposes an efficient two-stage underdetermined BSS (UBSS) algorithm to estimate the mixing matrix and achieve source recovery by exploiting time–frequency (TF) sparsity. First, we design a mixing matrix estimation method by precisely identifying high clustering property single-source TF points (HCP-SSPs) with a spatial vector dictionary based on the principle of matching pursuit (MP). Second, the problem of source recovery in the TF domain is reformulated as an equivalent sparse recovery model with a relaxed sparse condition, i.e., enabling the number of active sources at each auto-source TF point (ASP) to be larger than M. This sparse recovery model relies on the sparsity of an ASP matrix formed by stacking a set of predefined spatial TF vectors; current sparse recovery tools could be utilized to reconstruct N>2 sources. Experimental results are provided to demonstrate the effectiveness of the proposed UBSS algorithm with an easily configured two-sensor array.

Application of sparse S transform network with knowledge distillation in seismic attenuation delineation

Time-frequency analysis is a successfully used tool for analyzing the local features of seismic data. However, it suffers from several inevitable limitations, such as the restricted time-frequency resolution, the difficulty in selecting parameters, and the low computational efficiency. Inspired by deep learning, we suggest a deep learning-based workflow for seismic time-frequency analysis. The sparse S transform network (SSTNet) is first built to map the relationship between synthetic traces and sparse S transform spectra, which can be easily pre-trained by using synthetic traces and training labels. Next, we introduce knowledge distillation (KD) based transfer learning to re-train SSTNet by using a field data set without training labels, which is named the sparse S transform network with knowledge distillation (KD-SSTNet). In this way, we can effectively calculate the sparse time-frequency spectra of field data and avoid the use of field training labels. To test the availability of the suggested KD-SSTNet, we apply it to field data to estimate seismic attenuation for reservoir characterization and make detailed comparisons with the traditional time-frequency analysis methods.

Domain adaptation-based sparse time-frequency analysis and its application on seismic attenuation estimation

Time-frequency (TF) transform is a commonly used tool for geologic structure interpretation and attenuation estimation, mainly including the linear and nonlinear methods. The former consists of short-time Fourier transform, continuous wavelet transform, S-transform, etc., which can be efficiently implemented. However, they suffer from the Gabor uncertainty principle, which limits their TF readability. The latter can effectively enhance TF readability; nevertheless, it has several unavoidable drawbacks, such as low computational efficiency and parameter selection. For seismic sparse TF (STF) analysis (STFA), we develop a domain adaptation-based STFA (DASTFA) model. This model mainly contains two steps. First, we suggest an STF network (STFNet) for mapping a 1D seismic signal to a 2D STF spectrum, which is pretrained using synthetic traces and STF labels. Second, based on the pretrained STFNet, we design a DASTFA model for transferring to field data. Note that the synthetic traces are generated using well-log data and horizon at the study area, located in the Ordos Basin, China, which can reduce the gap between synthetic and field data. Afterward, we use synthetic traces with their STF labels for model pretraining in the first step and field data without STF labels for model transferring in the second step. Here, model transferring indicates transferring the pretrained model parameters based on field traces. Finally, to test the validity and effectiveness of DASTFA, we apply it to synthetic and field data. Moreover, we test the availability of seismic attenuation estimation by adopting the suggested model for 3D poststack field data volume, which achieved encouraging results.

Local Rényi entropy-based Gini index for measuring and optimizing sparse time-frequency distributions

This paper introduces a novel localized Gini index (GI) designed for the assessment and optimization of time-frequency distributions (TFDs). This approach employs the localized Rényi entropy (LRE) to quantify the local number of signal components, providing a unique perspective on interpreting time and frequency slice segments while considering the presence of auto-terms or cross-terms. The results demonstrate the effectiveness of the proposed LRE-based GI in overcoming the limitations of conventional concentration and sparsity measures, particularly in scenarios with varying component numbers and missing essential components that may arise during TFD reconstruction using the compressive sensing method. Furthermore, it proves as an efficient objective function in meta-heuristic optimization, ensuring the preservation of auto-terms and a significant enhancement in overall TFD quality. The performance of the proposed LRE-based GI is demonstrated on noisy synthetic and real-life signals.

Sparse time-frequency analysis of seismic data via convolutional neural network

Time-frequency (TF) analysis is commonly used to reveal the local properties of seismic signals, such as frequency and spectral contents varying with time/depth. Aiming to realize a highly localized TF representation of seismic signals, researchers treated the TF analysis as an inverse problem, and the regularization is adopted in the objective functions. Traditionally, the TF sparse inversion process is solved by the Lasso regression. It has been proven that the Lasso regression needs a large number of iterations to reach a high accurate solution for the convex problem. Recently, convolutional neural network (CNN) has been successfully used to solve the convex problem due to their high computational efficiency and strong nonlinear characterization ability. We use CNN to solve the sparse TF inversion, and our method is called STFA-CNN. The objective function in the neural network architecture consists of two portions. The first one is to minimize the difference between the local forward and backward Fourier transform of seismic signals. The second is minimizing the regularization ([Formula: see text] norm) of TF results. To demonstrate the effectiveness of our method, we apply it to synthetic and real seismic data. We further use the calculated TF spectra to compute the attenuation of seismic waveforms and apply the attenuation attribute to predict the hydrocarbons of a seismic survey acquired over the Ordos Basin, northwest of China.

Rolling bearing incipient fault feature extraction using impulse-enhanced sparse time-frequency representation

Incipient faults features are often extremely weak and susceptible to heavy noise, making it challenging to obtain the concentrated faulty energy ridges in the time-frequency domain. Thus, a novel impulse-enhanced sparse time-frequency representation (IESTFR) method is proposed in this paper. First, the time-rearranged multisynchrosqueezing transform is utilized to produce a time-frequency representation (TFR) with a high energy concentration for faulty impulses. Next, a new non-convex penalty function is constructed by the hyperbolic tangent function, which can enhance the periodic impulsivity of sparse TFR for more obvious fault characteristic frequency. Moreover, the time-frequency transform is evaluated and compared by simulated signals and a selection strategy for the regularization parameter is designed. Simulated signals and two experimental signals are applied to verify the effectiveness of IESTFR, and the results show that IESTFR is effective and superior in bearing incipient fault feature extraction.

Self-supervised time-frequency representation based on generative adversarial networks

Time-frequency (TF) transforms are commonly used to analyze local features of nonstationary seismic data and to help uncover structural or geologic information. Traditional TF transforms, such as short-time Fourier transform, continuous wavelet transform, and S-transform, suffer from the Heisenberg uncertainty principle, and their TF resolution is limited. The sparse TF (STF) transform has been proposed to address this disadvantage; however, expensive calculation and parameter selection present difficulties. We have developed a self-supervised TF representation based on a generative adversarial networks (STFR-GANs) model to map a 1D seismic signal into a 2D STF image. This model includes three components: a generator, a discriminator, and a reconstruction module. The generator is used to generate the STF spectrum of the input seismic trace, whereas the discriminator distinguishes if this generated STF spectrum is optimal. The reconstruction module serves as a physical constraint to ensure the accuracy of the generated STF spectrum. When implementing model training, the discriminator learns to identify the ideal STF and guides the generator to produce a TF spectrum closer to the ideal one. After model training, we applied the model to synthetic and field data to demonstrate its effectiveness and stability in characterizing the TF features of seismic data. Our results find that STFR-GAN can effectively provide TF representations with higher readability than those of traditional TF methods, further benefiting fluvial channel delineation.

Sparse Time-Frequency Distribution Reconstruction Using the Adaptive Compressed Sensed Area Optimized with the Multi-Objective Approach.

Compressive sensing (CS) of the signal ambiguity function (AF) and enforcing the sparsity constraint on the resulting signal time-frequency distribution (TFD) has been shown to be an efficient method for time-frequency signal processing. This paper proposes a method for adaptive CS-AF area selection, which extracts the magnitude-significant AF samples through a clustering approach using the density-based spatial clustering algorithm. Moreover, an appropriate criterion for the performance of the method is formalized, i.e., component concentration and preservation, as well as interference suppression, are measured utilizing the information obtained from the short-term and the narrow-band Rényi entropies, while component connectivity is evaluated using the number of regions with continuously-connected samples. The CS-AF area selection and reconstruction algorithm parameters are optimized using an automatic multi-objective meta-heuristic optimization method, minimizing the here-proposed combination of measures as objective functions. Consistent improvement in CS-AF area selection and TFD reconstruction performance has been achieved without requiring a priori knowledge of the input signal for multiple reconstruction algorithms. This was demonstrated for both noisy synthetic and real-life signals.

Sparse Time–Frequency Analysis of Seismic Data: Sparse Representation to Unrolled Optimization

Sparse Time–Frequency Analysis of Seismic Data: Sparse Representation to Unrolled Optimization

Robust sparse time‐frequency analysis for data missing scenarios

Sparse time-frequency analysis (STFA) can precisely achieve the spectrum of the local truncated signal. However, when the signal is disturbed by unexpected data loss, STFA cannot distinguish effective signals from missing data interferences. To address this issue and establish a robust STFA model for time-frequency analysis (TFA) in data loss scenarios, a stationary Framelet transform-based morphological component analysis is introduced in the STFA. In the proposed model, the processed signal is regarded as a sum of the cartoon, texture and data-missing parts. The cartoon and texture parts are reconstructed independently by taking advantage of the stationary Framelet transform. Then, the signal is reconstructed for STFA. The forward-backwards splitting method is employed to split the robust STFA model into the data recovery and robust time-frequency imaging stages. The two stages are then solved separately by using the alternating direction method of multipliers (ADMM). Finally, several experiments are conducted to show the performance of the proposed robust STFA method under different data loss levels, and it is compared with some existing state-of-the-art time-frequency methods. The results indicate that the proposed method outperforms the compared methods in obtaining the sparse spectrum of the effective signal when data are missing. The proposed method has a potential value in TFA in scenarios where data is easily lost.

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy.

Data-driven fault diagnosis methods for rotating machinery have developed rapidly with the help of deep learning methods. However, traditional intelligent fault diagnosis methods still have some limitations in fault feature extraction and the latest object detection theory has not been applied in fault diagnosis. To this end, a fault diagnosis method based on a sparse short-term Fourier transform (SSTFT) and object detection theory is developed in this paper. First, a sparse constraint is introduced in time-frequency analysis to improve the time-frequency resolution of the model without cross-term interference and proximal gradient descent (PGD) is adopted to quickly and effectively optimize the model to obtain a high-quality time-frequency representation (TFR). Second, a fault diagnosis model based on a region-based convolutional neural network (RCNN) is built; the model can extract multiple regions that can characterize fault features from the TFR. This process avoids the interference of irrelevant vibration components and improves the interpretability of the fault diagnosis model. Finally, multicategory rolling bearing fault identification is realized. The effectiveness of the proposed method is validated by simulation signals and bearing experiments. The results indicate that the proposed method is more effective than existing methods.

Unified Sparse Time–Frequency Analysis: Decomposition, Transformation, and Reassignment

Time–frequency (TF) analysis is essential for industrial engineering applications. However, the conventional TF analysis methods suffer from blurry TF energy. This article proposes a new unified sparse TA analysis (STFA) framework to concentrate the blurry energy, restrain noise, separate condition-related components, and retain the signal reconstruction property. The STFA framework leverages the weighted elastic net sparse regularization for sparsity- inducing and energy concentration and uses the reconstruction error term for condition-related component separation and signal reconstruction, which bridges the gaps among sparsity, decomposition, transformation, and reassignment. Theoretical analysis and comprehensive investigation of the proposed framework are performed in practical cases. Comparison results with the state-of-the-art methods demonstrate that the proposed framework has superior properties for TF feature energy concentration, denoising, component separation, and reconstruction, especially for the signals with the fast-varying features.

Time-frequency representation with reweighted regularization for fault diagnosis in a sparse way

In the field of fault diagnosis, time–frequency representation (TFR) is a very popular tool due to its good performance under time-varying condition. TFR provides both time and frequency information of fault signal, and the component related to fault characteristic frequency (FCF) can be found in the time–frequency image. To improve the time–frequency resolution of TFR, a special kind of TFR method named sparse time frequency representation (STFR) combines TFR and sparse theory, where the TFR is processed in a sparse way and the energy is more concentrated on FCF. However, the underestimation problem from the optimization process limits the efficiency of STFR. Concretely, the coefficients of the components of FCF are easy to be underestimated in the iterative process of solving coefficient, which will enhance other interference components. Especially for the weak faults from the early stage or the serious noise pollution, STFR is easy to be contaminated and is hard to reveal the components of FCF because of the underestimation problem. To solve the underestimation problem, we propose a novel STFR with reweighted regularization (RSTFR) for fault diagnosis. In the proposed method, the envelope of signal is divided into small segments, and each segment is decomposed into the Fourier basis. Naturally, the sparse coefficient represents the envelope spectrum of each segment. Meanwhile, the reweighted scheme is used to solve the underestimation problem. The components related to FCF are encouraged with low thresholds while other interference components are punished with high thresholds. At last, the envelope spectrums of all segments at different time form the TFR. The proposed method can provide a higher time–frequency resolution and diagnose the fault precisely. RSTFR is applied in the both simulation cases and experimental cases of bearing fault diagnosis, and it shows the overwhelming superiority compared to other four state-of-art TFR methods.

Reassignment-enable reweighted sparse time-frequency analysis for sparsity-assisted aeroengine rub-impact fault diagnosis

Time-frequency analysis (TFA) is an effective tool for the feature extraction of nonstationary signals. However, the energy concentration of the TF representation (TFR) obtained by conventional TFA is weakened when the instantaneous frequency (IF) of signals varies fast, which adversely affects the feature extraction and reconstruction. In this paper, a reassignment-enable reweighted sparse TF method (Re2STF) is proposed to achieve high energy concentration as well as highly accurate reconstruction when analyzing signals with fast-varying IF, and thus is effective to the vibration analysis of aeroengine rub-impact fault. A reweighted sparse TF model is constructed, which iteratively employs the TF reassignment representation into the reweighted strategy to suppress noise and match the fast-varying TF structure better. In particular, the reassignment-enable weight can highlight the TF ridge and suppress the TF coefficients elsewhere. Furthermore, an effective acceleration strategy for the fast iterative shrinkage threshold algorithm is proposed to speed up the model solving. The simulation study and the application in the vibration analysis of a dual-rotor turbofan engine show the improvement of Re2STF in denoising, TF energy concentration and reconstruction, thus proving the effectiveness in aeroengine rub-impact fault diagnosis.

Improving time–frequency sparsity for enhanced audio source separation in degenerate unmixing estimation technique algorithm

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.

Seismic Sparse Time-Frequency Network With Transfer Learning

Time-frequency analysis (TFA) is a powerful tool for describing time-frequency (TF) features of seismic data, such as short-time Fourier transform and S-transform. Recently, sparse time-frequency analysis (STFA) is proposed for enhancing TF readability of commonly used TFA tools. However, STFA is often solved via an optimal inverse problem with a prior regularization term, which is difficult to set in practice, where the key regularization parameters are sensitive to noise. Moreover, it often takes expensive calculation time, especially for 3D field data application. We build a deep learning based workflow for implementing STFA to obtain sparse time-frequency (STF) spectra, termed the sparse time-frequency network with transfer learning (STFNTL). We first adopt a Marmousi II reflectivity model and Ricker wavelets with different dominant frequencies to generate synthetic training data set. Then, we adopt a simplified STFA method with optimized parameters to generate synthetic training labels, i.e., sparse TF spectra. Afterward, we propose the sparse time-frequency network (STFN) based on a simplified Unet model, which is trained using synthetic training data and corresponding STF labels. Moreover, to enhance the generalization of STFN, we introduce an adaptive transfer learning strategy based on small samples of field data and their corresponding STF labels. Finally, synthetic and field data are utilized to illustrate the effectiveness and generalization ability of our proposed model.

Seismic Attenuation Estimation Using an Enhanced Log Spectral Ratio Method

Seismic attenuation estimation is a significant task for characterizing reservoirs and improving the resolution of seismic data. The logarithmic spectral ratio (LSR) is one of the widely used tools for seismic attenuation estimation. However, how to select a suitable frequency bandwidth for the LSR is a difficult task, especially for field data. Moreover, field data are often contained kinds of noises, which makes seismic attenuation estimation difficult and unstable. We proposed an enhanced LSR (ELSR) workflow to estimate seismic attenuation. First, we built a sparse S-transform (SST) to obtain a sparse time-frequency (TF) spectrum of the analyzed seismic trace. Then, based on the SST spectrum, we introduced an ELSR workflow to estimate seismic attenuation. It should be noticed that we provided an adaptive frequency band selection for the LSR. To demonstrate the effectiveness of the proposed workflow, we apply it on both synthetic and field data. Compared with the results from several traditional attenuation estimation methods, the proposed ELSR provides a more stable and more accurate attenuation estimation result and offers the potentials in improving the resolution of post-stacked seismic data.

Sparse time-frequency distribution reconstruction based on the 2D Rényi entropy shrinkage algorithm

Time-frequency distributions (TFD) provide a set of powerful tools for the non-stationary signal analysis. Although TFD overcomes signal representation limitations, the most commonly used TFDs generate unwanted artefacts, also called the cross-terms, which make the TFD application less feasible for noise-corrupted real-life signals. In this paper, we investigate the advantages of the TFD sparsity by using the compressive sensing based methods. We propose a sparse reconstruction algorithm which reconstructs a TFD from a small sub-set of samples taken from the signal ambiguity function. The proposed algorithm is based on the iterative shrinkage algorithm which performance and robustness have been improved by utilizing the short-term and narrow-band Rényi entropies. Furthermore, we have circumvented the limitations of global concentration measure by coupling it with the measure based on the local Rényi entropy. The introduced concentration measures have been used as objective functions in a multi-objective meta-heuristic optimization of the proposed algorithm parameters, resulting in high-resolution TFDs while avoiding disjunctions within signal components. The obtained results have been compared to the state-of-the-art sparse reconstruction algorithms, for both noisy synthetic and real-life signals.

Signal time–frequency representation and decomposition using partial fractions

Summary The Z-transform of a complex time signal (or the analytic signal of a real signal) is equal to the Z-transform of a prediction error divided by the Z-transform of the prediction error operator. This inverse is decomposed into a sum of partial fractions, which are used to obtain impulse response operators formed by non-causal filters that complex-conjugate symmetric coefficients. The time components are obtained by convolving the filters with the original signal, and the peak frequencies, corresponding to the poles of the prediction error operator, are used for mapping the time components into frequency components. For non-stationary signals, this decomposition is done in sliding time windows, and the signal component values, in the middle of each window, are attributed to the peak value of its frequency response that corresponds to the pole of this partial fraction component. The result is an exact, but non-unique, time–frequency representation of the input signal. A sparse signal decomposition can be obtained by summing along the frequency axis in patches with similar characteristics in the time–frequency domain. The peak amplitude frequency of each new time component is obtained by computing a scalar prediction error operator in sliding time windows, resulting in a sparse time–frequency representation. In both cases, the result is a time–frequency matrix where an estimate of the frequency content of the input signal can be obtained by summation over the time variable. The performance of the new method is demonstrated with excellent results on a synthetic time signal, the LIGO gravitational wave signal and seismic field data.