Sparse Time-frequency Distribution Research Articles

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 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 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.

Space-Range-Doppler Focus-Based Low-observable Moving Target Detection Using Frequency Diverse Array MIMO Radar

The radar echoes of moving targets in a clutter background are extremely weak and their characteristics are complex. A low-observable moving target detection technology has become a key constraint to radar performance, requiring the radar to provide flexible freedom and higher parameter estimation capabilities. In this paper, a frequency diverse array MIMO (FDA-MIMO) radar is used for moving target detection in a clutter background, which combines the information in spatial (azimuth)-range-frequency (Doppler) domains. Based on the signal model of the FDA-MIMO radar, a novel signal processing method is proposed named as space-range-Doppler focus (SRDF) processing. Theoretical and simulations analysis shows that this method can be regarded as the combination of multiple cascaded signal processing, such as beamforming, pulse compression, and Doppler filtering of a conventional array radar. It can distinguish clutter and moving targets in multidimensional space, improve signal-to-clutter ratio, and achieve high-precision measurement of target motion parameters via sparse time–frequency distributions. It will provide a new approach for moving target detection and classification in complex backgrounds.

A data driven compressive sensing approach for time-frequency signal enhancement

Signals with the time-varying frequency content are generally well represented in the joint time-frequency domain; however, the most commonly used methods for time-frequency distributions (TFDs) calculation generate unwanted artifacts, making the TFDs interpretation more difficult. This downside can be circumvented by compressive sensing (CS) of the signal ambiguity function (AF), followed by the TFD reconstruction based on the sparsity constraint. The most critical step in this approach is a proper CS-AF area selection, with the CS-AF size and shape being generally chosen experimentally, hence decreasing the overall reliability of the method. In this paper, we propose a method for an automatic data driven CS-AF area selection, which removes the need for the user input. The AF samples picked by the here-proposed algorithm ensure the optimal amount of data for the sparse TFD reconstruction, resulting in higher TFD concentration and faster sparse reconstruction algorithm convergence, as shown on examples of both synthetical and real-life signals.

Parameter estimation of maneuvering targets in OTHR based on sparse time-frequency representation

This paper proposes a new method for estimating the parameter of maneuvering targets based on sparse time-frequency transform in over-the-horizon radar (OTHR). In this method, the sparse time-frequency distribution of the radar echo is obtained by solving a sparse optimization problem based on the short-time Fourier transform. Then Hough transform is employed to estimate the parameter of the targets. The proposed algorithm has the following advantages: Compared with the Wigner-Hough transform method, the computational complexity of the sparse optimization is low due to the application of fast Fourier transform (FFT). And the computational cost of Hough transform is also greatly reduced because of the sparsity of the time-frequency distribution. Compared with the high order ambiguity function (HAF) method, the proposed method improves in terms of precision and robustness to noise. Simulation results show that compared with the HAF method, the required SNR and relative mean square error are 8 dB lower and 50 dB lower respectively in the proposed method. While processing the field experiment data, the execution time of Hough transform in the proposed method is only 4% of the Wigner-Hough transform method.

Reduced Interference Sparse Time-Frequency Distributions for Compressed Observations

Traditional quadratic time-frequency distributions are not designed to deal with randomly undersampled signals or data with missing samples. The compressed data measurements introduce noise-like artifacts in the ambiguity domain, compounding the problem of separating the signal auto-terms and cross-terms. In this paper, we propose a multi-task kernel design for suppressing both the artifacts and the cross-terms, while preserving the signal desirable auto-terms. The proposed approach results in highly concentrated time-frequency signature. We evaluate our approach using various polynomial phase signals and show its benefits, especially in the case of strong artifacts.

Intelligent fault diagnosis of rolling element bearings using sparse wavelet energy based on overcomplete DWT and basis pursuit

This paper explores sparse time-frequency distribution (TFD) using overcomplete discrete wavelet transform (DWT) and sparse representation techniques. This distribution is discovered for characterizing the periodic transient information embedded in rolling element bearings and extracting effective features that can discriminate different fault conditions. Based on the sparse TFD, a new sparse wavelet energy (SWE) feature is obtained by three main steps: first, an overcomplete discrete DWT is employed to decompose the fault signal and construct a redundant dictionary; second, the redundant dictionary is optimized by basis pursuit to obtain the sparsest TFD; finally, SWE is calculated from the new TFD to produce a feature vector for each signal. SWE features that combine the merits of overcomplete DWT and sparse representation techniques can precisely reveal fault-induced information, thereby exhibiting valuable properties for automatic fault identification by intelligent classifiers. The effectiveness and advantages of the proposed features are confirmed by simulation and the practical fault pattern recognition of rolling bearings.