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

Abstract

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.

Convolutional Neural Networks for Local Component Number Estimation from Time–Frequency Distributions of Multicomponent Nonstationary Signals

“…The performance evaluation of the CNN-based local component estimation method was conducted on four synthetic signals, each comprising N t = 256 samples. The first signal, labeled z S1 (t) and also used in prior works [19,39], consists of four LFM components with different amplitudes, expressed analytically as [1,11,39,47] and one representative of EEG seizure activity (the data and relevant code are publicly available at https:// github.com/nabeelalikhan1/EEG-Classification-IF-and-GD-features (accessed on 14 May 2024)) (z EEG (t)) [11,14,22,33,34,[48][49][50], were also employed for validation purposes. The preprocessing of the real-life signals involved established whitening and filtering techniques to enhance signal detection, as detailed in Table 2.…”

“…The utility of the iterative LRE is better suited for purposes such as extracting the strongest component, as demonstrated in [6], and for optimization purposes where cross-terms need to be detected, interpreting NC iter t as the number of total energy regions rather than the number of auto-terms [17]. Therefore, in this study, we opt to consider the original and more robust LRE method for comparison in Section 3, as has been widely utilized across various applications [11,[18][19][20][21][22]39]. (f) NC t , ⌊NC iter t ⌉ and ⌊NC t ⌉ corresponding to the LOADTFD in (c).…”

“…Finally, we embedded randomly selected signals into AWGN with SNR down to 0 dB. We selected EMB, SPWV, LOADTFD, and WVD as the training data TFDs, primarily for their widespread application in the LRE method as documented in previous studies [11,16,[18][19][20][21][22]39]. The inclusion of these TFDs facilitates a comprehensive comparison with the LRE method.…”

“…Conversely, smaller window sizes may emphasize unresolved cross-terms or noise samples, leading to reduced accuracy in estimated numbers and poorer curve smoothness [24]. Although local component numbers are typically rounded for practical applications [18][19][20][21]39,54], raw output from the proposed CNN may limit its usage in cases where the identification of local maxima is required. Therefore, our future research will explore refining the CNN's raw output through careful analysis of smoothing filters and methods while preserving its dynamic capabilities.…”