But these methods have their own limitations due to their inability to fully capture the dynamic complexity and non-stationary characteristics of such signals, often leading to suboptimal noise reduction and potential distortion of the underlying signals [25]. Various frequency-domain methods also have been employed to address noises in GB-SAR data [26], including wavelet transform [27], Fast Fourier Transform (FFT) [28], etc. The wavelet transform can decompose a signal into different frequency components at various scales, allowing for multi-resolution analysis. It provides a time-scale representation of the signal, which is useful for analyzing non-stationary signals. But the selection of the chosen wavelet basis and decomposition level are difficult, which can significantly affect the de-noising performance [29]. FFT is an algorithm widely used in signal processing for converting a sequence of values into their constituent frequencies. Although the FFT method can offer significant advantages in terms of efficiency and versatility, it also has some limitations [30]. FFT captures the frequency components of a signal and their amplitudes and phases, which are directly related to the time-domain signal through the duality principle. But it cannot show time information in the frequency domain. Additionally, the FFT assumes periodicity in the signal, which can lead to spectral leakage if the signal is not properly windowed. This can cause distortion in the frequency domain representation [31]. Time-frequency domain de-noising methods for nonlinear time-series signals are essential for extracting meaningful information from noisy data. These methods aim to analyze signals in both the time and frequency domains simultaneously, providing a more comprehensive view of the signal's behavior [32]. The empirical mode decomposition (EMD) method is widely used. It can adaptively decompose a signal into Intrinsic Mode Functions (IMFs), which proves useful for non-linear and non-stationary signals. But it is susceptible to mode mixing and end effects, and the number of IMFs can be subjective [33]. The Hilbert-huang transform method combines EMD with the Hilbert transform to provide a powerful tool for analyzing and de-noising complex signals [34]. But it is computationally intensive and requires careful selection of the sifting process. Ensemble Empirical Mode Decomposition (EEMD) and Complete EEMD (CEEMD) are decomposition methods used to process nonlinear and non-stationary signals. However, EEMD can be affected by noise during decomposition, potentially leading to increased computational costs. While CEEMD provides better de-noising results, it still faces limitations when processing complex signals [35; 36; 37]. Improved complete ensemble EMD(ICEEMDAN) is an advanced improvement of CEEMD, combining noise-assisted EMD with a de-noising adaptive noise model. It improves signal reconstruction through adaptive de-noising, offering better de-composition performance. However, it has higher computational complexity and requires careful parameter-tuning, making it less suitable for real-time processing [38; 39]. The extreme-point Symmetric Mode Decomposition (ESMD) method uses an internal extremum-symmetric interpolation approach to reduce the influence of uncertainties. However, each decomposed Intrinsic Mode Function (IMF) contains some noise due to its fully adaptive nature. In practical applications, this can result in the adequate information in the high-frequency components of the signal being almost entirely erased, which negatively impacts the accuracy of the analysis results [19; 40]. Empirical Wavelet Transform (EWT) is a signal processing method based on wavelet transform that effectively decomposes signals by adaptively adjusting the bandwidth. It overcomes the modal mixing problem caused by the discontinuity of time-frequency scales in signals, and is capable of accurately capturing local frequency features, such as transient signals. It is more suitable for processing single-channel signals [41; 42].