In summary, time-frequency domain de-noising methods offer powerful tools for analyzing nonlinear time-series signals, providing insights into both the time and frequency characteristics of the data. However, they also come with challenges related to computational complexity, parameter selection, and interpretation of results. Blind Source Separation (BSS) algorithms represent a significant advancement in signal processing for GB-SAR data. BSS techniques aim to separate a mixed signal into independent components without prior knowledge of the source signals or the mixing process. This approach is particularly advantageous for GB-SAR data, as it can effectively deal with the complex and often unknown nature of environmental noise [43; 44]. The Second-Order Blind Identification (SOBI) [45; 46] algorithm is a specific BSS technique that leverages the second-order statistics associated with the data to separate the sources. SOBI is particularly well-suited for GB-SAR applications, as SOBI effectively separates sources even when they exhibit high levels of correlation, which is common in GB-SAR data affected by environmental noise [47]. By relying on second-order statistics, SOBI requires fewer assumptions about the underlying signal or noise processes. It can recover independent source signals from their mixtures without prior knowledge of the sources or the mixing process. Additionally, SOBI has been shown to improve the signal-to-noise ratio in the separated signals, leading to clearer and more accurate measurements of bridge deflections. However, SOBI, like other BSS methods, assumes that the source signals are independent or uncorrelated. When this assumption is violated, the performance of SOBI can be significantly affected [44]. Thus, in this study, an innovative gradual noise reduction method is presented combining the improved SOBI (I-SOBI) and FFT with adaptive cutoff frequency selection (A-CFS). In the first de-noising stage, the I-SOBI algorithm is proposed and applied to recover source signals from noisy ones that have nonlinear characteristics or are non-Gaussian in distribution. It is capable of not only preserving the contributions of useful information gained from the separated signals during the reconstruction process, but also achieving the goal of reducing the impacts of noisy components on the reconstructed results. In the second de-noising stage, the FFT with the A-CFS method, proposed by [PERSON] et al. ([PERSON] et al., 2018), is used mainly for post-processing the signals de-noised by the I-SOBI algorithm. It can determine a proper cutoff frequency and ensure the quality of de-noised outputs for a given dataset. The purpose is to further deal with the residual high-frequency noises remaining in the signals after preliminary processing while preserving as much useful information as possible. The proposed gradual de-noising method is able to enhance the accuracy and reliability of bridge dynamic deflection monitored by GB-SAR, providing a more robust framework for the assessment of bridge health and performance under various environmental conditions. The paper is organized as follows. Section 2 provides the methodology of the proposed gradual de-noising method for GB-SAR bridge dynamic-deflection measurement by combining I-SOBI and FFT with A-CFS. Section 3 presents experimental results and corresponding analysis using both simulated and real-world data. Section 4 concludes the study and discusses the implications of the findings for future bridge monitoring practices.