A Nonlinear Least Squares Guided Multiscale Adaptive Regularized Savitzky-Golay Filtering (MARSG-NLS) for Suppressing Ultrasonic Grain Noise

In ultrasonic nondestructive testing (NDT), coarse-grain materials introduce significant grain noise, which severely interferes with obtaining the desired ultrasonic echo signals. This grain noise significantly impedes accurate time-of-flight (TOF) measurements and reduces the precision of length measurements. Traditional filtering methods can suppress noise but often struggle to balance noise suppression with signal preservation when dealing with nonstationary and non-Gaussian grain noise. To address this challenge, this work proposes a multiscale adaptive regularized Savitzky-Golay (S-G) filtering algorithm combined with nonlinear least squares (NLSs) fitting, referred to as multiscale adaptive regularized Savitzky-Golay (MARSG)-NLS. The algorithm extracts a physically meaningful baseline signal from the noisy signal using NLS, integrates adaptive S-G filtering with multiscale decomposition, and constrains the low-frequency components of the decomposed signal to match the baseline signal obtained from NLS. This approach effectively suppresses nonstationary grain noise and improves the signal-to-noise ratio (SNR). Simulation results show that, even when the direct wave is submerged by noise, MARSG-NLS outperforms other algorithms, such as CEEMDAN-WT, in terms of both SNR and signal fidelity. The proposed method significantly enhances the SNR to 22.44 dB for the simulated signal, an improvement of 3.65 dB over CEEMDAN-WT, which corresponds to an approximate 2.3-fold improvement in denoising effectiveness. It also surpasses MARSG and S-G filtering by 1.85 and 2.98 dB, respectively. Crucially, this enhanced signal clarity translates directly to measurement reliability in practical scenarios. For experimental signals, MARSG-NLS improves TOF estimation accuracy by up to 43.10% compared to CEEMDAN-WT, demonstrating its significance in enabling precise quantitative analysis where conventional methods fall short, especially in high-noise environments.