Local Structure- and Noise-Aware Spatially Adaptive SURE Wavelet Denoising for Polarization-Modulated Laser Ranging

In polarization-modulated laser ranging systems, noise-induced waveform distortion and shifts in extremum position severely limit ranging accuracy. To address the difficulty of conventional filters in balancing noise suppression against preservation of extremum features, this paper proposes a local structure- and noise-aware spatially adaptive Stein’s Unbiased Risk Estimate (SURE) wavelet denoising method. Within the SURE minimum-mean-square-error framework, a local second-derivative structural feature and local noise are introduced to construct a spatially adaptive threshold-adjustment mechanism at individual wavelet coefficients. This mechanism reduces the shrinkage strength in extremum neighborhoods characterized by strong local second-order variation to protect key structural features, while enhancing shrinkage in relatively flat and noisy regions to improve denoising performance. Experimental results show that, relative to mean filtering, Savitzky–Golay (SG) filtering, and standard SURE wavelet denoising, the proposed method markedly improves the stability of extremum positions while maintaining the signal-to-noise ratio (SNR), and reduces the ranging root-mean-square error (RMSE) by 27.3 μm, 21.5 μm, and 4.0 μm on average across all tested distances, respectively. Extremum stability and ranging error exhibit a significant positive correlation (r = 0.863, R2 = 0.745, p < 0.001), confirming the critical influence of extremum structural stability on ranging accuracy. This study is of value for extending precision measurement systems based on feature extraction.