This article proposes an improved wavelet threshold denoising for laser self-mixing interference signals. The improved wavelet threshold function exhibits smoothness and continuity near the threshold. By replacing hard or soft wavelet threshold with the improved wavelet threshold, it can eliminate the generation of fake self-mixing interference peaks due to local oscillation induced by hard wavelet threshold, as well as the loss of self-mixing interference peaks due to over-smoothness induced by the soft wavelet threshold. Compared with hard and soft wavelet threshold denoising, theoretical simulations and experimental results demonstrate that the displacement of vibrations are well reconstructed based on the improved wavelet threshold denoising.

In this paper, a Wiener filtering algorithm in the wavelet domain is proposed to filter the laser self-mixing interference (SMI) signals, which is used to improve the accuracy of displacement reconstruction. The Wiener filter is theoretically constructed and applied to filter both high-frequency coefficients and low-frequency coefficients in the wavelet domain, which are obtained by two-level discrete wavelet transformation (DWT) decomposition from unfiltered SMI signals. Two-level wavelet decomposition in wavelet threshold filtering is determined without any manual judgment. Subsequently, the inverse DWT is employed to generate the filtered SMI signals. Compared with that, using wavelet threshold denoising, the results of the simulation and experiments demonstrate that the displacement reconstruction from the filtered SMI signals exhibits better accuracy when using Wiener filtering in the wavelet domain with two levels of wavelet decomposition. Also, the fake peaks due to local oscillation caused by wavelet threshold filtering can be eliminated effectively. The proposed method employs two-level wavelet decomposition, ensuring computational efficiency and achieving an 11.3% improvement in displacement reconstruction accuracy compared to wavelet threshold filtering. The maximum error ratio of the micro-displacement reconstruction is reduced to 2.7% using the Wiener filter in the wavelet domain.