Interferometric optical gyroscopes are central to high‑precision navigation, yet their performance is often curtailed by non‑Gaussian noise. Here we introduce a real‑time adaptive wavelet thresholding approach that explicitly models the noise statistics while preserving sharp signal features. During a brief static calibration (~1 s), our denoising algorithm estimates the parameters of a generalized‑Gaussian noise model together with a Laplacian prior for clean coefficients, derives a maximum‑a‑posteriori threshold, and modulates it online via a merit factor linked to instantaneous signal‑to‑noise ratio and frequency content. Streaming data are processed with a seven‑level Daubechies‑4 discrete wavelet transform updated by single‑sample shifts, yielding near‑zero latency and modest computational cost. Implemented on a laboratory interferometric fibre‑optic gyro comprising a 500 m polarization‑maintaining coil and standard optoelectronic components, our algorithm consistently outperforms Kalman filtering and classical wavelet shrinkage across canonical traces (blocks, Doppler, heavisine, step), delivering up to 12.4 dB improvement in output SNR while maintaining waveform integrity and steeply suppressing high‑frequency noise.