Motion estimation from noisy data with unknown distributions using multi-frame phase-preserving denoising

Phase-based motion estimation method is promising due to its high resolution and wide measurement range. Generally, noise exists in digital images and ruins the constant phase assumption of the same target among different frames. However, traditional image-denoising techniques do not consider the phase and result in inaccurate motion estimation. A novel phase-preserving denoising method considering multiple frames is proposed. In this approach, multi-scale and multi-orientation quadrature filters transform noisy images into complex pyramids to preserve the phase of the content. An instability indicator is designed to evaluate the relative noise intensity at each level of the complex pyramid among multiple frames. The threshold is then estimated to retain the phase of interest and reconstruct a denoised image with unknown noise distributions. Numerical and experimental examples demonstrate that the proposed method effectively preserves the phase of interest and decreases the error of the estimated motion, outperforming other typical denoising methods under various types of noise.