The motion magnification algorithm facilitates visualization and quantification of sub-pixel displacements associated with subtle motions that are otherwise imperceptible to the naked eye. This study presents a video decomposition and image pyramid construction method based on the non-decimated dual-tree complex wavelet transform (NDDTCWT), specifically designed to amplify minute motions and compute optical flow. The paper reviews limitations inherent in conventional motion magnification algorithms and advocates the NDDTCWT as a solution, owing to its edge-preserving properties and shift-invariance. A comparative analysis reveals that the NDDTCWT maintains reconstruction accuracy near machine precision, whereas the traditional complex steerable pyramid accumulates significant errors with increasing layers. Leveraging this advantage, a motion magnification algorithm based on the NDDTCWT is developed. The effectiveness of the proposed algorithm has been validated using both simulated and experimental videos, demonstrating its superior capabilities in motion magnification visualization and optical flow computation. The proposed method demonstrates robust performance on videos captured using low-cost imaging devices, maintaining stable motion magnification results under practical acquisition conditions. In terms of displacement measurement, the proposed method achieves displacement measurement accuracy comparable to state-of-the-art optical flow approaches such as RAFT under sub-pixel random vibration scenarios, and introduces fewer visual artifacts in motion magnification compared with conventional methods.