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Rapid advancement in vision recording technologies is increasing the importance and production of video data in a wide range of applications. This paper proposed a novel perspective of multifrequency phase inference for characterizing especially challenging nonstationary and often small motions in optical measurement. The model estimates and adjusts the phase information by the multi-frequency phase retrieval, which is derived from the maximum likelihood formulation with block matching 3D sparsity priors. Estimated phase jumps are removed by a robust solution of the 2D phase unwrapping problem. These considerations are supported by applications of dynamic response identification in structural health monitoring. When compared to state-of-the-art techniques, the proposed method readily yielded high-quality magnifications on real videos, with less noise and better anti-noise performance. The proposed method also demonstrated uniformly high skill in extracting clearer time-domain motion estimation of video components.

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The ability to discern subtle image changes over time is useful in applications such as product quality control, civil engineering structure evaluation, medical video analysis, music entertainment, and so on. However, tiny yet useful variations are often combined with large motions, which severely distorts current video amplification methods bounded by external constraints. This paper presents a novel use of spectra to make motion magnification robust to large movements. By exploiting spectra, artificial limitations and the magnification of small motions are avoided at similar frequency levels while ignoring large ones at distinct spectral pixels. To achieve this, this paper constructs spline-kerneled chirplet transform (SCT) into an empirical Bayesian paradigm that applies to the entire time series, giving powerful spectral resolution and robust performance to noise in nonstationary nonlinear signal analysis. The important advance reported is Bayesian-rule embedded SCT (BE-SCT); two numerical experiments show its superiority over current approaches. For applying to spectrum-aware motion magnification, an elaborate analytical framework is established that captures global motion, and use of the proposed BE-SCT for dynamic filtering enables a frequency-based motion isolation. Our approach is demonstrated on real-world and synthetic videos. This approach shows superior qualitative and quantitative results with less visual artifacts and more local details over the state-of-the-art methods.