Estimating small structural motions based on sparsity enforcement
Enjian Cai, Yi Zhang, Xinzheng Lu, Xiaodong Ji, Yinbin Li, Jianying Li, Xinyu Song, Hong Zhang, Yong Liu
Abstract
This paper proposed a novel, efficient method to estimate challenging small structural motions from noisy video. To eliminate the phase limitation, ill‐posed problem, and high computational burden, the structural motion function is resampled and recovered. Because video signals have tremendous redundancies in spatial, block, and time domains, the objective is achieved by enforcing three levels of sparsity constraints. In the first step, the ill‐posed optimization is solved using the multi‐hypothesis prediction embedded with the Tikhonov regularization, to resample and recover the video signal in the spatial domain. The second step is to characterize the measurement uncertainty in the block domain, in which two weight matrices are proposed into the regularization terms of the sparse coding. Finally, the temporal correlation of video frames is exploited by the reweighted residual sparsity. The superiority of the sparsity‐enforcement method over existing methods was demonstrated through several case studies. Among the comparisons, the sparsity‐enforcement method yielded video magnifications, structural motions, and modal information more accurately. Meanwhile, it has the lowest computational burden.