Video denoising using separable 4D nonlocal spatiotemporal transforms.

We propose a powerful video denoising algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative ltering, where a higher-dimensional transform-domain representation is leveraged to enforce sparsity and thus regularize the data. The proposed algorithm exploits the mutual similarity between 3-D spatiotemporal volumes constructed by tracking blocks along trajectories dened by the motion vectors. Mutually similar volumes are grouped together by stacking them along an additional fourth dimension, thus producing a 4-D structure, termed group, where dierent types of data correlation exist along the dierent dimensions: local correlation along the two dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation (i.e. self-similarity) along the fourth dimension. Collaborative ltering is realized by transforming each group through a decorrelating 4-D separable transform and then by shrinkage and inverse transformation. In this way, collaborative ltering provides estimates for each volume stacked in the group, which are then returned and adaptively aggregated to their original position in the video. Experimental results demonstrate the eectiveness of the proposed procedure which outperforms the state of the art