An adaptive rank-sparsity K-SVD algorithm for image sequence denoising

• We propose an algorithm for removing Gaussian noise from a given image sequence.
• We formulate it as an optimization problem on a propagated dictionary.
• The propagated dictionary is adaptively trained by a rank-sparsity representation.
• Restoration of signals is adaptively determined in terms of the noise level.

In this paper, we propose an algorithm for the removal of additive white Gaussian noise (AWGN) from a given image sequence. By extending a frame in the spatial and temporal dimensions, the sequence is transformed into the volumetric data in which each frame includes both the spatial and temporal correlation. Image sequence denoising is then formulated as an optimization problem that can be iteratively solved by constructing a rank-sparsity representation on a propagated dictionary. The proposed algorithm effectively trains this dictionary by adaptively determining the required number of iterations. Restoration of the volumetric data is adaptively determined in terms of the noise level. The results on some standard data sets show that the proposed algorithm outperforms the K-singular value decomposition (K-SVD) algorithm and the sparse K-SVD algorithm. If a sequence is characterized by global motion (the moving objects in a scene with similar trajectories, i.e., they moves as a unit) or high motion activity, the performance of the proposed algorithm is comparable to that of block-matching and 4-D filtering (BM4D) and video block-matching and 4-D filtering (V-BM4D).