Suppression of speckle artifact in optical coherence tomography (OCT) is necessary for high quality quantitative assessment of ocular disorders associated with vision loss. However, due to its dual role as a source of noise and as a carrier of information about tissue microstructure, complete suppression of speckle is not desirable. That is what represents challenge in development of methods for speckle suppression. We propose method for additive decomposition of a matrix into low-rank and group sparsity constrained terms. Group sparsity constraint represents novelty in relation to state-of-the-art in low-rank sparse additive matrix decompositions. Group sparsity enforces more noise-related speckle to be absorbed by the sparse term of decomposition. Thus, the low-rank term is expected to enhance the OCT image further. In particular, proposed method uses the elastic net regularizer to induce the grouping effect. Its proximity operator is shrunken version of the soft-thresholding operator. Thus, the group sparsity regularization adds no extra computational complexity in comparison with the ℓ<sub>1</sub> norm regularized problem. We derive alternating direction method of multipliers based algorithm for related optimization problem. New method for speckle suppression is automatic and computationally efficient. The method is validated in comparison with state-of-the-art on ten 3D macular-centered OCT images of normal eyes. It yields OCT image with improved contrast-to-noise ratio, signal-to-noise ratio, contrast and edge fidelity (sharpness).