A new dictionary learning model is introduced where the dictionary matrix is constrained as a sum of R Kronecker products of K terms. It offers a more compact representation and requires fewer training data than the general dictionary learning model, while generalizing Tucker dictionary learning. The proposed Higher Order Sum of Kroneckers model can be computed by merging dictionary learning approaches with the tensor Canonic Polyadic Decomposition. Experiments on image denoising illustrate the advantages of the proposed approach.