Sequential dictionary learning algorithms have been successfully applied to a number of image processing problems. In a number of these problems however, the data used for dictionary learning are structured matrices with notions of smoothness in the column direction. This prior information which can be traduced as a smoothness constraint on the learned dictionary atoms has not been included in existing dictionary learning algorithms. In this paper, we remedy to this situation by proposing a regularized sequential dictionary learning algorithm. The proposed algorithm differs from the existing ones in their dictionary update stage. The proposed algorithm generates smooth dictionary atoms via the solution of a regularized rank-one matrix approximation problem where regularization is introduced via penalization in the dictionary update stage. Experimental results on synthetic and real data illustrating the performance of the proposed algorithm are provided.