Sparse dictionary learning means that learning for a dictionary which has sparse representation on a known base dictionary.In the paper

with block-relaxation

the sparse dictionary learning can be translated into respective optimization of dictionary and coefficients.It means that the target function can be optimized respectively with fixed dictionary or fixed coefficients by optimization method of surrogate function.Through above process

the update algorithm of coefficients with fixed dictionary and update algorithm of dictionary with fixed coefficients can be obtained.Then the sparse dictionary learning algorithm is obtained.The convergence of the algorithm is illuminated theoretically.Comparison in simulation indicates that the algorithm put forward in this paper is superior to sparse K-SVD algorithm in convergence and operating efficiency.