基于代理函数优化的稀疏性字典学习

Sparse Dictionary Learning Based on Optimization of Surrogate Function

稀疏性字典学习是指对在某个已知的基字典上具有稀疏表示的字典的学习.论文利用块松弛思想,将稀疏性字典学习问题转化为字典和系数的分别优化问题,利用代理函数优化方法分别对固定字典和固定系数情况下的目标函数进行优化处理,得到固定字典情况下的系数更新算法和固定系数情况下的字典更新算法,进而得到稀疏性字典学习算法.理论分析说明了本文算法的收敛性.仿真对比表明了本文算法在收敛性和运算效率方面均优于稀疏性K-SVD算法.

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.