The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of residual-based surrogate hyperplane sparse Kaczmarz method is introduced and the implementations are well discussed. Their convergence theories are proved and the linear convergence rates are studied and compared in details. Numerical experiments verify the efficiency of the proposed methods.

翻译：稀疏Kaczmarz方法是求解正则化基追踪问题中著名且广泛使用的迭代方法。本文提出了代理超平面稀疏Kaczmarz方法的一般框架，特别引入了一类基于残差的代理超平面稀疏Kaczmarz方法，并对其实现方式进行了深入探讨。我们证明了该方法的收敛理论，详细研究并比较了其线性收敛速率。数值实验验证了所提出方法的有效性。