regularization method_l1regularization_魔方fridrichmethod

给出了一个奇特的正则化方法的理论分析并用来解决（非线性）反问题，从而将正则化方法推广到稀疏域上。考察特定的Tikhonov正则化方法的稳定性和收敛性。将这种正则化方法用于传统的连续的lp 空间，由于这是稀疏域上的正则化方法，所以将p限定于0到1之间。当p＜1时三角不等式不再成立并且会得到一个带有非凸限制条件的伪Banach空间，证明了在传统的环境下最小值的存在性、稳定性和连续性。还给出在各自的传统假设下拓扑Hilbert空间下的收敛速度。regularization methodregularization method

This paper presents a peculiar regularization method of theoretical ysis is used to solve the in-verse problem of ( nonlinear) so as to promote the regularization method to the sparse domain.We look at spe-cific Tikhonov regularization method of stability and convergence.We are going to the regularization method is used in the traditional continuous lp space,So we will be limited p between 0 to 1,while p<1,Triangle ine-quality is no longer set up and well get a pseudo Banach space with non convex constraints.We are going to prove the existence of the minimum value in the traditional environment, the stability and continuity.In addi-tion, we will also be given in the respective topological Hilbert space under the traditional assumptions of the convergence speed.

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