本文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，所以我们将 p 限定于0到1之间。当 p 约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。我们将要证明在传统的环境下最小值的存在性，稳定性和连续性。除此之外，还将给出在各自的传统假设下拓扑 Hilbert 空间下的收敛速度。%This paper presents a new regularization method in theoretical analysis and in solving the inverse problem(of nonlinear). This regularization method is also promoted in the sparse domain. We examined the sta-bility and convergence of the specific Tikhonov regularization method and applied it in the traditional continuous l p space. We limited p between 0 to 1. While p < 1,Triangle inequality is no longer set up and we got a pseudo Ba-nach space with non convex constraints. We proved the existence,stability and continuity of the minimum value in the traditional environment. In addition,we put forward their respective convergence speed in topological Hil-bert space under the traditional assumptions.
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