组模偏正则化及其应用

GROUP PARTIAL REGULARIZATION AND ITS APPLICATIONS

本文研究组模下偏正则最小化问题，证明了解的存在性，稀疏性．研究了零空间性质对最优解的刻画．仔细探讨了解的一种单调性，并应用这种单调性说明最优化问题的求解可以分解到各组中．最后给出了一个所证定理在地震反演的应用．

By introducing the group norm, the paper proves the existence and sparsity theorems concerning minimization with partial regularization. Null space properties are considered to characterize optimal solutions. Monotone properties are discussed in depth, which justifies the approach that solving the minimization problem can be done separately in each group. The results are applied to an example of seismic inversion.