l^2序列空间上的非凸集稀疏正则化

Non-convex Sparse Regularisation on the Sequence Space l^2

利用l2序列空间上独立作用于已知序列的系数的加权的非二次罚项的Tikhonov正则化的正则化性质可以推导出保证罚项的适定的充分条件,而且重点是带有稀疏约束的求解算子方程的应用。从在罚项在零点的线性增长,可以证明所有正则化解的稀疏。

The regularising properties of Tikhonov regularisation on the sequence space l2 with weighted non-quadratic penalty term acting separately on the coeffeients of a given sequence can be used to derive sufficient conditions for the penalty term that guarantee the wellposedness of the method, and the focus is the application to the solution of operator equations with sparsity constraints. Assuming a linear growth of the penalty term at zero, the sparsity of all regularised solutions can be proved.