Multikernel Adaptive Filtering with Double Regularization

摘要

We propose an efficient multikernel adaptive filtering algorithm with double regularizers. One is a block e_1 norm for kernel groups which contributes to selecting relevant kernels adaptively from many possible kernels employed, preventing a nonlinear filter from overfitting noisy data. The other regularizer is a block e_1 norm for data groups which contributes to updating the dictionary adaptively. As the resulting cost function contains two nonsmooth (but proximable) terms, we approximate the latter regularizer by its Moreau envelope and apply the adaptive proximal forward-backward splitting method to the approximated cost function. Numerical examples show the efficacy of the proposed algorithm.