Fractional norm regularization using inverse perturbation

Abstract

A computation technique, known as inverse perturbation-fractional norm regularization (IP-FNR), is proposed in this wok for a sparse signal recovery problem. The objective function of this method is derived using a general ℓp norm, when p is a positive fractional number. Numerical examples are conducted for both noiseless and noisy cases. Performance of the proposed approach in terms of root-mean-square relative error (RMSRE), mean normalized squared error, standard deviation mean, occupied memory during the computation, and computational time is compared to several previous methods. It is found that in the noiseless case, the IP-FNR method significantly outperforms the former fixed-point algorithms for a certain range of the norm exponent p, provided that the perturbation parameter and the regularization multiplier are properly chosen. In the noisy case, at the expense of computational time, the IP-FNR approach provides noticeably lower RMSRE when the signal-to-noise ratio or the sparsity ratio is high and the compression ratio is quite low.