| Summary: | Radio frequency interference (RFI) mitigation for pulsar signals is a long perplexing issue in astrophysical measurements. Linear mitigation methods are often criticized for limited RFI excision range and weakness of RFI modeling. Meanwhile, thresholding methods (e.g., the SumThreshold) suffer from empirical factors. In our opinion, the main defect of the current status is the lack of a concise definition to distinguish signals from RFI with the aid of certain techniques, e.g., sparse representation. This point is the root cause of these problems and also forms our motivation. This paper aims to expand the excision range (e.g., the on-pulse and quasiperiodic RFI) and cut down some empirical factors. The main contribution is that we give a definition and derive a widely practicable nonlinear framework for RFI excision. This framework can overcome the susceptibility of the least-square criterion to RFI, and excise almost all types of RFI once and for all. A robust LnCosh criterion based nonlinear maximum likelihood-type (M-type) penalized smoothing estimator is introduced. The novelty is that this estimator is first embedded into the iterative shrinkage-thresholding algorithm (ISTA) and the fast ISTA. Nonlinearity highlights this method. Curvelet sparsity gives satisfying approximation for pulsar signals containing dispersion feature. Finally, useful signal details will be retrieved from the excision residual by a morphological component analysis. This method is applied to the time-frequency signals collected by the Nanshan 26 m Radio Telescope. The numerical experiments can persuasively prove that it has desired application prospects.
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