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In this paper, we investigate the compressed sensing (CS) algorithms for modeling a super-resolution near-field structure (super-RENS) disc system with a sparse Volterra filter. It is well known that the super-RENS disc system has severe nonlinear inter-symbol interference (ISI). A nonlinear system with memory can be well described with the Volterra series. Furthermore, CS can restore sparse or compressed signals from measurements. For these reasons, we employ the CS algorithms to estimate a sparse super-RENS read-out channel. The evaluation results show that the CS algorithms can efficiently construct a sparse Volterra model for the super-RENS read-out channel and that observable nonlinear interactions take place among restricted components in the read-out channel.