Sidelobe suppression of Barker codes via MRH method

The Barker code is widely used in ultrasonic testing to enhance transmitted energy and achieve high-resolution pulse compression through a matched filter. However, the inherent sidelobe of the Barker code can obscure defect echoes under tough testing environments. To solve this problem, a combined processing method integrating a matched filter, Richardson-Lucy (RL) deconvolution, and a high-pass filter (MRH) is proposed, which simultaneously suppresses the sidelobe and improves the signal-to-noise ratio (SNR). Building upon conventional matched filtering, the method constructs a symmetrized point spread function (PSF), h(t)=0.5×[s(t)+s(-t)], where s(t) is the matched filter, as prior to the RL algorithm. A subsequent high-pass filter stage removes residual low-frequency noise. The simulation results demonstrate that the proposed MRH method substantially outperforms conventional matched filtering across various noise levels in terms of SNR. Experimental validation is carried out on coarse-grained materials, where severe structural scattering and anisotropy pose significant detection challenges. In experiments of coarse-grained materials, a pair of probes with 500 kHz center frequency is selected to transmit and receive ultrasonic reflection or through-transmission signals on one side of the specimen. The MRH method improves the SNR of the back-wall echo from 22.07 dB to 45.23 dB. These results show the effectiveness of the MRH method in high-scattering environments. Future work will explore integration with neural networks to enhance computational efficiency and extend the method to other phase-coded sequences.