Zhao, Y., Li, Y., Shao, D. and Yang, B.J., 2020. Desert seismic exploration low-frequency noise attenuation based on improved co-sparse analysis model. Journal of Seismic Exploration, 29: 505-525. Desert low-frequency noise is a kind of noise in desert seismic exploration records, with significant low-frequency characteristics. Severe frequency aliasing occurs because the noise is in the same frequency band as the seismic signal. In addition, the interference noise has strong energy over whole time period of seismic records, which makes the signal easily submerged in the noise. These characteristics of desert low-frequency noise challenge traditional denoising methods. Aiming at the noise attenuation of low signal-to-noise ratio (SNR) seismic exploration records in desert areas, first half-quadratic optimization approach is proposed to solve the energy minimization problem instead of common optimization methods in the co-sparse analysis model. And then, shrinkage function is introduced into the model by the additive form of half-quadratic optimization, which makes the model remove the restriction of sparsity promoting function. Finally, according to the characteristics of seismic exploration records, the training data are normalized and then trained. Both the synthetic and real data experiments prove that the improved model can better overcome the frequency aliasing and more thoroughly remove the low-frequency noise compared with the traditional co-sparse analysis model.