The estimation of random noise, which is sparse in time-frequency domain, is a significant operator in seismic data processing. In this paper, we propose a new random noise attenuation method with a non-convex sparse regularization in wavelet domain. A progressive and exactly analytical wavelet family called the generalized beta wavelets (GBW), which can constitute a tight frame, is introduced in the proposed method. Then, the random noise attenuation is reformulated as a linear least squares minimization problem with a sparse regularization term. The sparse regularization of this linear equation is implemented by a multivariate generalization of the minimax-concave (GMC) penalty function that estimates spare solution more accurate and maintains the convexity of the cost function. The exponential decreasing threolding scheme is applied to improve the convergence rate of the iterative solution. Synthetic and field data examples are provided to demonstrate the validity of the proposed method.


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