Seismic Random Noise Attenuation Using Sparse Low-Rank Estimation of the Signal in the Time–Frequency Domain

Suppression of random noise in seismic data is a challenging preprocessing task. We propose a new denoising method, which includes the following steps. First, the short-time Fourier transform of the noisy seismic signal is computed. Then, a sparse low-rank matrix is estimated based on solving a nonconvex penalty function. A threshold function associated with the penalty function based on the optimal shrinkage of the singular values is employed to solve the penalty function. The nonconvex penalty function induces sparsity to the time–frequency (TF) matrix, and the optimal shrinkage optimizes the thresholding function to extract the singular values. Finally, the seismic signal is synthesized based on the estimated sparse low-rank TF matrix. We evaluate the proposed method by using a synthetic seismic section contaminated by random noise and a prestack real seismic dataset from an oil field in the southwest of Iran. The synchrosqueezed wavelet transform-OptShrink, synchrosqueezed wavelet transform-Go Decomposition, and classical $f-x$ singular spectrum analysis methods are selected to compare the performance of the proposed method. The results indicate the superiority of the proposed method compared to the other state-of-the-art noise suppression methods.