Non-Subsampled Shearlet Transform Based Seismic Data Denoising via Proximal Classifier with Consistency

The sparse transform based seismic denoising is one of the most effective and widely used approaches in seismic data processing. In this paper, we present a novel and unconventional seismic data denoising method based on the non-subsampled shearlet transform (NSST) and proximal classifier with consistency (PCC). NSST is an emerging and excellent multi-scale, multi-direction and optimal sparsity analysis method, which can provide nearly optimal approximation of the decomposed seismic effective signals. Unlike traditional sparse transform based methods that often use a thresholding operator and corresponding inverse transform to denoise seismic data, our proposed method employs a superior performance PCC to classify the NSST coefficients of seismic data before thresholding operator. The added step can effectively divide the NSST coefficients into reflected signal information-related coefficients and noise-related coefficients, which can preserve the edge of reflected signals and keep the information of events intact as much as possible. In addition, we also introduce an adaptive threshold computing method and a soft-thresholding method to achieve seismic data denoising better. A typical synthetic example is used to demonstrate the superior performance of the proposed method over two well-known sparse transform based denoising methods. Besides, we also apply the proposed method to real seismic data, achieving the satisfactory denoising results.