Geophysical data denoising using dictionary learning method with Ramanujan sums for oil and minerals exploration

Denoising is an important preprocessing step in seismic exploration that improves the signal-to-noise ratio (SNR) and helps identify oil and minerals. Dictionary learning (DL) is a promising method for noise attenuation. The DL extracts sparse features from noisy seismic data using over-complete dictionaries and performs denoising based on a threshold. However, the choice of threshold in DL greatly impacts the denoising results and the improvement in output SNR. Ramanujan’s sum(s) (RS) is a signal processing tool that exhibits derivative behavior and finds applications in edge detection and noise estimation of signals. Hence, we propose a novel DL method with threshold estimation based on RS to improve the output SNR. In this work, we estimate the noise variance of seismic data based on RS and use it as a threshold value for the DL method to perform denoising. We analyze the results of the proposed work on synthetically generated and field data sets. We perform simulations on noisy seismic data across a wide range of SNR values and tabulate the denoised results using the performance metrics SNR and mean squared error. The results indicate that the proposed method provides superior SNR and reduced mean squared error compared to MAD, SURE-based, and adaptive soft-thresholding techniques.