# Joint Seismic Data Denoising and Interpolation with Double-Sparsity Dictionary Learning

## TL;DR

This paper introduces a novel double-sparsity dictionary learning method for simultaneous seismic data denoising and interpolation, improving data quality by adaptively learning from corrupted data and preserving subtle features.

## Contribution

It extends previous denoising techniques to handle both interpolation and denoising simultaneously using an adapted double-sparsity dictionary learning approach.

## Key findings

- Preserves subtle seismic features better than traditional methods
- Avoids pseudo-Gibbs artifacts in reconstructed data
- Outperforms directional multiscale transform methods like curvelets

## Abstract

Seismic data quality is vital to geophysical applications, so methods of data recovery, including denoising and interpolation, are common initial steps in the seismic data processing flow. We present a method to perform simultaneous interpolation and denoising, which is based on double-sparsity dictionary learning. This extends previous work that was for denoising only. The original double sparsity dictionary learning algorithm is modified to track the traces with missing data by defining a masking operator that is integrated into the sparse representation of the dictionary. A weighted low-rank approximation algorithm is adopted to handle the dictionary updating as a sparse recovery optimization problem constrained by the masking operator. Compared to traditional sparse transforms with fixed dictionaries that lack the ability to adapt to complex data structures, the double-sparsity dictionary learning method learns the signal adaptively from selected patches of the corrupted seismic data while preserving compact forward and inverse transform operators. Numerical experiments on synthetic seismic data indicate that this new method preserves more subtle features in the dataset without introducing pseudo-Gibbs artifacts when compared to other directional multiscale transform methods such as curvelets.