# Simultaneous seismic data interpolation and denoising using SVD-free low-rank matrix factorization.

This applications is available only in the software release for members of SINBAD consortium.

This software provides an algorithm for simultaneous seismic data interpolation and denoising (using Generalized SPGl1 as solver). The algorithm solves the system in parallel over frequencies. The missing trace interpolation and denoising is done using robust-rank regularized formulation. We illustrate the advantages of the new approach using a seismic line from Gulf of Suez.

Author: Rajiv Kumar (rakumar@eos.ubc.ca)

Date: April,2013

## Contents

## Downloading & Dependencies

The synthetic examples code can be found in the SLIM software release under `applications/Processing/LowRankInterpolationAndDenoising`.

The code has been tested with *Matlab R2012b* and require the Parallel Computing Toolbox.

This code uses the following packages, also found in the `tools` part of the SLIM software release.

*utilities/SPOT-SLIM*- object oriented framework for matrix-free linear algebra.*tools/algorithms/LowRankMinimization*- Matrix factorization based low-rank optimization algorithm.*tools/solvers/GenSPGL1*- Generalized SPGL1.

## Running & Parallelism

All the examples and results are produced by the scripts found in this software release under `/applications/Processing/LowRankInterpolationAndDenoising/examples/`. Start matlab from `/applications/Processing/LowRankInterpolationAndDenoising` to add the appropriate paths.

To run the scripts follow the instrictions in the README file enclosed with the code.

## Functions

The missing trace interpolation and denoising code can be found in ` tools/algorithms/LowRankMinimization`. The main components are listed below

*algorithms/LowRankMinimization*

`runinterp`- Read the input parameter and data with missing tarces and/ or noise.`opSR2MH`- Transform monochromatic frequency slice from source-receiver domian to midpoint-offset domain.`LowRank_2D`- Perform missing trace interpolation and denoising in midpoint-offset domain.

## Examples and results

An examples of interpolation and denoising can be found in `applications/Processing/LowRankInterpolationAndDenoising`

Results of missing-trace interpolation and denoising is shown in GofS_Interp.m.

## References

[1] A.Y. Aravkin, R. Kumar, H. Mansour, B. Recht, F. J. Herrmann, 2013. An SVD-free Pareto curve approach to rank minimization.

[2] R. Kumar, A.Y. Aravkin, H. Mansour, B. Recht, F. J. Herrmann, 2013. Seismic data interpolation and denoising using SVD-free low-rank matrix factorization, EAGE.

## Acknowledgements

Thanks to our sponsors and NSERC for their financial support.