# Efficient least-squares imaging with sparsity promotion and compressive sensing

This software release includes an parallel framework in Matlab for L1 migration [1,2], which based on the ideas from compressive-sensing and stochastic optimization, where the least-squares imaging result are computed from random subsets of the data via curvelet-domain sparsity-promotion. There are two different subset sampling strategies are considered in this package: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs. There is also a small example based on a small one- layer model which can allow users to test the algorithm in a short time

Author: Xiang Li Date : April, 2013

## Contents

## Downloading & Dependencies

The code can be found in the SLIM sofware release under `/applications/Imaging/L1MIGRATIONbasic/`.

The code has been tested with *Matlab R2012a* and requires the Parallel Computing Toolbox.

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

*utilities/SPOT*- object oriented framework for matrix-free linear algebra.*utilities/pSPOT*- parallel extension of SPOT.*transforms/CurveLab-2.1.2-SLIM/*- Curvelet transform toolbox

## Running & Parallelism

All the examples and results are produced by the scripts found in this software release under `/applications/Imaging/L1MIGRATIONbasic/`. Start matlab from that directory or run `startup` in that directory to add the appropriate paths.

To run the scripts follow the instrictions in the README file enclosed with the code. The scripts can be run in serial mode but parallel mode is advised.

Read more about SLIM's approach to parallel computing in Matlab.

## Examples and results

Scripts to reproduce imaging from one-layer model, as well as results from sevaral papers [1],[2] can be foundin the `scripts` directory. The results are shown here.

## References

[1] Felix J. Herrmann and Xiang Li, Efficient least-squares imaging with sparsity promotion and compressive sensing, Geophysical Prospecting, vol. 60, p. 696-712, 2012.

[2] Felix J. Herrmann and Xiang Li, Randomized dimensionality reduction for full-waveform inversion, in EAGE Technical Program Expanded Abstracts, 2010.

## Acknowledgements

The synthetic Compass model was provided by the BG-GROUP, see also the disclaimer.