oa From Wiggins’ MED to Compressive Sensing: Sparsity in Seismic Data Processing

The field of compressive sensing has revitalized interest in the development of methods that use sparse representation models for seismic data processing. However, it should be noted that sparsitydriven methods for seismic signal processing are not new to geophysicists. I would like to use this opportunity to discuss early ideas of sparse signal representation for blind deconvolution (MED), velocity analysis, high-resolution Radon transforms, and Fourier synthesis for wavefield reconstruction. I will also discuss their connection to new developments arising under the field of compressive sensing, paying particular attention to the conceptual simplicity of these methods, assumptions and proven industry-strength results rather than to algorithmic considerations.