Over the past two decades Compressive Sensing (CS), also called compressed sampling, has rapidly evolved into a versatile framework for acquiring and reconstructing signals far below their traditional Nyquist sampling rates. At its core, CS leverages two key ideas. First, many real world signals are sparse or compressible in some transform domain (e.g., wavelet, curvelet, or Fourier); that is, only a small subset of coefficients carries most of the meaningful information. Second, if one designs acquisition schemes that measure the right set of incoherent linear projections, it is mathematically possible to recover the full high resolution signal from surprisingly few observations via nonlinear optimization (typically ℓ₁ minimization or greedy pursuit algorithms). Those twin principles, sparsity and incoherence, have already revolutionized magnetic resonance imaging, reducing scan times by factors of two to eight in clinical practice, and have inspired new sensor designs in remote sensing and telecommunications. Seismic exploration stands to benefit enormously from the same paradigm shift. Conventional 2 D and 3 D surveys still rely on densely spaced source and receiver grids to guarantee adequate spatial bandwidth, leading to high acquisition costs, significant environmental footprints, and intricate logistical challenges, especially in sensitive or inaccessible terrain. CS offers a compelling alternative: by strategically subsampling source points, receiver stations, or even entire shot records according to predefined random or deterministic under-sampling patterns, one can slash the total number of shots or channels while preserving the information content needed for high fidelity imaging. Critically, the burden then shifts from the field crew to advanced reconstruction algorithms executed in the processing center, where computational resources are abundant. In this study we first review the theoretical foundations of CS emphasizing three pillars that are particularly relevant to seismic data: Transform-domain sparsity of reflection data (e.g., curvelet decomposition) as demonstrated by Hennenfent 2014).
Badawi et al. (Tue,) studied this question.