Simply denoise: wavefield reconstruction via jittered undersampling

Conclusions

Successful wavefield recovery depends on three key factors, namely, the existence of a sparsifying transform, a favorable sampling scheme and a sparsity-promoting recovery method. In this paper, we focused on an undersampling scheme that is designed for localized Fourier-like signal representations such as the curvelet transform. Our scheme builds on the fundamental observation that irregularities in sub-Nyquist sampling are good for nonlinear sparsity-promoting wavefield reconstruction algorithms because they turn harmful coherent aliases into relatively harmless incoherent random noise. The interpolation problem effectively becomes a much simpler denoising problem in this case.

Undersampling with a discrete random uniform distribution lacks control on the maximum gap size in the acquisition, which causes problems for transforms that consist of localized elements. Our jittered undersampling schemes remedy this lack of control, while preserving the beneficial properties of randomness in the acquisition grid. Our numerical findings on a stylized series of experiments confirm these theoretically-predicted benefits.

Curvelet-based wavefield reconstruction results from jittered undersampled synthetic and field datasets are better than results obtained from regularly decimated data. In addition, our findings indicate an improved performance compared to traces taken randomly according to an uniform distribution. This is a major result, with wide ranging applications, since it entails an increased probability for successful recovery with localized transform elements. In practice, this translates into more robust wavefield reconstruction.

Simply denoise: wavefield reconstruction via jittered undersampling