Seismic data interpolation using nonlinear shaping regularization |

where is the transformed domain data such that , is a tight frame such that and (e.g. Fourier transform), is a nonlinear thresholding operator, and denotes adjoint. Considering that , and , combined with equation 7, we get:

which is equal to equation 6 with chosen as and taken as an identity operator. Thus, we prove that the IST and shaping regularization are actually mathematically equivalent.

Seismic data interpolation using nonlinear shaping regularization |

2015-11-24