Patent Document ID: 9158016
Application ID: 13564195
Patent Flag: 1

Claim One:
1. A process for overcoming aliasing in a minimum weighted norm interpolation (MWNI) technique, the process comprising: computing, by a processor, an initial, regularly interpolated model; computing a plurality of initial spectral weights using the initial, regularly interpolated model; converting the initial, regularly interpolated model into a frequency domain, and, unknown spectral weights P k in x′=|(T H T+μF −1 |P k | −2 F) −1 T H d, a from frequency data at each frequency slice of the initial, regularly interpolated model using Fourier transform, wherein μ is a weighing factor controlling tradeoff between model norm and misfit of observations, H is a conjugate transpose operator, x H is a conjugate transpose of x, F is a multi-dimensional forward Fourier transform, F −1 is a multi-dimensional inverse Fourier transform, and x′ is a least-squared solution with a minimum weighted norm (MWNI) to recover missing data; wherein the process results in reducing aliasing artifacts and improving reconstruction of multi-dimensional data regularization from otherwise irregular data.