In order to demonstrate how 3D regularization and interpolation is done was made through a didactic example, like in previous section. Knowing that the regularization algorithms in \textit{f-x}, Fourier methods, for example, take the data initially in the \textit{t-xy} domain, in case, and after a partial transform for the \textit{f-xy} domain, it initiates the regularization or spatial interpolation. Taking the temporal frequencies, one by one, as if they were 2D slices of the full dataset, containing the partial Fourier spectrum, the general scheme is to transform to the full Fourier domain, \textit{f-$k_x k_y$}, find the largest coefficients to use in an optimal spectrum and go back to the \textit{f-xy} domain. Doing this for all the temporal frequencies and finally returning to the \textit{t-xy} domain, its finding the final result of regularization. During spatial regularization, as described above, we can think of these 2D slices as being 2D functions distributed in the $xy$ plane, something of the form: …show more content…
The input data were randomly decimated, leaving a data matrix of 68 samples are recognized (60 missing samples) in $x$ and 36 samples (28 missing samples) in $y$, Figure 3b. All parameters can be found in Table 1. In other words, it will be necessary to apply the reconstruction in both directions ($x$ and $y$) to obtain the (128x64) positions as in the original data. Was used the same data (Figure 3b) to reconstruct. In Figures 3c, 3e and 3g are presented the MWNI, ALFT and Matching Pursuit data reconstructions,