GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 67 approach to irregularities, for this reason, a manual trace decimation is made: one third of traces is randomly selected and discarded. After this procedure the input dataset sampling shows strong irregularities. In this case the reconstruction method is applied for both filling gaps and upsampling, as Fig. 2 shows. The last example performs a strong upsampling along crossline direction: since input sampling is very coarse along crossline direction, the algorithm upsamples input data by a factor 8, in order to obtain a crossline sampling spacing which is comparable to the inline sampling spacing. All three figures report the comparison among the result of the MP approach ((b), first panel) and the one of the CGP approach ((b), last panel), together with the input data ((b), middle panel). Figures show how CGP produce comparable results in terms of accuracy in all three examples, both in case of almost regular input sampling and strongly irregular input sampling. Once the reconstruction capability of the CGP method is ascertained, the next step is to show what big improvement this approach represents in terms of computational costs. For obtaining such a high accuracy on all three results, the MP method needs to perform 1000 iterations. This leads to very high computational costs, which even increase when the performed upsampling (as in third example) is by a large factor. On the other hand, the CGP approach needs very few iterations, in particular in the first and third example, in which the input geometry is almost regular: at each iteration half of the components can be selected and 2 total iterations are enough to get to the same result as with MP. Also for CGP an hard upsampling needs more time for being performed than a soft one, but anyway CGP execution times are negligible if compared to the MP ones. The only case in which the number of iteration needs to be high is when the input geometry shows strong irregularities, as in the second example, in this situation, as already discussed in the technical sections, only few components per iterations can be selected due to the spectral leakage phenomenon: in our example we pick 0.1% of total components per iteration which means a single component in most of temporal frequency slices. With such a configuration, the number of iterations needed for getting to a result which is as accurate as the MP is equal to 40, thus we see that even with the same number of components selected at each iteration, the updating step leads CGP approach to gain a lot in terms of number of iterations over the MP. Even if the CGP iteration is more complex than MP one, the final CGP execution time is again much lower than MP time. Tab. 1 reports a summary of all execution times. Conclusion. We have presented a data interpolation algorithm belonging to the class of sparsity promoting Fourier methods. It differs from already presented methods (such as ALFT, MP and similar ones) for making use of the novel Conjugate Gradient Pursuit method with the Stagewise selection strategy. The algorithm operates iteratively, as the above mentioned ones, but selects a number of dominant components instead of a single one per each iteration. Moreover, after the coefficients selection, all so far collected components are recalculated by Fig. 3 – Hard upsampling example: a) geometry description: sampling before (left) and after (right) processing; b) results of the interpolation, crossline visualization, from left to right: MP result, input data, CGP result.