Inverse noise covariance

If we apply fitting goals (9) in an attempt to create multiple models with about the same level and type of noise, we obtain the models seen in Figure . These models have about the right amplitude of noise but have a higher frequency noise component than our synthetic test. The reason for this discrepancy is that the noise filter does not effectively describe the noise spectrum in our synthetic. Figure  shows the spectrum of the noise added in our synthetic test (the noise seen in the left panel of Figure ). Note how the spectrum outside a very small band is zero. Emulating this behavior with a filter is nearly impossible and requires a prohibitively large filter. As a result, we are limited in what type of noise we can describe by the practicality of building a filter that accurately captures its spectrum.

 

inc
Figure 10 Four realizations using the fitting goals (9). Note how the amplitude of the noise is consistent with our synthetic experiment but the spectrum shows more energy and large wavenumbers.

 

noise Figure 11 The spectrum of the noise added in the synthetic problem shown in Figures -.