| Abstract: |
| We consider passive imaging with randomly excited waves in order to reconstruct coefficients of a differential operator or the shape of a domain. Primary data are measurements of waves excited by independent realizations of the source. From this one can compute correlations as approximations of the covariance operator of the random solution to the differential equation restricted to the measurement domain, which serve is input data for the inverse problem. Challenges occur in the huge size of correlation data, often too large to be stored or computed, and very large pointwise noise levels. We present a computational technique which addresses both of these challenges by using only the primary data while exploiting the full information content of the correlation data and respecting the distribution of the correlation data by taking into account the forth order moments of the primary data. The efficiency of this technique is demonstrated on real and synthetic data from helioseismology. |
|