On the role of non-random errors in inverse problems in radiative transfer and other applications

Abstract

The inverse solution of the radiative transfer equation—which here serves as an example for the more general case of multi-dimensional inverse problems—is affected by measurement noise and by uncertain model parameters. We propose to transform the model parameter uncertainties into the measurement domain and include related signal uncertainties in the measurement covariance matrix. The solution of the inverse problem where the Jacobian is weighted by this extended covariance matrix rather than by the pure measurement covariance matrix is shown to be equivalent to an optimal estimation solution where the uncertain parameter is treated as an additional unknown parameter. The advantage of the proposed approach is that, contrary to the optimal estimation approach, the number of fit variables does not increase with the number of uncertain model parameters.