Multidimensional recursive filter preconditioning in geophysical estimation problems

Review of regularization in estimation problems

The basic linear system of equations for least-squares optimization can be written in the form

$$\mathbf{d - L m \approx 0}\;,$$ (1)

where $\mathbf{m}$ is the vector of model parameters, $\mathbf{d}$ is the vector of experimental data values, $\mathbf{L}$ is the modeling operator, and the approximate equality implies finding the solution by minimizing the power of the left-hand side. The goal of linear estimation is to estimate an optimal $\mathbf{m}$ for a given $\mathbf{d}$.