Multidimensional recursive filter preconditioning in geophysical estimation problems |

in geophysical estimation problems

Constraining ill-posed inverse problems often requires
regularized optimization. We consider two alternative approaches
to regularization. The first approach involves a column operator
and an extension of the data space. It requires a regularization
operator which enhances the undesirable features of the model.
The second approach constructs a row operator and expands the
model space. It employs a preconditioning operator, which
enforces a desirable behavior, such as smoothness, of the model.
In large-scale problems, when iterative optimization is incomplete,
the second method is preferable, because it often leads to
faster convergence. We propose a method for constructing
preconditioning operators by multidimensional recursive
filtering. The recursive filters are constructed by imposing
helical boundary conditions. Several examples with
synthetic and real data demonstrate an order of magnitude
efficiency gain achieved by applying the proposed technique to
data interpolation problems.

- Introduction
- Review of regularization in estimation problems

- One-dimensional synthetic examples

- Multidimensional recursive filter preconditioning
- Multidimensional examples
- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

Multidimensional recursive filter preconditioning in geophysical estimation problems |

2013-03-03