Obtaining smooth solutions to large, linear, inverse problems

Obtaining smooth solutions to large, linear, inverse problems

It is not uncommon now for geophysical inverse problems to be parameterized by 10 to 105 unknowns associated with upwards of 106 to 107 data constraints. The matrix problem defining the linearization of such a system (e.g., ~m = b) is usually solved with a least-squares criterion (m = (~t~ -) ~ tb). The size of the matrix, however, discourages the direct solution of the system and researchers o...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Tracking Solutions of Time Varying Linear Inverse Problems

The reconstruction of a signal from only a few measurements, deconvolving, or denoising are only a few interesting signal processing applications that can be formulated as linear inverse problems. Commonly, one overcomes the ill-posedness of such problems by finding solutions which best match some prior assumptions. These are often sparsity assumptions as in the theory of Compressive Sensing. I...

Solutions to Space-Time Inverse Problems

A Method for Obtaining Continuous Solutions to Multiparametric Linear Programs

A modification of the geometric algorithm for solving multiparametric linear programs (mp-LP) is presented. The modification preserves the simplicity of the algorithm and ensures that the optimal, piecewise affine, mapping from parameter to solution space is continuous. When the mp-LP has non-unique solutions, the optimizer with the least Euclidian norm is selected. Copyright c © IFAC 2005