Based on minimizing a piecewise diierentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for ill-posed inverse problems. We examine computational challenges of solving this regularization problem. Possible minimization algorithms such as the steepest descent method, iteratively weighted least squares (IRLS) met...

this paper presents results of applying a new approach on 2d inversion of magnetotelluric (mt) data in order to enhance resolution and stability of the inversion results. due to non-linearity and limited coverage of data acquisition in an mt field campaign, minimizing the error by linearization of the problem in least squares inversion usually leads to an ill-posed problem. in general, an inver...

The dynamical systems method (DSM), for solving operator equations, especially nonlinear and ill-posed, is developed in this paper. Consider an operator equation F (u) = 0 in a Hilbert space H and assume that this equation is solvable. Let us call the problem of solving this equation illposed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. The DSM for solving linea...

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...

The inverse kinematics problem for redundant manipulators is ill-posed and nonlinear. There are two fundamentally different issues which result in the need for some form of regularization; the existence of multiple solution branches (global ill-posedness) and the existence of excess degrees of freedom (local illposedness). For certain classes of manipulators, learning methods applied to input-o...

A ‘correct’ interpretation of the computational complexity of an ill-posed problem is formulated as a cost/effectiveness balance for the use of available data to obtain adequate solutions for an application. This composition with an application, is seen as the real problem, leading to the conclusion that some apparently ill-posed problems are, in context, really well-posed with a reasonable ass...