Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L2 , regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the prese...

Many problems of physical chemistry belong to the class of inverse problems, in which from known experimental data of the object we need to determine some of its properties based on a certain model connecting these properties with measured characteristics. Inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e. to the ill-posed problems. Thi...

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Baye...

Based on minimizing a piecewise differentiable 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) me...

We consider an operator equation) (, A R f f Au ∈ = , (1) where is the linear continuous operator between real Hilbert spaces H and F. In general our problem is ill-posed: the range R(A) may be non-closed, the kernel N(A) may be non-trivial. We suppose that instead of exact right-hand side f we have only an approximation) , (F H L A ∈ F f ∈ δ , δ δ ≤ − f f. To get regularized solution of the eq...

In this paper we shall be concerned with the construction of an adaptive Landweber iteration for solving linear ill-posed and inverse problems. Classical Landweber iteration schemes provide in combination with suitable regularization parameter rules order optimal regularization schemes. However, for many applications the implementation of Landweber’s method is numerically very intensive. Theref...

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...