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...

The concept of inverse problems is now a familiar one to most scientists and engineers, particularly in the field of imaging systems and computer vision. Inverse problems arise whenever we want to infer an unknown quantity f(r) which is not directly observable through a measurement system H which gives access to an observable quantity g(s). The mathematical equations linking these two quantitie...

Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435–1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems concerning the determination of defects of various types by different kinds of boundary measurements and we show that these problems are exponentially ill-posed.

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...

The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...

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...

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...

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...

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...