In this work, we focus on investigating ill-posed problems (according to the definition given by Hadamard) in topic of its application. Specifically, present some theories about properties problem image processing. By using discrete Fourier transform and fast methods, several results processing topic. Finally, illustrative examples are presented through algorithms running Python software.

The paper [39] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. results include regularity assumptions on perturbation and involve excluding also constructs response a quasi-periodically perturbed (ill-posed evolution) problem. In this paper, we use several classical methods (freezing coefficients, alternative for nonlinear equations) exte...

Information complexity of ill-posed problems may be seen as controversial. On the one hand side there were pessimistic results stating that the complexity is in nite, while on the other hand side the theory of ill-posed problems is well developed. In contrast to well-posed problems (continuous solution operators) the complexity analysis of ill-posed problems (discontinuous solution operators) i...

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...

Instead of the Tikhonov regularization method which with a scalar being the regularization parameter, Liu et al. [1] have proposed a novel regularization method with a vector as being the regularization parameter. As a continuation we further propose an optimally scaled vector regularization method (OSVRM) to solve the ill-posed linear problems, which is better than the Tikhonov regularization ...

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 ill-posed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. A general method, Dynamical Systems Method (DSM), for solving linear and nonlinear illposed problems in H is presented. This method consists of the constructio...