On regularization methods for inverse problems of dynamic type

Newton-type regularization methods for nonlinear inverse problems

Inverse problems arise whenever one searches for unknown causes based on observation of their effects. Such problems are usually ill-posed in the sense that their solutions do not depend continuously on the data. In practical applications, one never has the exact data; instead only noisy data are available due to errors in the measurements. Thus, the development of stable methods for solving in...

Variable-smoothing Regularization Methods for Inverse Problems

Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To eeectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative \local regularization" approach in which a decomposit...

Iterated Regularization Methods for Solving Inverse Problems

On multiple level-set regularization methods for inverse problems

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional Gα based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikh...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...