Basis mapping methods for forward and inverse problems

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...

Optical tomography: forward and inverse problems

This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider direct and numerical approaches to the inverse problems which arise at each of these scales. Finally, we outline future directions and open problems in the f...

Computational and Variational Methods for Inverse Problems

Forward-Backward EM-TV methods for inverse problems with Poisson noise

We address the task of reconstructing images corrupted by Poisson noise, which is important in various applications, such as fluorescence microscopy, positron emission tomography (PET), or astronomical imaging. In this work, we focus on reconstruction strategies, combining the expectation-maximization (EM) algorithm and total variation (TV) based regularization, and present a detailed analysis ...

Nonlinear methods for inverse statistical problems

In the uncertainty treatment framework considered in this paper, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution the dispersion of which is independent of the sample size since intrinsic variability is at stake based on observation of some model outputs. More...