On inverse problems in physics

Unfolding in particle physics: A window on solving inverse problems

Unfolding is the ensemble of techniques aimed at resolving inverse, ill-posed problems. A pedagogical introduction to the origin and main problems related to unfolding is presented and used as the the stepping stone towards the illustration of some of the most common techniques that are currently used in particle physics experiments.

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...

Reconstructions for some coupled-physics inverse problems

This letter announces and summarizes results obtained in [8] and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from knowledge of a sufficiently large number of its solutions. We present this derivation and extend it to show which parameters may or may not be reconstructed for several h...

Statistical Physics and Information Theory Perspectives on Linear Inverse Problems

Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector x is measured by a matrix A, resulting in a vector y=Ax+z, where z denotes the noise; we call this a single measurement vector (SMV) problem. Sometimes, multiple dependent vectors x^{(j)}, j\in {1,...,J}, are measured at the same time, forming the so-called multi-measurement vector ...

Inverse problems in space physics Part 1: Examples