Inverse Problem

An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth's gravity field, then we might ask the question: "given the data that we have available, what can we say about the density distribution of the Earth in that area?" The solution to this problem (i.e. the density distribution that best matches the data) is useful because it generally tells us something about a physical parameter that we cannot directly observe. Thus, inverse problems are some of the most important and well-studied mathematical problems in science and mathematics. Inverse problems arise in many branches of science and mathematics, including computer vision, natural language processing, machine learning, statistics, statistical inference, geophysics, medical imaging (such as computed axial tomography and EEG/ERP), remote sensing, ocean acoustic tomography, nondestructive testing, astronomy, physics and many other fields.

Read more about Inverse Problem:  History, Conceptual Understanding, General Statement of The Problem, Linear Inverse Problems, Non-linear Inverse Problems, Mathematical Considerations, Inverse Problems Societies

Other articles related to "inverse problem, inverse problems, problems, problem":

Linear Inverse Problems - Examples - Earth's Gravitational Field
... Therefore, most inverse problems are considered to be underdetermined, meaning that we do not have unique solutions to the inverse problem ... we cannot directly invert the observation matrix, we use methods from optimization to solve the inverse problem ... To do so, we define a goal, also known as an objective function, for the inverse problem ...
Magnetoencephalography - Source Localization - The Inverse Problem
... Problems such as this, where model parameters (the location of the activity) have to be estimated from measured data (the SQUID signals) are referred to as inverse problems (in contrast to forward problems where the ... is to be estimated.) The primary difficulty is that the inverse problem does not have a unique solution (i.e ... there are infinite possible "correct" answers), and the problem of defining the "best" solution is itself the subject of intensive research ...
Inverse Problems Societies
... Inverse Problems International Association Finnish Inverse Problems Society. ...
Fast Kalman Filter - Optimum Calibration - Inverse Problem
... The computing load of the inverse problem of an ordinary Kalman recursion is roughly proportional to the cube of the number of the measurements processed simultaneously ... In Satellite Geodesy problems (Brockmann, 1997), the computing load of the HWB (and FKF) method is only roughly proportional to the square of the number of the state parameters (and not of the measurements whose ...
Wiener Index - Inverse Problem
... Gutman Yeh (1995) considered the problem of determining which numbers can be represented as the Wiener index of a graph ...

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