Process of calculating the causal factors that produced a set of observations
For the use in geodesy, see Inverse geodetic problem.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects.
Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in system identification, optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision,[1][2] geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning,[3] nondestructive testing, slope stability analysis[4] and many other fields.[citation needed]
^Mohamad-Djafari, Ali (2013-01-29). Inverse Problems in Vision and 3D Tomography. John Wiley & Sons. ISBN 978-1-118-60046-7.
^Pizlo, Zygmunt. "Perception viewed as an inverse problem." Vision research 41.24 (2001): 3145-3161.
^Vito, Ernesto De, et al. "Learning from examples as an inverse problem." Journal of Machine Learning Research 6.May (2005): 883-904.
^Cardenas, IC (2019). "On the use of Bayesian networks as a meta-modeling approach to analyse uncertainties in slope stability analysis". Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards. 13 (1): 53–65. doi:10.1080/17499518.2018.1498524. S2CID 216590427.
An inverseproblem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating...
kinematic animation problem uses the kinematics equations to determine the pose given the joint angles. The inverse kinematics problem computes the joint...
(more unsolved problems in mathematics) In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois...
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a solution to a restricted form of the inverseproblem using only PIFS; the general form of the inverseproblem remains unsolved. As of 1995, all fractal...
Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square...
of the interesting problems in Schumann resonances studies is determining the lightning source characteristics (the "inverseproblem"). Temporally resolving...
The inverseproblem in optics (or the inverse optics problem) refers to the fundamentally ambiguous mapping between sources of retinal stimulation and...
InverseProblems is a peer-reviewed, broad-based interdisciplinary journal for pure and applied mathematicians and physicists produced by IOP Publishing...
the inverse model, f → − 1 {\displaystyle {\vec {f}}^{-1}} . If the problem is linear we can use some type of matrix inverse method—often the problem is...
In mathematics, the inverseproblem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations can...
to b {\displaystyle \mathbf {b} } . Therefore, in solving the inverse-problem, the inverse mapping operates as a high-pass filter that has the undesirable...
multimodal, some moments may not be defined, etc.). When analyzing an inverseproblem, obtaining a maximum likelihood model is usually not sufficient, as...
difficulty is that the inverseproblem does not have a unique solution (i.e., there are infinite possible "correct" answers), and the problem of defining the...
b{\sqrt {1+e'^{2}\cos ^{2}\alpha _{0}}}} and b {\displaystyle b} .) The "inverseproblem" is the determination of s 12 {\displaystyle s_{12}} , α 1 {\displaystyle...
(n-m)\times m} . After some algebra, it can be shown that a solution to the inverseproblem can be expressed as: x = Q [ ( R 1 T ) − 1 b 0 ] {\displaystyle \mathbf...
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the inverse lithography technology (ILT) is an approach to photomask design. This is basically an approach to solve an inverse imaging problem: to calculate...
solving the inverseproblem: given f ( x ) = y , {\displaystyle f(x)=y,} one is solving for x, and thus the condition number of the (local) inverse must be...
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at a time by any sort of a Kalman filter. The computing load of the inverseproblem of an ordinary Kalman recursion is roughly proportional to the cube...
Based InverseProblems – via ProQuest. Coskun, Huseyin; Li, Yi; Mackey, Mackey A. (Jan 2007). "Ameboid cell motility: a model and inverseproblem, with...
work on regularization of inverseproblems also worked on this problem. He explains in detail how to solve the ERT problem in a simple case of 2-layered...
from primary structure. Structure prediction is different from the inverseproblem of protein design. Protein structure prediction is one of the most...
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