Editing Inverse problem (section)

{{Short description|Process of calculating the causal factors that produced a set of observations}}
{{For|the use in [[geodesy]]|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]], [[sound source reconstruction|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 can be found in [[system identification]], [[optics]], [[radar]], [[acoustics]], [[communication theory]], [[signal processing]], [[medical imaging]], [[computer vision]],<ref>{{Cite book| last=Mohamad-Djafari|first=Ali| url=https://books.google.com/books?id=ef8DREm_9OMC&q=%22inverse+problem%22| title=Inverse Problems in Vision and 3D Tomography| date=2013-01-29| publisher=John Wiley & Sons|isbn=978-1-118-60046-7|language=en}}</ref><ref>Pizlo, Zygmunt. "[https://www.sciencedirect.com/science/article/pii/S0042698901001730 Perception viewed as an inverse problem]." Vision research 41.24 (2001): 3145-3161.</ref> [[geophysics]], [[oceanography]], [[astronomy]], [[remote sensing]], [[natural language processing]], [[machine learning]],<ref>Vito, Ernesto De, et al. "[http://www.jmlr.org/papers/volume6/devito05a/devito05a.pdf Learning from examples as an inverse problem]." Journal of Machine Learning Research 6.May (2005): 883-904.</ref> [[nondestructive testing]], slope stability analysis<ref>{{cite journal |last1= Cardenas |first1=IC|title= On the use of Bayesian networks as a meta-modeling approach to analyse uncertainties in slope stability analysis| journal =Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards|date=2019 | volume=13|issue=1|pages=53–65 |doi=10.1080/17499518.2018.1498524 |bibcode=2019GAMRE..13...53C |s2cid=216590427}}</ref> and many other fields.{{citation needed|date=September 2020}}