Inverse problem

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]

  1. ^ Mohamad-Djafari, Ali (2013-01-29). Inverse Problems in Vision and 3D Tomography. John Wiley & Sons. ISBN 978-1-118-60046-7.
  2. ^ Pizlo, Zygmunt. "Perception viewed as an inverse problem." Vision research 41.24 (2001): 3145-3161.
  3. ^ Vito, Ernesto De, et al. "Learning from examples as an inverse problem." Journal of Machine Learning Research 6.May (2005): 883-904.
  4. ^ 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. Bibcode:2019GAMRE..13...53C. doi:10.1080/17499518.2018.1498524. S2CID 216590427.