Category: Inverse problems

Phase retrieval
Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal , of amplitude , and phase : where x is an M-dimensional spatial coordinate and k is an
Inverse problem for Lagrangian mechanics
In mathematics, the inverse problem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations can arise as the Euler–Lagrange equations for some
Besov measure
In mathematics — specifically, in the fields of probability theory and inverse problems — Besov measures and associated Besov-distributed random variables are generalisations of the notions of Gaussia
Regularization by spectral filtering
Spectral regularization is any of a class of regularization techniques used in machine learning to control the impact of noise and prevent overfitting. Spectral regularization can be used in a broad r
Electrical capacitance tomography
Electrical capacitance tomography (ECT) is a method for determination of the dielectric permittivity distribution in the interior of an object from external capacitance measurements. It is a close rel
Seismic tomography
Seismic tomography or seismotomography is a technique for imaging the subsurface of the Earth with seismic waves produced by earthquakes or explosions. P-, S-, and surface waves can be used for tomogr
Unisolvent functions
In mathematics, a set of n functions f1, f2, ..., fn is unisolvent (meaning "uniquely solvable") on a domain Ω if the vectors are linearly independent for any choice of n distinct points x1, x2 ... xn
Inverse kinematics
In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulato
Tikhonov regularization
No description available.
Inverse 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 rec
Reverse Monte Carlo
The Reverse Monte Carlo (RMC) modelling method is a variation of the standard Metropolis–Hastings algorithm to solve an inverse problem whereby a model is adjusted until its parameters have the greate
Vector field reconstruction
Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system. A differe
Phase problem
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, wher
Landweber iteration
The Landweber iteration or Landweber algorithm is an algorithm to solve ill-posed linear inverse problems, and it has been extended to solve non-linear problems that involve constraints. The method wa
Regularized least squares
Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. T
Isoline retrieval
Isoline retrieval is a remote sensing inverse method that retrieves one or more isolines of a trace atmospheric constituent or variable. When used to validate another contour, it is the most accurate
SAMV (algorithm)
SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation, direction-of-arrival (DOA) estimation and tomog
Optimal estimation
In applied statistics, optimal estimation is a regularized matrix inverse method based on Bayes' theorem.It is used very commonly in the geosciences, particularly for atmospheric sounding.A matrix inv
Electrical impedance tomography
Electrical impedance tomography (EIT) is a noninvasive type of medical imaging in which the electrical conductivity, permittivity, and impedance of a part of the body is inferred from surface electrod
Regularization (mathematics)
In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often us
Simultaneous algebraic reconstruction technique
Simultaneous algebraic reconstruction technique (SART) is a computerized tomography (CT) imaging algorithm useful in cases when the projection data is limited; it was proposed by and Avinash Kak in 19
Backus–Gilbert method
In mathematics, the Backus–Gilbert method, also known as the optimally localized average (OLA) method is named for its discoverers, geophysicists George E. Backus and James Freeman Gilbert. It is a re
Inverse problem in optics
The inverse problem in optics (or the inverse optics problem) refers to the fundamentally ambiguous mapping between sources of retinal stimulation and the retinal images that are caused by those sourc
Linear inverse problem
No description available.
Inverse lithography
In semiconductor device fabrication, the inverse lithography technology (ILT) is an approach to photomask design. This is basically an approach to solve an inverse imaging problem: to calculate the sh
Inverse dynamics
Inverse dynamics is an inverse problem. It commonly refers to either inverse rigid body dynamics or inverse structural dynamics. Inverse rigid-body dynamics is a method for computing forces and/or mom
EIDORS is an open-source software tool box written mainly in MATLAB/GNU Octave designed primarily for image reconstruction from electrical impedance tomography (EIT) data, in a biomedical, industrial
Inverse scattering problem
In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inver
Collocation (remote sensing)
Collocation is a procedure used in remote sensing to match measurements from two or more different instruments.This is done for two main reasons: for validation purposes when comparing measurements of
Ridge regression
Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including
Electrical resistivity tomography
Electrical resistivity tomography (ERT) or electrical resistivity imaging (ERI) is a geophysical technique for imaging sub-surface structures from electrical resistivity measurements made at the surfa
Differential optical absorption spectroscopy
In atmospheric chemistry, differential optical absorption spectroscopy (DOAS) is used to measure concentrations of trace gases. When combined with basic optical spectrometers such as prisms or diffrac
Vertical electrical sounding
Vertical electrical sounding (VES) is a geophysical method for investigation of a geological medium. The method is based on the estimation of the electrical conductivity or resistivity of the medium.
Tomographic reconstruction
Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis fo