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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

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

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